%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PHI044_1 : TPTP v9.0.0. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:22:48 AM UTC 2025
% Result : Unsatisfiable 0.40s 0.58s
% Output : Proof 0.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : PHI044_1 : TPTP v9.0.0. Released v7.5.0.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.11/0.31 % Computer : n016.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Fri Jun 20 02:19:32 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.40/0.58 % SZS status Unsatisfiable
% 0.40/0.58 % SZS output start Proof
% 0.40/0.58 tff(tptp_fun_Z_10_type, type, (
% 0.40/0.58 tptp_fun_Z_10: option)).
% 0.40/0.58 tff(tptp_fun_Z_4_type, type, (
% 0.40/0.58 tptp_fun_Z_4: ( option_set * option ) > option)).
% 0.40/0.58 tff(tptp_fun_B_8_type, type, (
% 0.40/0.58 tptp_fun_B_8: option_set)).
% 0.40/0.58 tff(member_type, type, (
% 0.40/0.58 member: ( option * option_set ) > $o)).
% 0.40/0.58 tff(tptp_fun_X_12_type, type, (
% 0.40/0.58 tptp_fun_X_12: option)).
% 0.40/0.58 tff(tptp_fun_Z_5_type, type, (
% 0.40/0.58 tptp_fun_Z_5: ( option_set * option ) > option)).
% 0.40/0.58 tff(tptp_fun_A_9_type, type, (
% 0.40/0.58 tptp_fun_A_9: option_set)).
% 0.40/0.58 tff(tptp_fun_Y_11_type, type, (
% 0.40/0.58 tptp_fun_Y_11: option)).
% 0.40/0.58 tff(tptp_fun_D_6_type, type, (
% 0.40/0.58 tptp_fun_D_6: option_set)).
% 0.40/0.58 tff(tptp_fun_C_7_type, type, (
% 0.40/0.58 tptp_fun_C_7: option_set)).
% 0.40/0.58 tff(required_preference_type, type, (
% 0.40/0.58 required_preference: ( option * option ) > $o)).
% 0.40/0.58 tff(permitted_preference_type, type, (
% 0.40/0.58 permitted_preference: ( option * option ) > $o)).
% 0.40/0.58 tff(better_type, type, (
% 0.40/0.58 better: ( option_set * option_set ) > $o)).
% 0.40/0.58 tff(weakly_better_type, type, (
% 0.40/0.58 weakly_better: ( option_set * option_set ) > $o)).
% 0.42/0.58 tff(tptp_fun_Z_1_type, type, (
% 0.42/0.58 tptp_fun_Z_1: ( option_set * option * option ) > option)).
% 0.42/0.58 tff(tptp_fun_Z_2_type, type, (
% 0.42/0.58 tptp_fun_Z_2: ( option_set * option ) > option)).
% 0.42/0.58 tff(subset_type, type, (
% 0.42/0.58 subset: ( option_set * option_set ) > $o)).
% 0.42/0.58 tff(tptp_fun_X_0_type, type, (
% 0.42/0.58 tptp_fun_X_0: ( option_set * option_set ) > option)).
% 0.42/0.58 tff(tptp_fun_V_3_type, type, (
% 0.42/0.58 tptp_fun_V_3: ( option * option_set * option_set ) > option)).
% 0.42/0.58 tff(1,assumption,(~(member(tptp_fun_Z_5(A!9, X!12), A!9) <=> (tptp_fun_Z_5(A!9, X!12) = X!12))), introduced(assumption)).
% 0.42/0.58 tff(2,plain,
% 0.42/0.58 (^[U: option] : refl((member(U, A!9) <=> (U = X!12)) <=> (member(U, A!9) <=> (U = X!12)))),
% 0.42/0.58 inference(bind,[status(th)],[])).
% 0.42/0.58 tff(3,plain,
% 0.42/0.58 (![U: option] : (member(U, A!9) <=> (U = X!12)) <=> ![U: option] : (member(U, A!9) <=> (U = X!12))),
% 0.42/0.58 inference(quant_intro,[status(thm)],[2])).
% 0.42/0.58 tff(4,plain,
% 0.42/0.58 ((permitted_preference(X!12, Y!11) & permitted_preference(Y!11, X!12) & required_preference(Z!10, X!12) & required_preference(Z!10, Y!11) & member(X!12, A!9) & member(Z!10, B!8) & member(X!12, C!7) & member(Y!11, C!7) & member(X!12, D!6) & member(Y!11, D!6) & member(Z!10, D!6) & ![U: option] : (member(U, A!9) <=> (U = X!12)) & ![U: option] : (member(U, B!8) <=> (U = Z!10)) & ![U: option] : (member(U, C!7) <=> ((U = Y!11) | (U = X!12))) & ![U: option] : (member(U, D!6) <=> ((U = Z!10) | (U = Y!11) | (U = X!12)))) <=> (permitted_preference(X!12, Y!11) & permitted_preference(Y!11, X!12) & required_preference(Z!10, X!12) & required_preference(Z!10, Y!11) & member(X!12, A!9) & member(Z!10, B!8) & member(X!12, C!7) & member(Y!11, C!7) & member(X!12, D!6) & member(Y!11, D!6) & member(Z!10, D!6) & ![U: option] : (member(U, A!9) <=> (U = X!12)) & ![U: option] : (member(U, B!8) <=> (U = Z!10)) & ![U: option] : (member(U, C!7) <=> ((U = Y!11) | (U = X!12))) & ![U: option] : (member(U, D!6) <=> ((U = Z!10) | (U = Y!11) | (U = X!12))))),
% 0.42/0.58 inference(rewrite,[status(thm)],[])).
% 0.42/0.58 tff(5,plain,
% 0.42/0.58 (?[X: option, Y: option, Z: option, A: option_set, B: option_set, C: option_set, D: option_set] : (permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X) & required_preference(Z, Y) & member(X, A) & member(Z, B) & member(X, C) & member(Y, C) & member(X, D) & member(Y, D) & member(Z, D) & ![U: option] : (member(U, A) <=> (U = X)) & ![U: option] : (member(U, B) <=> (U = Z)) & ![U: option] : (member(U, C) <=> ((U = Y) | (U = X))) & ![U: option] : (member(U, D) <=> ((U = Z) | (U = Y) | (U = X)))) <=> ?[X: option, Y: option, Z: option, A: option_set, B: option_set, C: option_set, D: option_set] : (permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X) & required_preference(Z, Y) & member(X, A) & member(Z, B) & member(X, C) & member(Y, C) & member(X, D) & member(Y, D) & member(Z, D) & ![U: option] : (member(U, A) <=> (U = X)) & ![U: option] : (member(U, B) <=> (U = Z)) & ![U: option] : (member(U, C) <=> ((U = Y) | (U = X))) & ![U: option] : (member(U, D) <=> ((U = Z) | (U = Y) | (U = X))))),
% 0.42/0.58 inference(rewrite,[status(thm)],[])).
% 0.42/0.58 tff(6,plain,
% 0.42/0.58 (^[X: option, Y: option, Z: option, A: option_set, B: option_set, C: option_set, D: option_set] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((permitted_preference(X, Y) & permitted_preference(Y, X)) & required_preference(Z, X)) <=> (permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X))), ((((permitted_preference(X, Y) & permitted_preference(Y, X)) & required_preference(Z, X)) & required_preference(Z, Y)) <=> ((permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X)) & required_preference(Z, Y)))), rewrite(((permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X)) & required_preference(Z, Y)) <=> (permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X) & required_preference(Z, Y))), ((((permitted_preference(X, Y) & permitted_preference(Y, X)) & required_preference(Z, X)) & required_preference(Z, Y)) <=> (permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X) & required_preference(Z, Y)))), (((((permitted_preference(X, Y) & permitted_preference(Y, X)) & required_preference(Z, X)) & required_preference(Z, Y)) & member(X, A)) <=> ((permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X) & required_preference(Z, Y)) & member(X, A)))), rewrite(((permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X) & required_preference(Z, Y)) & member(X, A)) <=> (permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X) & required_preference(Z, Y) & member(X, A))), (((((permitted_preference(X, Y) & permitted_preference(Y, X)) & required_preference(Z, X)) & required_preference(Z, Y)) & member(X, A)) <=> (permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X) & required_preference(Z, Y) & member(X, A)))), ((((((permitted_preference(X, Y) & permitted_preference(Y, X)) & required_preference(Z, X)) & required_preference(Z, Y)) & member(X, A)) & member(Z, B)) <=> ((permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X) & required_preference(Z, Y) & member(X, A)) & member(Z, B)))), rewrite(((permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X) & required_preference(Z, Y) & member(X, A)) & member(Z, B)) <=> (permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X) & required_preference(Z, Y) & member(X, A) & member(Z, B))), ((((((permitted_preference(X, Y) & permitted_preference(Y, X)) & required_preference(Z, X)) & required_preference(Z, Y)) & member(X, A)) & member(Z, B)) <=> (permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X) & required_preference(Z, Y) & member(X, A) & member(Z, B)))), (((((((permitted_preference(X, Y) & permitted_preference(Y, X)) & required_preference(Z, X)) & required_preference(Z, Y)) & member(X, A)) & member(Z, B)) & member(X, C)) <=> ((permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X) & required_preference(Z, Y) & member(X, A) & member(Z, B)) & member(X, C)))), rewrite(((permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X) & required_preference(Z, Y) & member(X, A) & member(Z, B)) & member(X, C)) <=> (permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X) & required_preference(Z, Y) & member(X, A) & member(Z, B) & member(X, C))), (((((((permitted_preference(X, Y) & permitted_preference(Y, X)) & required_preference(Z, X)) & required_preference(Z, Y)) & member(X, A)) & member(Z, B)) & member(X, C)) <=> (permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X) & required_preference(Z, Y) & member(X, A) & member(Z, B) & member(X, C)))), ((((((((permitted_preference(X, Y) & permitted_preference(Y, X)) & required_preference(Z, X)) & required_preference(Z, Y)) & member(X, A)) & member(Z, B)) & member(X, C)) & member(Y, C)) <=> ((permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X) & required_preference(Z, Y) & member(X, A) & member(Z, B) & member(X, C)) & member(Y, C)))), rewrite(((permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X) & required_preference(Z, Y) & member(X, A) & member(Z, B) & member(X, C)) & member(Y, C)) <=> (permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X) & required_preference(Z, Y) & member(X, A) & member(Z, B) & member(X, C) & member(Y, C))), ((((((((permitted_preference(X, Y) & permitted_preference(Y, X)) & required_preference(Z, X)) & required_preference(Z, Y)) & member(X, A)) & member(Z, B)) & member(X, C)) & member(Y, C)) <=> (permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X) & required_preference(Z, Y) & member(X, A) & member(Z, B) & member(X, C) & member(Y, C)))), (((((((((permitted_preference(X, Y) & permitted_preference(Y, X)) & required_preference(Z, X)) & required_preference(Z, Y)) & member(X, A)) & member(Z, B)) & member(X, C)) & member(Y, C)) & member(X, D)) <=> ((permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X) & required_preference(Z, Y) & member(X, A) & member(Z, B) & member(X, C) & member(Y, C)) & member(X, D)))), rewrite(((permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X) & required_preference(Z, Y) & member(X, A) & member(Z, B) & member(X, C) & member(Y, C)) & member(X, D)) <=> (permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X) & required_preference(Z, Y) & member(X, A) & member(Z, B) & member(X, C) & member(Y, C) & member(X, D))), (((((((((permitted_preference(X, Y) & permitted_preference(Y, X)) & required_preference(Z, X)) & required_preference(Z, Y)) & member(X, A)) & member(Z, B)) & member(X, C)) & member(Y, C)) & member(X, D)) <=> (permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X) & required_preference(Z, Y) & member(X, A) & member(Z, B) & member(X, C) & member(Y, C) & member(X, D)))), ((((((((((permitted_preference(X, Y) & permitted_preference(Y, X)) & required_preference(Z, X)) & required_preference(Z, Y)) & member(X, A)) & member(Z, B)) & member(X, C)) & member(Y, C)) & member(X, D)) & member(Y, D)) <=> ((permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X) & required_preference(Z, Y) & member(X, A) & member(Z, B) & member(X, C) & member(Y, C) & member(X, D)) & member(Y, D)))), rewrite(((permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X) & required_preference(Z, Y) & member(X, A) & member(Z, B) & member(X, C) & member(Y, C) & member(X, D)) & member(Y, D)) <=> (permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X) & required_preference(Z, Y) & member(X, A) & member(Z, B) & member(X, C) & member(Y, C) & member(X, D) & member(Y, D))), ((((((((((permitted_preference(X, Y) & permitted_preference(Y, X)) & required_preference(Z, X)) & required_preference(Z, Y)) & member(X, A)) & member(Z, B)) & member(X, C)) & member(Y, C)) & member(X, D)) & member(Y, D)) <=> (permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X) & required_preference(Z, Y) & member(X, A) & member(Z, B) & member(X, C) & member(Y, C) & member(X, D) & member(Y, D)))), (((((((((((permitted_preference(X, Y) & permitted_preference(Y, X)) & required_preference(Z, X)) & required_preference(Z, Y)) & member(X, A)) & member(Z, B)) & member(X, C)) & member(Y, C)) & member(X, D)) & member(Y, D)) & member(Z, D)) <=> ((permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X) & required_preference(Z, Y) & member(X, A) & member(Z, B) & member(X, C) & member(Y, C) & member(X, D) & member(Y, D)) & member(Z, D)))), rewrite(((permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X) & required_preference(Z, Y) & member(X, A) & member(Z, B) & member(X, C) & member(Y, C) & member(X, D) & member(Y, D)) & member(Z, D)) <=> (permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X) & required_preference(Z, Y) & member(X, A) & member(Z, B) & member(X, C) & member(Y, C) & member(X, D) & member(Y, D) & member(Z, D))), (((((((((((permitted_preference(X, Y) & permitted_preference(Y, X)) & required_preference(Z, X)) & required_preference(Z, Y)) & member(X, A)) & member(Z, B)) & member(X, C)) & member(Y, C)) & member(X, D)) & member(Y, D)) & member(Z, D)) <=> (permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X) & required_preference(Z, Y) & member(X, A) & member(Z, B) & member(X, C) & member(Y, C) & member(X, D) & member(Y, D) & member(Z, D)))), ((((((((((((permitted_preference(X, Y) & permitted_preference(Y, X)) & required_preference(Z, X)) & required_preference(Z, Y)) & member(X, A)) & member(Z, B)) & member(X, C)) & member(Y, C)) & member(X, D)) & member(Y, D)) & member(Z, D)) & ![U: option] : (member(U, A) <=> (U = X))) <=> ((permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X) & required_preference(Z, Y) & member(X, A) & member(Z, B) & member(X, C) & member(Y, C) & member(X, D) & member(Y, D) & member(Z, D)) & ![U: option] : (member(U, A) <=> (U = X))))), rewrite(((permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X) & required_preference(Z, Y) & member(X, A) & member(Z, B) & member(X, C) & member(Y, C) & member(X, D) & member(Y, D) & member(Z, D)) & ![U: option] : (member(U, A) <=> (U = X))) <=> (permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X) & required_preference(Z, Y) & member(X, A) & member(Z, B) & member(X, C) & member(Y, C) & member(X, D) & member(Y, D) & member(Z, D) & ![U: option] : (member(U, A) <=> (U = X)))), ((((((((((((permitted_preference(X, Y) & permitted_preference(Y, X)) & required_preference(Z, X)) & required_preference(Z, Y)) & member(X, A)) & member(Z, B)) & member(X, C)) & member(Y, C)) & member(X, D)) & member(Y, D)) & member(Z, D)) & ![U: option] : (member(U, A) <=> (U = X))) <=> (permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X) & required_preference(Z, Y) & member(X, A) & member(Z, B) & member(X, C) & member(Y, C) & member(X, D) & member(Y, D) & member(Z, D) & ![U: option] : (member(U, A) <=> (U = X))))), (((((((((((((permitted_preference(X, Y) & permitted_preference(Y, X)) & required_preference(Z, X)) & required_preference(Z, Y)) & member(X, A)) & member(Z, B)) & member(X, C)) & member(Y, C)) & member(X, D)) & member(Y, D)) & member(Z, D)) & ![U: option] : (member(U, A) <=> (U = X))) & ![U: option] : (member(U, B) <=> (U = Z))) <=> ((permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X) & required_preference(Z, Y) & member(X, A) & member(Z, B) & member(X, C) & member(Y, C) & member(X, D) & member(Y, D) & member(Z, D) & ![U: option] : (member(U, A) <=> (U = X))) & ![U: option] : (member(U, B) <=> (U = Z))))), rewrite(((permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X) & required_preference(Z, Y) & member(X, A) & member(Z, B) & member(X, C) & member(Y, C) & member(X, D) & member(Y, D) & member(Z, D) & ![U: option] : (member(U, A) <=> (U = X))) & ![U: option] : (member(U, B) <=> (U = Z))) <=> (permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X) & required_preference(Z, Y) & member(X, A) & member(Z, B) & member(X, C) & member(Y, C) & member(X, D) & member(Y, D) & member(Z, D) & ![U: option] : (member(U, A) <=> (U = X)) & ![U: option] : (member(U, B) <=> (U = Z)))), (((((((((((((permitted_preference(X, Y) & permitted_preference(Y, X)) & required_preference(Z, X)) & required_preference(Z, Y)) & member(X, A)) & member(Z, B)) & member(X, C)) & member(Y, C)) & member(X, D)) & member(Y, D)) & member(Z, D)) & ![U: option] : (member(U, A) <=> (U = X))) & ![U: option] : (member(U, B) <=> (U = Z))) <=> (permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X) & required_preference(Z, Y) & member(X, A) & member(Z, B) & member(X, C) & member(Y, C) & member(X, D) & member(Y, D) & member(Z, D) & ![U: option] : (member(U, A) <=> (U = X)) & ![U: option] : (member(U, B) <=> (U = Z))))), quant_intro(proof_bind(^[U: option] : rewrite((member(U, C) <=> ((U = X) | (U = Y))) <=> (member(U, C) <=> ((U = Y) | (U = X))))), (![U: option] : (member(U, C) <=> ((U = X) | (U = Y))) <=> ![U: option] : (member(U, C) <=> ((U = Y) | (U = X))))), ((((((((((((((permitted_preference(X, Y) & permitted_preference(Y, X)) & required_preference(Z, X)) & required_preference(Z, Y)) & member(X, A)) & member(Z, B)) & member(X, C)) & member(Y, C)) & member(X, D)) & member(Y, D)) & member(Z, D)) & ![U: option] : (member(U, A) <=> (U = X))) & ![U: option] : (member(U, B) <=> (U = Z))) & ![U: option] : (member(U, C) <=> ((U = X) | (U = Y)))) <=> ((permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X) & required_preference(Z, Y) & member(X, A) & member(Z, B) & member(X, C) & member(Y, C) & member(X, D) & member(Y, D) & member(Z, D) & ![U: option] : (member(U, A) <=> (U = X)) & ![U: option] : (member(U, B) <=> (U = Z))) & ![U: option] : (member(U, C) <=> ((U = Y) | (U = X)))))), rewrite(((permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X) & required_preference(Z, Y) & member(X, A) & member(Z, B) & member(X, C) & member(Y, C) & member(X, D) & member(Y, D) & member(Z, D) & ![U: option] : (member(U, A) <=> (U = X)) & ![U: option] : (member(U, B) <=> (U = Z))) & ![U: option] : (member(U, C) <=> ((U = Y) | (U = X)))) <=> (permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X) & required_preference(Z, Y) & member(X, A) & member(Z, B) & member(X, C) & member(Y, C) & member(X, D) & member(Y, D) & member(Z, D) & ![U: option] : (member(U, A) <=> (U = X)) & ![U: option] : (member(U, B) <=> (U = Z)) & ![U: option] : (member(U, C) <=> ((U = Y) | (U = X))))), ((((((((((((((permitted_preference(X, Y) & permitted_preference(Y, X)) & required_preference(Z, X)) & required_preference(Z, Y)) & member(X, A)) & member(Z, B)) & member(X, C)) & member(Y, C)) & member(X, D)) & member(Y, D)) & member(Z, D)) & ![U: option] : (member(U, A) <=> (U = X))) & ![U: option] : (member(U, B) <=> (U = Z))) & ![U: option] : (member(U, C) <=> ((U = X) | (U = Y)))) <=> (permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X) & required_preference(Z, Y) & member(X, A) & member(Z, B) & member(X, C) & member(Y, C) & member(X, D) & member(Y, D) & member(Z, D) & ![U: option] : (member(U, A) <=> (U = X)) & ![U: option] : (member(U, B) <=> (U = Z)) & ![U: option] : (member(U, C) <=> ((U = Y) | (U = X)))))), quant_intro(proof_bind(^[U: option] : rewrite((member(U, D) <=> (((U = X) | (U = Y)) | (U = Z))) <=> (member(U, D) <=> ((U = Z) | (U = Y) | (U = X))))), (![U: option] : (member(U, D) <=> (((U = X) | (U = Y)) | (U = Z))) <=> ![U: option] : (member(U, D) <=> ((U = Z) | (U = Y) | (U = X))))), (((((((((((((((permitted_preference(X, Y) & permitted_preference(Y, X)) & required_preference(Z, X)) & required_preference(Z, Y)) & member(X, A)) & member(Z, B)) & member(X, C)) & member(Y, C)) & member(X, D)) & member(Y, D)) & member(Z, D)) & ![U: option] : (member(U, A) <=> (U = X))) & ![U: option] : (member(U, B) <=> (U = Z))) & ![U: option] : (member(U, C) <=> ((U = X) | (U = Y)))) & ![U: option] : (member(U, D) <=> (((U = X) | (U = Y)) | (U = Z)))) <=> ((permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X) & required_preference(Z, Y) & member(X, A) & member(Z, B) & member(X, C) & member(Y, C) & member(X, D) & member(Y, D) & member(Z, D) & ![U: option] : (member(U, A) <=> (U = X)) & ![U: option] : (member(U, B) <=> (U = Z)) & ![U: option] : (member(U, C) <=> ((U = Y) | (U = X)))) & ![U: option] : (member(U, D) <=> ((U = Z) | (U = Y) | (U = X)))))), rewrite(((permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X) & required_preference(Z, Y) & member(X, A) & member(Z, B) & member(X, C) & member(Y, C) & member(X, D) & member(Y, D) & member(Z, D) & ![U: option] : (member(U, A) <=> (U = X)) & ![U: option] : (member(U, B) <=> (U = Z)) & ![U: option] : (member(U, C) <=> ((U = Y) | (U = X)))) & ![U: option] : (member(U, D) <=> ((U = Z) | (U = Y) | (U = X)))) <=> (permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X) & required_preference(Z, Y) & member(X, A) & member(Z, B) & member(X, C) & member(Y, C) & member(X, D) & member(Y, D) & member(Z, D) & ![U: option] : (member(U, A) <=> (U = X)) & ![U: option] : (member(U, B) <=> (U = Z)) & ![U: option] : (member(U, C) <=> ((U = Y) | (U = X))) & ![U: option] : (member(U, D) <=> ((U = Z) | (U = Y) | (U = X))))), (((((((((((((((permitted_preference(X, Y) & permitted_preference(Y, X)) & required_preference(Z, X)) & required_preference(Z, Y)) & member(X, A)) & member(Z, B)) & member(X, C)) & member(Y, C)) & member(X, D)) & member(Y, D)) & member(Z, D)) & ![U: option] : (member(U, A) <=> (U = X))) & ![U: option] : (member(U, B) <=> (U = Z))) & ![U: option] : (member(U, C) <=> ((U = X) | (U = Y)))) & ![U: option] : (member(U, D) <=> (((U = X) | (U = Y)) | (U = Z)))) <=> (permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X) & required_preference(Z, Y) & member(X, A) & member(Z, B) & member(X, C) & member(Y, C) & member(X, D) & member(Y, D) & member(Z, D) & ![U: option] : (member(U, A) <=> (U = X)) & ![U: option] : (member(U, B) <=> (U = Z)) & ![U: option] : (member(U, C) <=> ((U = Y) | (U = X))) & ![U: option] : (member(U, D) <=> ((U = Z) | (U = Y) | (U = X))))))),
% 0.42/0.59 inference(bind,[status(th)],[])).
% 0.42/0.59 tff(7,plain,
% 0.42/0.59 (?[X: option, Y: option, Z: option, A: option_set, B: option_set, C: option_set, D: option_set] : ((((((((((((((permitted_preference(X, Y) & permitted_preference(Y, X)) & required_preference(Z, X)) & required_preference(Z, Y)) & member(X, A)) & member(Z, B)) & member(X, C)) & member(Y, C)) & member(X, D)) & member(Y, D)) & member(Z, D)) & ![U: option] : (member(U, A) <=> (U = X))) & ![U: option] : (member(U, B) <=> (U = Z))) & ![U: option] : (member(U, C) <=> ((U = X) | (U = Y)))) & ![U: option] : (member(U, D) <=> (((U = X) | (U = Y)) | (U = Z)))) <=> ?[X: option, Y: option, Z: option, A: option_set, B: option_set, C: option_set, D: option_set] : (permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X) & required_preference(Z, Y) & member(X, A) & member(Z, B) & member(X, C) & member(Y, C) & member(X, D) & member(Y, D) & member(Z, D) & ![U: option] : (member(U, A) <=> (U = X)) & ![U: option] : (member(U, B) <=> (U = Z)) & ![U: option] : (member(U, C) <=> ((U = Y) | (U = X))) & ![U: option] : (member(U, D) <=> ((U = Z) | (U = Y) | (U = X))))),
% 0.42/0.59 inference(quant_intro,[status(thm)],[6])).
% 0.42/0.59 tff(8,axiom,(?[X: option, Y: option, Z: option, A: option_set, B: option_set, C: option_set, D: option_set] : ((((((((((((((permitted_preference(X, Y) & permitted_preference(Y, X)) & required_preference(Z, X)) & required_preference(Z, Y)) & member(X, A)) & member(Z, B)) & member(X, C)) & member(Y, C)) & member(X, D)) & member(Y, D)) & member(Z, D)) & ![U: option] : (member(U, A) <=> (U = X))) & ![U: option] : (member(U, B) <=> (U = Z))) & ![U: option] : (member(U, C) <=> ((U = X) | (U = Y)))) & ![U: option] : (member(U, D) <=> (((U = X) | (U = Y)) | (U = Z))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','existence_of_dominated_diversity')).
% 0.42/0.59 tff(9,plain,
% 0.42/0.59 (?[X: option, Y: option, Z: option, A: option_set, B: option_set, C: option_set, D: option_set] : (permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X) & required_preference(Z, Y) & member(X, A) & member(Z, B) & member(X, C) & member(Y, C) & member(X, D) & member(Y, D) & member(Z, D) & ![U: option] : (member(U, A) <=> (U = X)) & ![U: option] : (member(U, B) <=> (U = Z)) & ![U: option] : (member(U, C) <=> ((U = Y) | (U = X))) & ![U: option] : (member(U, D) <=> ((U = Z) | (U = Y) | (U = X))))),
% 0.42/0.59 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.42/0.59 tff(10,plain,
% 0.42/0.59 (?[X: option, Y: option, Z: option, A: option_set, B: option_set, C: option_set, D: option_set] : (permitted_preference(X, Y) & permitted_preference(Y, X) & required_preference(Z, X) & required_preference(Z, Y) & member(X, A) & member(Z, B) & member(X, C) & member(Y, C) & member(X, D) & member(Y, D) & member(Z, D) & ![U: option] : (member(U, A) <=> (U = X)) & ![U: option] : (member(U, B) <=> (U = Z)) & ![U: option] : (member(U, C) <=> ((U = Y) | (U = X))) & ![U: option] : (member(U, D) <=> ((U = Z) | (U = Y) | (U = X))))),
% 0.42/0.59 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.42/0.59 tff(11,plain,
% 0.42/0.59 (permitted_preference(X!12, Y!11) & permitted_preference(Y!11, X!12) & required_preference(Z!10, X!12) & required_preference(Z!10, Y!11) & member(X!12, A!9) & member(Z!10, B!8) & member(X!12, C!7) & member(Y!11, C!7) & member(X!12, D!6) & member(Y!11, D!6) & member(Z!10, D!6) & ![U: option] : (member(U, A!9) <=> (U = X!12)) & ![U: option] : (member(U, B!8) <=> (U = Z!10)) & ![U: option] : (member(U, C!7) <=> ((U = Y!11) | (U = X!12))) & ![U: option] : (member(U, D!6) <=> ((U = Z!10) | (U = Y!11) | (U = X!12)))),
% 0.42/0.59 inference(modus_ponens,[status(thm)],[10, 4])).
% 0.42/0.59 tff(12,plain,
% 0.42/0.59 (![U: option] : (member(U, A!9) <=> (U = X!12))),
% 0.42/0.59 inference(and_elim,[status(thm)],[11])).
% 0.42/0.59 tff(13,plain,
% 0.42/0.59 (![U: option] : (member(U, A!9) <=> (U = X!12))),
% 0.42/0.59 inference(modus_ponens,[status(thm)],[12, 3])).
% 0.42/0.59 tff(14,plain,
% 0.42/0.59 ((~![U: option] : (member(U, A!9) <=> (U = X!12))) | (member(tptp_fun_Z_5(A!9, X!12), A!9) <=> (tptp_fun_Z_5(A!9, X!12) = X!12))),
% 0.42/0.59 inference(quant_inst,[status(thm)],[])).
% 0.42/0.59 tff(15,plain,
% 0.42/0.59 ($false),
% 0.42/0.59 inference(unit_resolution,[status(thm)],[14, 13, 1])).
% 0.42/0.59 tff(16,plain,(member(tptp_fun_Z_5(A!9, X!12), A!9) <=> (tptp_fun_Z_5(A!9, X!12) = X!12)), inference(lemma,lemma(discharge,[]))).
% 0.42/0.59 tff(17,assumption,(~(member(tptp_fun_Z_1(C!7, Y!11, X!12), C!7) <=> ((tptp_fun_Z_1(C!7, Y!11, X!12) = X!12) | (tptp_fun_Z_1(C!7, Y!11, X!12) = Y!11)))), introduced(assumption)).
% 0.42/0.59 tff(18,plain,
% 0.42/0.59 (^[U: option] : refl((member(U, C!7) <=> ((U = Y!11) | (U = X!12))) <=> (member(U, C!7) <=> ((U = Y!11) | (U = X!12))))),
% 0.42/0.59 inference(bind,[status(th)],[])).
% 0.42/0.59 tff(19,plain,
% 0.42/0.59 (![U: option] : (member(U, C!7) <=> ((U = Y!11) | (U = X!12))) <=> ![U: option] : (member(U, C!7) <=> ((U = Y!11) | (U = X!12)))),
% 0.42/0.59 inference(quant_intro,[status(thm)],[18])).
% 0.42/0.59 tff(20,plain,
% 0.42/0.59 (![U: option] : (member(U, C!7) <=> ((U = Y!11) | (U = X!12)))),
% 0.42/0.59 inference(and_elim,[status(thm)],[11])).
% 0.42/0.59 tff(21,plain,
% 0.42/0.59 (![U: option] : (member(U, C!7) <=> ((U = Y!11) | (U = X!12)))),
% 0.42/0.59 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.42/0.59 tff(22,plain,
% 0.42/0.59 (((~![U: option] : (member(U, C!7) <=> ((U = Y!11) | (U = X!12)))) | (member(tptp_fun_Z_1(C!7, Y!11, X!12), C!7) <=> ((tptp_fun_Z_1(C!7, Y!11, X!12) = X!12) | (tptp_fun_Z_1(C!7, Y!11, X!12) = Y!11)))) <=> ((~![U: option] : (member(U, C!7) <=> ((U = Y!11) | (U = X!12)))) | (member(tptp_fun_Z_1(C!7, Y!11, X!12), C!7) <=> ((tptp_fun_Z_1(C!7, Y!11, X!12) = X!12) | (tptp_fun_Z_1(C!7, Y!11, X!12) = Y!11))))),
% 0.42/0.59 inference(rewrite,[status(thm)],[])).
% 0.42/0.59 tff(23,plain,
% 0.42/0.59 ((member(tptp_fun_Z_1(C!7, Y!11, X!12), C!7) <=> ((tptp_fun_Z_1(C!7, Y!11, X!12) = Y!11) | (tptp_fun_Z_1(C!7, Y!11, X!12) = X!12))) <=> (member(tptp_fun_Z_1(C!7, Y!11, X!12), C!7) <=> ((tptp_fun_Z_1(C!7, Y!11, X!12) = X!12) | (tptp_fun_Z_1(C!7, Y!11, X!12) = Y!11)))),
% 0.42/0.59 inference(rewrite,[status(thm)],[])).
% 0.42/0.59 tff(24,plain,
% 0.42/0.59 (((~![U: option] : (member(U, C!7) <=> ((U = Y!11) | (U = X!12)))) | (member(tptp_fun_Z_1(C!7, Y!11, X!12), C!7) <=> ((tptp_fun_Z_1(C!7, Y!11, X!12) = Y!11) | (tptp_fun_Z_1(C!7, Y!11, X!12) = X!12)))) <=> ((~![U: option] : (member(U, C!7) <=> ((U = Y!11) | (U = X!12)))) | (member(tptp_fun_Z_1(C!7, Y!11, X!12), C!7) <=> ((tptp_fun_Z_1(C!7, Y!11, X!12) = X!12) | (tptp_fun_Z_1(C!7, Y!11, X!12) = Y!11))))),
% 0.42/0.59 inference(monotonicity,[status(thm)],[23])).
% 0.42/0.59 tff(25,plain,
% 0.42/0.59 (((~![U: option] : (member(U, C!7) <=> ((U = Y!11) | (U = X!12)))) | (member(tptp_fun_Z_1(C!7, Y!11, X!12), C!7) <=> ((tptp_fun_Z_1(C!7, Y!11, X!12) = Y!11) | (tptp_fun_Z_1(C!7, Y!11, X!12) = X!12)))) <=> ((~![U: option] : (member(U, C!7) <=> ((U = Y!11) | (U = X!12)))) | (member(tptp_fun_Z_1(C!7, Y!11, X!12), C!7) <=> ((tptp_fun_Z_1(C!7, Y!11, X!12) = X!12) | (tptp_fun_Z_1(C!7, Y!11, X!12) = Y!11))))),
% 0.42/0.60 inference(transitivity,[status(thm)],[24, 22])).
% 0.42/0.60 tff(26,plain,
% 0.42/0.60 ((~![U: option] : (member(U, C!7) <=> ((U = Y!11) | (U = X!12)))) | (member(tptp_fun_Z_1(C!7, Y!11, X!12), C!7) <=> ((tptp_fun_Z_1(C!7, Y!11, X!12) = Y!11) | (tptp_fun_Z_1(C!7, Y!11, X!12) = X!12)))),
% 0.42/0.60 inference(quant_inst,[status(thm)],[])).
% 0.42/0.60 tff(27,plain,
% 0.42/0.60 ((~![U: option] : (member(U, C!7) <=> ((U = Y!11) | (U = X!12)))) | (member(tptp_fun_Z_1(C!7, Y!11, X!12), C!7) <=> ((tptp_fun_Z_1(C!7, Y!11, X!12) = X!12) | (tptp_fun_Z_1(C!7, Y!11, X!12) = Y!11)))),
% 0.42/0.60 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.42/0.60 tff(28,plain,
% 0.42/0.60 ($false),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[27, 21, 17])).
% 0.42/0.60 tff(29,plain,(member(tptp_fun_Z_1(C!7, Y!11, X!12), C!7) <=> ((tptp_fun_Z_1(C!7, Y!11, X!12) = X!12) | (tptp_fun_Z_1(C!7, Y!11, X!12) = Y!11))), inference(lemma,lemma(discharge,[]))).
% 0.42/0.60 tff(30,assumption,(~((tptp_fun_Z_1(C!7, Y!11, X!12) = X!12) | (tptp_fun_Z_1(C!7, Y!11, X!12) = Y!11) | (~member(tptp_fun_Z_1(C!7, Y!11, X!12), C!7)))), introduced(assumption)).
% 0.42/0.60 tff(31,plain,
% 0.42/0.60 (((tptp_fun_Z_1(C!7, Y!11, X!12) = X!12) | (tptp_fun_Z_1(C!7, Y!11, X!12) = Y!11) | (~member(tptp_fun_Z_1(C!7, Y!11, X!12), C!7))) | member(tptp_fun_Z_1(C!7, Y!11, X!12), C!7)),
% 0.42/0.60 inference(tautology,[status(thm)],[])).
% 0.42/0.60 tff(32,plain,
% 0.42/0.60 (member(tptp_fun_Z_1(C!7, Y!11, X!12), C!7)),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.42/0.60 tff(33,plain,
% 0.42/0.60 (((tptp_fun_Z_1(C!7, Y!11, X!12) = X!12) | (tptp_fun_Z_1(C!7, Y!11, X!12) = Y!11) | (~member(tptp_fun_Z_1(C!7, Y!11, X!12), C!7))) | (~(tptp_fun_Z_1(C!7, Y!11, X!12) = X!12))),
% 0.42/0.60 inference(tautology,[status(thm)],[])).
% 0.42/0.60 tff(34,plain,
% 0.42/0.60 (~(tptp_fun_Z_1(C!7, Y!11, X!12) = X!12)),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[33, 30])).
% 0.42/0.60 tff(35,plain,
% 0.42/0.60 (((tptp_fun_Z_1(C!7, Y!11, X!12) = X!12) | (tptp_fun_Z_1(C!7, Y!11, X!12) = Y!11) | (~member(tptp_fun_Z_1(C!7, Y!11, X!12), C!7))) | (~(tptp_fun_Z_1(C!7, Y!11, X!12) = Y!11))),
% 0.42/0.60 inference(tautology,[status(thm)],[])).
% 0.42/0.60 tff(36,plain,
% 0.42/0.60 (~(tptp_fun_Z_1(C!7, Y!11, X!12) = Y!11)),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[35, 30])).
% 0.42/0.60 tff(37,plain,
% 0.42/0.60 ((~((tptp_fun_Z_1(C!7, Y!11, X!12) = X!12) | (tptp_fun_Z_1(C!7, Y!11, X!12) = Y!11))) | (tptp_fun_Z_1(C!7, Y!11, X!12) = X!12) | (tptp_fun_Z_1(C!7, Y!11, X!12) = Y!11)),
% 0.42/0.60 inference(tautology,[status(thm)],[])).
% 0.42/0.60 tff(38,plain,
% 0.42/0.60 (~((tptp_fun_Z_1(C!7, Y!11, X!12) = X!12) | (tptp_fun_Z_1(C!7, Y!11, X!12) = Y!11))),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[37, 36, 34])).
% 0.42/0.60 tff(39,plain,
% 0.42/0.60 ((~(member(tptp_fun_Z_1(C!7, Y!11, X!12), C!7) <=> ((tptp_fun_Z_1(C!7, Y!11, X!12) = X!12) | (tptp_fun_Z_1(C!7, Y!11, X!12) = Y!11)))) | (~member(tptp_fun_Z_1(C!7, Y!11, X!12), C!7)) | ((tptp_fun_Z_1(C!7, Y!11, X!12) = X!12) | (tptp_fun_Z_1(C!7, Y!11, X!12) = Y!11))),
% 0.42/0.60 inference(tautology,[status(thm)],[])).
% 0.42/0.60 tff(40,plain,
% 0.42/0.60 ($false),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[39, 38, 32, 29])).
% 0.42/0.60 tff(41,plain,((tptp_fun_Z_1(C!7, Y!11, X!12) = X!12) | (tptp_fun_Z_1(C!7, Y!11, X!12) = Y!11) | (~member(tptp_fun_Z_1(C!7, Y!11, X!12), C!7))), inference(lemma,lemma(discharge,[]))).
% 0.42/0.60 tff(42,assumption,(~(member(tptp_fun_Z_2(A!9, X!12), A!9) <=> (tptp_fun_Z_2(A!9, X!12) = X!12))), introduced(assumption)).
% 0.42/0.60 tff(43,plain,
% 0.42/0.60 ((~![U: option] : (member(U, A!9) <=> (U = X!12))) | (member(tptp_fun_Z_2(A!9, X!12), A!9) <=> (tptp_fun_Z_2(A!9, X!12) = X!12))),
% 0.42/0.60 inference(quant_inst,[status(thm)],[])).
% 0.42/0.60 tff(44,plain,
% 0.42/0.60 ($false),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[43, 13, 42])).
% 0.42/0.60 tff(45,plain,(member(tptp_fun_Z_2(A!9, X!12), A!9) <=> (tptp_fun_Z_2(A!9, X!12) = X!12)), inference(lemma,lemma(discharge,[]))).
% 0.42/0.60 tff(46,assumption,(~((~member(tptp_fun_Z_2(A!9, X!12), A!9)) | (tptp_fun_Z_2(A!9, X!12) = X!12))), introduced(assumption)).
% 0.42/0.60 tff(47,plain,
% 0.42/0.60 (((~member(tptp_fun_Z_2(A!9, X!12), A!9)) | (tptp_fun_Z_2(A!9, X!12) = X!12)) | member(tptp_fun_Z_2(A!9, X!12), A!9)),
% 0.42/0.60 inference(tautology,[status(thm)],[])).
% 0.42/0.60 tff(48,plain,
% 0.42/0.60 (member(tptp_fun_Z_2(A!9, X!12), A!9)),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.42/0.60 tff(49,plain,
% 0.42/0.60 (((~member(tptp_fun_Z_2(A!9, X!12), A!9)) | (tptp_fun_Z_2(A!9, X!12) = X!12)) | (~(tptp_fun_Z_2(A!9, X!12) = X!12))),
% 0.42/0.60 inference(tautology,[status(thm)],[])).
% 0.42/0.60 tff(50,plain,
% 0.42/0.60 (~(tptp_fun_Z_2(A!9, X!12) = X!12)),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[49, 46])).
% 0.42/0.60 tff(51,plain,
% 0.42/0.60 ((~(member(tptp_fun_Z_2(A!9, X!12), A!9) <=> (tptp_fun_Z_2(A!9, X!12) = X!12))) | (~member(tptp_fun_Z_2(A!9, X!12), A!9)) | (tptp_fun_Z_2(A!9, X!12) = X!12)),
% 0.42/0.60 inference(tautology,[status(thm)],[])).
% 0.42/0.60 tff(52,plain,
% 0.42/0.60 ($false),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[51, 50, 48, 45])).
% 0.42/0.60 tff(53,plain,((~member(tptp_fun_Z_2(A!9, X!12), A!9)) | (tptp_fun_Z_2(A!9, X!12) = X!12)), inference(lemma,lemma(discharge,[]))).
% 0.42/0.60 tff(54,plain,
% 0.42/0.60 (member(Y!11, C!7)),
% 0.42/0.60 inference(and_elim,[status(thm)],[11])).
% 0.42/0.60 tff(55,plain,
% 0.42/0.60 (member(X!12, C!7)),
% 0.42/0.60 inference(and_elim,[status(thm)],[11])).
% 0.42/0.60 tff(56,plain,
% 0.42/0.60 (member(X!12, A!9)),
% 0.42/0.60 inference(and_elim,[status(thm)],[11])).
% 0.42/0.60 tff(57,plain,
% 0.42/0.60 (permitted_preference(Y!11, X!12)),
% 0.42/0.60 inference(and_elim,[status(thm)],[11])).
% 0.42/0.60 tff(58,plain,
% 0.42/0.60 (permitted_preference(X!12, Y!11)),
% 0.42/0.60 inference(and_elim,[status(thm)],[11])).
% 0.42/0.60 tff(59,plain,
% 0.42/0.60 (^[X: option, Y: option, U: option_set, V: option_set] : refl((better(U, V) | (~permitted_preference(X, Y)) | (~permitted_preference(Y, X)) | (~member(X, U)) | (~member(Y, U)) | (~member(X, V)) | (~((tptp_fun_Z_1(U, Y, X) = X) | (tptp_fun_Z_1(U, Y, X) = Y) | (~member(tptp_fun_Z_1(U, Y, X), U)))) | (~((~member(tptp_fun_Z_2(V, X), V)) | (tptp_fun_Z_2(V, X) = X)))) <=> (better(U, V) | (~permitted_preference(X, Y)) | (~permitted_preference(Y, X)) | (~member(X, U)) | (~member(Y, U)) | (~member(X, V)) | (~((tptp_fun_Z_1(U, Y, X) = X) | (tptp_fun_Z_1(U, Y, X) = Y) | (~member(tptp_fun_Z_1(U, Y, X), U)))) | (~((~member(tptp_fun_Z_2(V, X), V)) | (tptp_fun_Z_2(V, X) = X)))))),
% 0.42/0.60 inference(bind,[status(th)],[])).
% 0.42/0.60 tff(60,plain,
% 0.42/0.60 (![X: option, Y: option, U: option_set, V: option_set] : (better(U, V) | (~permitted_preference(X, Y)) | (~permitted_preference(Y, X)) | (~member(X, U)) | (~member(Y, U)) | (~member(X, V)) | (~((tptp_fun_Z_1(U, Y, X) = X) | (tptp_fun_Z_1(U, Y, X) = Y) | (~member(tptp_fun_Z_1(U, Y, X), U)))) | (~((~member(tptp_fun_Z_2(V, X), V)) | (tptp_fun_Z_2(V, X) = X)))) <=> ![X: option, Y: option, U: option_set, V: option_set] : (better(U, V) | (~permitted_preference(X, Y)) | (~permitted_preference(Y, X)) | (~member(X, U)) | (~member(Y, U)) | (~member(X, V)) | (~((tptp_fun_Z_1(U, Y, X) = X) | (tptp_fun_Z_1(U, Y, X) = Y) | (~member(tptp_fun_Z_1(U, Y, X), U)))) | (~((~member(tptp_fun_Z_2(V, X), V)) | (tptp_fun_Z_2(V, X) = X))))),
% 0.42/0.60 inference(quant_intro,[status(thm)],[59])).
% 0.42/0.60 tff(61,plain,
% 0.42/0.60 (^[X: option, Y: option, U: option_set, V: option_set] : trans(monotonicity(trans(monotonicity(rewrite((~((tptp_fun_Z_1(U, Y, X) = X) | (tptp_fun_Z_1(U, Y, X) = Y) | (~member(tptp_fun_Z_1(U, Y, X), U)))) <=> (~((tptp_fun_Z_1(U, Y, X) = X) | (tptp_fun_Z_1(U, Y, X) = Y) | (~member(tptp_fun_Z_1(U, Y, X), U))))), (((~permitted_preference(X, Y)) | (~permitted_preference(Y, X)) | (~member(X, U)) | (~member(Y, U)) | (~member(X, V)) | (~((tptp_fun_Z_1(U, Y, X) = X) | (tptp_fun_Z_1(U, Y, X) = Y) | (~member(tptp_fun_Z_1(U, Y, X), U)))) | (~((~member(tptp_fun_Z_2(V, X), V)) | (tptp_fun_Z_2(V, X) = X)))) <=> ((~permitted_preference(X, Y)) | (~permitted_preference(Y, X)) | (~member(X, U)) | (~member(Y, U)) | (~member(X, V)) | (~((tptp_fun_Z_1(U, Y, X) = X) | (tptp_fun_Z_1(U, Y, X) = Y) | (~member(tptp_fun_Z_1(U, Y, X), U)))) | (~((~member(tptp_fun_Z_2(V, X), V)) | (tptp_fun_Z_2(V, X) = X)))))), rewrite(((~permitted_preference(X, Y)) | (~permitted_preference(Y, X)) | (~member(X, U)) | (~member(Y, U)) | (~member(X, V)) | (~((tptp_fun_Z_1(U, Y, X) = X) | (tptp_fun_Z_1(U, Y, X) = Y) | (~member(tptp_fun_Z_1(U, Y, X), U)))) | (~((~member(tptp_fun_Z_2(V, X), V)) | (tptp_fun_Z_2(V, X) = X)))) <=> ((~permitted_preference(X, Y)) | (~permitted_preference(Y, X)) | (~member(X, U)) | (~member(Y, U)) | (~member(X, V)) | (~((tptp_fun_Z_1(U, Y, X) = X) | (tptp_fun_Z_1(U, Y, X) = Y) | (~member(tptp_fun_Z_1(U, Y, X), U)))) | (~((~member(tptp_fun_Z_2(V, X), V)) | (tptp_fun_Z_2(V, X) = X))))), (((~permitted_preference(X, Y)) | (~permitted_preference(Y, X)) | (~member(X, U)) | (~member(Y, U)) | (~member(X, V)) | (~((tptp_fun_Z_1(U, Y, X) = X) | (tptp_fun_Z_1(U, Y, X) = Y) | (~member(tptp_fun_Z_1(U, Y, X), U)))) | (~((~member(tptp_fun_Z_2(V, X), V)) | (tptp_fun_Z_2(V, X) = X)))) <=> ((~permitted_preference(X, Y)) | (~permitted_preference(Y, X)) | (~member(X, U)) | (~member(Y, U)) | (~member(X, V)) | (~((tptp_fun_Z_1(U, Y, X) = X) | (tptp_fun_Z_1(U, Y, X) = Y) | (~member(tptp_fun_Z_1(U, Y, X), U)))) | (~((~member(tptp_fun_Z_2(V, X), V)) | (tptp_fun_Z_2(V, X) = X)))))), ((((~permitted_preference(X, Y)) | (~permitted_preference(Y, X)) | (~member(X, U)) | (~member(Y, U)) | (~member(X, V)) | (~((tptp_fun_Z_1(U, Y, X) = X) | (tptp_fun_Z_1(U, Y, X) = Y) | (~member(tptp_fun_Z_1(U, Y, X), U)))) | (~((~member(tptp_fun_Z_2(V, X), V)) | (tptp_fun_Z_2(V, X) = X)))) | better(U, V)) <=> (((~permitted_preference(X, Y)) | (~permitted_preference(Y, X)) | (~member(X, U)) | (~member(Y, U)) | (~member(X, V)) | (~((tptp_fun_Z_1(U, Y, X) = X) | (tptp_fun_Z_1(U, Y, X) = Y) | (~member(tptp_fun_Z_1(U, Y, X), U)))) | (~((~member(tptp_fun_Z_2(V, X), V)) | (tptp_fun_Z_2(V, X) = X)))) | better(U, V)))), rewrite((((~permitted_preference(X, Y)) | (~permitted_preference(Y, X)) | (~member(X, U)) | (~member(Y, U)) | (~member(X, V)) | (~((tptp_fun_Z_1(U, Y, X) = X) | (tptp_fun_Z_1(U, Y, X) = Y) | (~member(tptp_fun_Z_1(U, Y, X), U)))) | (~((~member(tptp_fun_Z_2(V, X), V)) | (tptp_fun_Z_2(V, X) = X)))) | better(U, V)) <=> (better(U, V) | (~permitted_preference(X, Y)) | (~permitted_preference(Y, X)) | (~member(X, U)) | (~member(Y, U)) | (~member(X, V)) | (~((tptp_fun_Z_1(U, Y, X) = X) | (tptp_fun_Z_1(U, Y, X) = Y) | (~member(tptp_fun_Z_1(U, Y, X), U)))) | (~((~member(tptp_fun_Z_2(V, X), V)) | (tptp_fun_Z_2(V, X) = X))))), ((((~permitted_preference(X, Y)) | (~permitted_preference(Y, X)) | (~member(X, U)) | (~member(Y, U)) | (~member(X, V)) | (~((tptp_fun_Z_1(U, Y, X) = X) | (tptp_fun_Z_1(U, Y, X) = Y) | (~member(tptp_fun_Z_1(U, Y, X), U)))) | (~((~member(tptp_fun_Z_2(V, X), V)) | (tptp_fun_Z_2(V, X) = X)))) | better(U, V)) <=> (better(U, V) | (~permitted_preference(X, Y)) | (~permitted_preference(Y, X)) | (~member(X, U)) | (~member(Y, U)) | (~member(X, V)) | (~((tptp_fun_Z_1(U, Y, X) = X) | (tptp_fun_Z_1(U, Y, X) = Y) | (~member(tptp_fun_Z_1(U, Y, X), U)))) | (~((~member(tptp_fun_Z_2(V, X), V)) | (tptp_fun_Z_2(V, X) = X))))))),
% 0.42/0.60 inference(bind,[status(th)],[])).
% 0.42/0.60 tff(62,plain,
% 0.42/0.60 (![X: option, Y: option, U: option_set, V: option_set] : (((~permitted_preference(X, Y)) | (~permitted_preference(Y, X)) | (~member(X, U)) | (~member(Y, U)) | (~member(X, V)) | (~((tptp_fun_Z_1(U, Y, X) = X) | (tptp_fun_Z_1(U, Y, X) = Y) | (~member(tptp_fun_Z_1(U, Y, X), U)))) | (~((~member(tptp_fun_Z_2(V, X), V)) | (tptp_fun_Z_2(V, X) = X)))) | better(U, V)) <=> ![X: option, Y: option, U: option_set, V: option_set] : (better(U, V) | (~permitted_preference(X, Y)) | (~permitted_preference(Y, X)) | (~member(X, U)) | (~member(Y, U)) | (~member(X, V)) | (~((tptp_fun_Z_1(U, Y, X) = X) | (tptp_fun_Z_1(U, Y, X) = Y) | (~member(tptp_fun_Z_1(U, Y, X), U)))) | (~((~member(tptp_fun_Z_2(V, X), V)) | (tptp_fun_Z_2(V, X) = X))))),
% 0.42/0.60 inference(quant_intro,[status(thm)],[61])).
% 0.42/0.60 tff(63,plain,
% 0.42/0.60 (![X: option, Y: option, U: option_set, V: option_set] : ((~(permitted_preference(X, Y) & permitted_preference(Y, X) & member(X, U) & member(Y, U) & member(X, V) & ![Z: option] : ((Z = X) | (Z = Y) | (~member(Z, U))) & ![Z: option] : ((~member(Z, V)) | (Z = X)))) | better(U, V)) <=> ![X: option, Y: option, U: option_set, V: option_set] : ((~(permitted_preference(X, Y) & permitted_preference(Y, X) & member(X, U) & member(Y, U) & member(X, V) & ![Z: option] : ((Z = X) | (Z = Y) | (~member(Z, U))) & ![Z: option] : ((~member(Z, V)) | (Z = X)))) | better(U, V))),
% 0.42/0.60 inference(rewrite,[status(thm)],[])).
% 0.42/0.60 tff(64,plain,
% 0.42/0.60 (^[X: option, Y: option, U: option_set, V: option_set] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((permitted_preference(X, Y) & permitted_preference(Y, X)) & member(X, U)) <=> (permitted_preference(X, Y) & permitted_preference(Y, X) & member(X, U))), ((((permitted_preference(X, Y) & permitted_preference(Y, X)) & member(X, U)) & member(Y, U)) <=> ((permitted_preference(X, Y) & permitted_preference(Y, X) & member(X, U)) & member(Y, U)))), rewrite(((permitted_preference(X, Y) & permitted_preference(Y, X) & member(X, U)) & member(Y, U)) <=> (permitted_preference(X, Y) & permitted_preference(Y, X) & member(X, U) & member(Y, U))), ((((permitted_preference(X, Y) & permitted_preference(Y, X)) & member(X, U)) & member(Y, U)) <=> (permitted_preference(X, Y) & permitted_preference(Y, X) & member(X, U) & member(Y, U)))), (((((permitted_preference(X, Y) & permitted_preference(Y, X)) & member(X, U)) & member(Y, U)) & member(X, V)) <=> ((permitted_preference(X, Y) & permitted_preference(Y, X) & member(X, U) & member(Y, U)) & member(X, V)))), rewrite(((permitted_preference(X, Y) & permitted_preference(Y, X) & member(X, U) & member(Y, U)) & member(X, V)) <=> (permitted_preference(X, Y) & permitted_preference(Y, X) & member(X, U) & member(Y, U) & member(X, V))), (((((permitted_preference(X, Y) & permitted_preference(Y, X)) & member(X, U)) & member(Y, U)) & member(X, V)) <=> (permitted_preference(X, Y) & permitted_preference(Y, X) & member(X, U) & member(Y, U) & member(X, V)))), quant_intro(proof_bind(^[Z: option] : trans(monotonicity(rewrite(((Z = X) | (Z = Y)) <=> ((Z = X) | (Z = Y))), ((member(Z, U) => ((Z = X) | (Z = Y))) <=> (member(Z, U) => ((Z = X) | (Z = Y))))), rewrite((member(Z, U) => ((Z = X) | (Z = Y))) <=> ((Z = X) | (Z = Y) | (~member(Z, U)))), ((member(Z, U) => ((Z = X) | (Z = Y))) <=> ((Z = X) | (Z = Y) | (~member(Z, U)))))), (![Z: option] : (member(Z, U) => ((Z = X) | (Z = Y))) <=> ![Z: option] : ((Z = X) | (Z = Y) | (~member(Z, U))))), ((((((permitted_preference(X, Y) & permitted_preference(Y, X)) & member(X, U)) & member(Y, U)) & member(X, V)) & ![Z: option] : (member(Z, U) => ((Z = X) | (Z = Y)))) <=> ((permitted_preference(X, Y) & permitted_preference(Y, X) & member(X, U) & member(Y, U) & member(X, V)) & ![Z: option] : ((Z = X) | (Z = Y) | (~member(Z, U)))))), rewrite(((permitted_preference(X, Y) & permitted_preference(Y, X) & member(X, U) & member(Y, U) & member(X, V)) & ![Z: option] : ((Z = X) | (Z = Y) | (~member(Z, U)))) <=> (permitted_preference(X, Y) & permitted_preference(Y, X) & member(X, U) & member(Y, U) & member(X, V) & ![Z: option] : ((Z = X) | (Z = Y) | (~member(Z, U))))), ((((((permitted_preference(X, Y) & permitted_preference(Y, X)) & member(X, U)) & member(Y, U)) & member(X, V)) & ![Z: option] : (member(Z, U) => ((Z = X) | (Z = Y)))) <=> (permitted_preference(X, Y) & permitted_preference(Y, X) & member(X, U) & member(Y, U) & member(X, V) & ![Z: option] : ((Z = X) | (Z = Y) | (~member(Z, U)))))), quant_intro(proof_bind(^[Z: option] : rewrite((member(Z, V) => (Z = X)) <=> ((~member(Z, V)) | (Z = X)))), (![Z: option] : (member(Z, V) => (Z = X)) <=> ![Z: option] : ((~member(Z, V)) | (Z = X)))), (((((((permitted_preference(X, Y) & permitted_preference(Y, X)) & member(X, U)) & member(Y, U)) & member(X, V)) & ![Z: option] : (member(Z, U) => ((Z = X) | (Z = Y)))) & ![Z: option] : (member(Z, V) => (Z = X))) <=> ((permitted_preference(X, Y) & permitted_preference(Y, X) & member(X, U) & member(Y, U) & member(X, V) & ![Z: option] : ((Z = X) | (Z = Y) | (~member(Z, U)))) & ![Z: option] : ((~member(Z, V)) | (Z = X))))), rewrite(((permitted_preference(X, Y) & permitted_preference(Y, X) & member(X, U) & member(Y, U) & member(X, V) & ![Z: option] : ((Z = X) | (Z = Y) | (~member(Z, U)))) & ![Z: option] : ((~member(Z, V)) | (Z = X))) <=> (permitted_preference(X, Y) & permitted_preference(Y, X) & member(X, U) & member(Y, U) & member(X, V) & ![Z: option] : ((Z = X) | (Z = Y) | (~member(Z, U))) & ![Z: option] : ((~member(Z, V)) | (Z = X)))), (((((((permitted_preference(X, Y) & permitted_preference(Y, X)) & member(X, U)) & member(Y, U)) & member(X, V)) & ![Z: option] : (member(Z, U) => ((Z = X) | (Z = Y)))) & ![Z: option] : (member(Z, V) => (Z = X))) <=> (permitted_preference(X, Y) & permitted_preference(Y, X) & member(X, U) & member(Y, U) & member(X, V) & ![Z: option] : ((Z = X) | (Z = Y) | (~member(Z, U))) & ![Z: option] : ((~member(Z, V)) | (Z = X))))), ((((((((permitted_preference(X, Y) & permitted_preference(Y, X)) & member(X, U)) & member(Y, U)) & member(X, V)) & ![Z: option] : (member(Z, U) => ((Z = X) | (Z = Y)))) & ![Z: option] : (member(Z, V) => (Z = X))) => better(U, V)) <=> ((permitted_preference(X, Y) & permitted_preference(Y, X) & member(X, U) & member(Y, U) & member(X, V) & ![Z: option] : ((Z = X) | (Z = Y) | (~member(Z, U))) & ![Z: option] : ((~member(Z, V)) | (Z = X))) => better(U, V)))), rewrite(((permitted_preference(X, Y) & permitted_preference(Y, X) & member(X, U) & member(Y, U) & member(X, V) & ![Z: option] : ((Z = X) | (Z = Y) | (~member(Z, U))) & ![Z: option] : ((~member(Z, V)) | (Z = X))) => better(U, V)) <=> ((~(permitted_preference(X, Y) & permitted_preference(Y, X) & member(X, U) & member(Y, U) & member(X, V) & ![Z: option] : ((Z = X) | (Z = Y) | (~member(Z, U))) & ![Z: option] : ((~member(Z, V)) | (Z = X)))) | better(U, V))), ((((((((permitted_preference(X, Y) & permitted_preference(Y, X)) & member(X, U)) & member(Y, U)) & member(X, V)) & ![Z: option] : (member(Z, U) => ((Z = X) | (Z = Y)))) & ![Z: option] : (member(Z, V) => (Z = X))) => better(U, V)) <=> ((~(permitted_preference(X, Y) & permitted_preference(Y, X) & member(X, U) & member(Y, U) & member(X, V) & ![Z: option] : ((Z = X) | (Z = Y) | (~member(Z, U))) & ![Z: option] : ((~member(Z, V)) | (Z = X)))) | better(U, V))))),
% 0.42/0.60 inference(bind,[status(th)],[])).
% 0.42/0.60 tff(65,plain,
% 0.42/0.60 (![X: option, Y: option, U: option_set, V: option_set] : (((((((permitted_preference(X, Y) & permitted_preference(Y, X)) & member(X, U)) & member(Y, U)) & member(X, V)) & ![Z: option] : (member(Z, U) => ((Z = X) | (Z = Y)))) & ![Z: option] : (member(Z, V) => (Z = X))) => better(U, V)) <=> ![X: option, Y: option, U: option_set, V: option_set] : ((~(permitted_preference(X, Y) & permitted_preference(Y, X) & member(X, U) & member(Y, U) & member(X, V) & ![Z: option] : ((Z = X) | (Z = Y) | (~member(Z, U))) & ![Z: option] : ((~member(Z, V)) | (Z = X)))) | better(U, V))),
% 0.42/0.60 inference(quant_intro,[status(thm)],[64])).
% 0.42/0.60 tff(66,axiom,(![X: option, Y: option, U: option_set, V: option_set] : (((((((permitted_preference(X, Y) & permitted_preference(Y, X)) & member(X, U)) & member(Y, U)) & member(X, V)) & ![Z: option] : (member(Z, U) => ((Z = X) | (Z = Y)))) & ![Z: option] : (member(Z, V) => (Z = X))) => better(U, V))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','value_of_rational_diversity')).
% 0.42/0.60 tff(67,plain,
% 0.42/0.60 (![X: option, Y: option, U: option_set, V: option_set] : ((~(permitted_preference(X, Y) & permitted_preference(Y, X) & member(X, U) & member(Y, U) & member(X, V) & ![Z: option] : ((Z = X) | (Z = Y) | (~member(Z, U))) & ![Z: option] : ((~member(Z, V)) | (Z = X)))) | better(U, V))),
% 0.42/0.60 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.42/0.60 tff(68,plain,
% 0.42/0.60 (![X: option, Y: option, U: option_set, V: option_set] : ((~(permitted_preference(X, Y) & permitted_preference(Y, X) & member(X, U) & member(Y, U) & member(X, V) & ![Z: option] : ((Z = X) | (Z = Y) | (~member(Z, U))) & ![Z: option] : ((~member(Z, V)) | (Z = X)))) | better(U, V))),
% 0.42/0.60 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.42/0.60 tff(69,plain,(
% 0.42/0.60 ![X: option, Y: option, U: option_set, V: option_set] : (((~permitted_preference(X, Y)) | (~permitted_preference(Y, X)) | (~member(X, U)) | (~member(Y, U)) | (~member(X, V)) | (~((tptp_fun_Z_1(U, Y, X) = X) | (tptp_fun_Z_1(U, Y, X) = Y) | (~member(tptp_fun_Z_1(U, Y, X), U)))) | (~((~member(tptp_fun_Z_2(V, X), V)) | (tptp_fun_Z_2(V, X) = X)))) | better(U, V))),
% 0.42/0.60 inference(skolemize,[status(sab)],[68])).
% 0.42/0.60 tff(70,plain,
% 0.42/0.60 (![X: option, Y: option, U: option_set, V: option_set] : (better(U, V) | (~permitted_preference(X, Y)) | (~permitted_preference(Y, X)) | (~member(X, U)) | (~member(Y, U)) | (~member(X, V)) | (~((tptp_fun_Z_1(U, Y, X) = X) | (tptp_fun_Z_1(U, Y, X) = Y) | (~member(tptp_fun_Z_1(U, Y, X), U)))) | (~((~member(tptp_fun_Z_2(V, X), V)) | (tptp_fun_Z_2(V, X) = X))))),
% 0.42/0.60 inference(modus_ponens,[status(thm)],[69, 62])).
% 0.42/0.60 tff(71,plain,
% 0.42/0.60 (![X: option, Y: option, U: option_set, V: option_set] : (better(U, V) | (~permitted_preference(X, Y)) | (~permitted_preference(Y, X)) | (~member(X, U)) | (~member(Y, U)) | (~member(X, V)) | (~((tptp_fun_Z_1(U, Y, X) = X) | (tptp_fun_Z_1(U, Y, X) = Y) | (~member(tptp_fun_Z_1(U, Y, X), U)))) | (~((~member(tptp_fun_Z_2(V, X), V)) | (tptp_fun_Z_2(V, X) = X))))),
% 0.42/0.60 inference(modus_ponens,[status(thm)],[70, 60])).
% 0.42/0.60 tff(72,plain,
% 0.42/0.60 (((~![X: option, Y: option, U: option_set, V: option_set] : (better(U, V) | (~permitted_preference(X, Y)) | (~permitted_preference(Y, X)) | (~member(X, U)) | (~member(Y, U)) | (~member(X, V)) | (~((tptp_fun_Z_1(U, Y, X) = X) | (tptp_fun_Z_1(U, Y, X) = Y) | (~member(tptp_fun_Z_1(U, Y, X), U)))) | (~((~member(tptp_fun_Z_2(V, X), V)) | (tptp_fun_Z_2(V, X) = X))))) | ((~permitted_preference(X!12, Y!11)) | (~permitted_preference(Y!11, X!12)) | (~member(X!12, A!9)) | (~((~member(tptp_fun_Z_2(A!9, X!12), A!9)) | (tptp_fun_Z_2(A!9, X!12) = X!12))) | (~member(Y!11, C!7)) | (~member(X!12, C!7)) | (~((tptp_fun_Z_1(C!7, Y!11, X!12) = X!12) | (tptp_fun_Z_1(C!7, Y!11, X!12) = Y!11) | (~member(tptp_fun_Z_1(C!7, Y!11, X!12), C!7)))) | better(C!7, A!9))) <=> ((~![X: option, Y: option, U: option_set, V: option_set] : (better(U, V) | (~permitted_preference(X, Y)) | (~permitted_preference(Y, X)) | (~member(X, U)) | (~member(Y, U)) | (~member(X, V)) | (~((tptp_fun_Z_1(U, Y, X) = X) | (tptp_fun_Z_1(U, Y, X) = Y) | (~member(tptp_fun_Z_1(U, Y, X), U)))) | (~((~member(tptp_fun_Z_2(V, X), V)) | (tptp_fun_Z_2(V, X) = X))))) | (~permitted_preference(X!12, Y!11)) | (~permitted_preference(Y!11, X!12)) | (~member(X!12, A!9)) | (~((~member(tptp_fun_Z_2(A!9, X!12), A!9)) | (tptp_fun_Z_2(A!9, X!12) = X!12))) | (~member(Y!11, C!7)) | (~member(X!12, C!7)) | (~((tptp_fun_Z_1(C!7, Y!11, X!12) = X!12) | (tptp_fun_Z_1(C!7, Y!11, X!12) = Y!11) | (~member(tptp_fun_Z_1(C!7, Y!11, X!12), C!7)))) | better(C!7, A!9))),
% 0.42/0.60 inference(rewrite,[status(thm)],[])).
% 0.42/0.60 tff(73,plain,
% 0.42/0.60 ((better(C!7, A!9) | (~permitted_preference(X!12, Y!11)) | (~permitted_preference(Y!11, X!12)) | (~member(X!12, C!7)) | (~member(Y!11, C!7)) | (~member(X!12, A!9)) | (~((tptp_fun_Z_1(C!7, Y!11, X!12) = X!12) | (tptp_fun_Z_1(C!7, Y!11, X!12) = Y!11) | (~member(tptp_fun_Z_1(C!7, Y!11, X!12), C!7)))) | (~((~member(tptp_fun_Z_2(A!9, X!12), A!9)) | (tptp_fun_Z_2(A!9, X!12) = X!12)))) <=> ((~permitted_preference(X!12, Y!11)) | (~permitted_preference(Y!11, X!12)) | (~member(X!12, A!9)) | (~((~member(tptp_fun_Z_2(A!9, X!12), A!9)) | (tptp_fun_Z_2(A!9, X!12) = X!12))) | (~member(Y!11, C!7)) | (~member(X!12, C!7)) | (~((tptp_fun_Z_1(C!7, Y!11, X!12) = X!12) | (tptp_fun_Z_1(C!7, Y!11, X!12) = Y!11) | (~member(tptp_fun_Z_1(C!7, Y!11, X!12), C!7)))) | better(C!7, A!9))),
% 0.42/0.60 inference(rewrite,[status(thm)],[])).
% 0.42/0.60 tff(74,plain,
% 0.42/0.60 ((~((tptp_fun_Z_1(C!7, Y!11, X!12) = X!12) | (tptp_fun_Z_1(C!7, Y!11, X!12) = Y!11) | (~member(tptp_fun_Z_1(C!7, Y!11, X!12), C!7)))) <=> (~((tptp_fun_Z_1(C!7, Y!11, X!12) = X!12) | (tptp_fun_Z_1(C!7, Y!11, X!12) = Y!11) | (~member(tptp_fun_Z_1(C!7, Y!11, X!12), C!7))))),
% 0.42/0.60 inference(rewrite,[status(thm)],[])).
% 0.42/0.60 tff(75,plain,
% 0.42/0.60 ((better(C!7, A!9) | (~permitted_preference(X!12, Y!11)) | (~permitted_preference(Y!11, X!12)) | (~member(X!12, C!7)) | (~member(Y!11, C!7)) | (~member(X!12, A!9)) | (~((tptp_fun_Z_1(C!7, Y!11, X!12) = X!12) | (tptp_fun_Z_1(C!7, Y!11, X!12) = Y!11) | (~member(tptp_fun_Z_1(C!7, Y!11, X!12), C!7)))) | (~((~member(tptp_fun_Z_2(A!9, X!12), A!9)) | (tptp_fun_Z_2(A!9, X!12) = X!12)))) <=> (better(C!7, A!9) | (~permitted_preference(X!12, Y!11)) | (~permitted_preference(Y!11, X!12)) | (~member(X!12, C!7)) | (~member(Y!11, C!7)) | (~member(X!12, A!9)) | (~((tptp_fun_Z_1(C!7, Y!11, X!12) = X!12) | (tptp_fun_Z_1(C!7, Y!11, X!12) = Y!11) | (~member(tptp_fun_Z_1(C!7, Y!11, X!12), C!7)))) | (~((~member(tptp_fun_Z_2(A!9, X!12), A!9)) | (tptp_fun_Z_2(A!9, X!12) = X!12))))),
% 0.42/0.61 inference(monotonicity,[status(thm)],[74])).
% 0.42/0.61 tff(76,plain,
% 0.42/0.61 ((better(C!7, A!9) | (~permitted_preference(X!12, Y!11)) | (~permitted_preference(Y!11, X!12)) | (~member(X!12, C!7)) | (~member(Y!11, C!7)) | (~member(X!12, A!9)) | (~((tptp_fun_Z_1(C!7, Y!11, X!12) = X!12) | (tptp_fun_Z_1(C!7, Y!11, X!12) = Y!11) | (~member(tptp_fun_Z_1(C!7, Y!11, X!12), C!7)))) | (~((~member(tptp_fun_Z_2(A!9, X!12), A!9)) | (tptp_fun_Z_2(A!9, X!12) = X!12)))) <=> ((~permitted_preference(X!12, Y!11)) | (~permitted_preference(Y!11, X!12)) | (~member(X!12, A!9)) | (~((~member(tptp_fun_Z_2(A!9, X!12), A!9)) | (tptp_fun_Z_2(A!9, X!12) = X!12))) | (~member(Y!11, C!7)) | (~member(X!12, C!7)) | (~((tptp_fun_Z_1(C!7, Y!11, X!12) = X!12) | (tptp_fun_Z_1(C!7, Y!11, X!12) = Y!11) | (~member(tptp_fun_Z_1(C!7, Y!11, X!12), C!7)))) | better(C!7, A!9))),
% 0.42/0.61 inference(transitivity,[status(thm)],[75, 73])).
% 0.42/0.61 tff(77,plain,
% 0.42/0.61 (((~![X: option, Y: option, U: option_set, V: option_set] : (better(U, V) | (~permitted_preference(X, Y)) | (~permitted_preference(Y, X)) | (~member(X, U)) | (~member(Y, U)) | (~member(X, V)) | (~((tptp_fun_Z_1(U, Y, X) = X) | (tptp_fun_Z_1(U, Y, X) = Y) | (~member(tptp_fun_Z_1(U, Y, X), U)))) | (~((~member(tptp_fun_Z_2(V, X), V)) | (tptp_fun_Z_2(V, X) = X))))) | (better(C!7, A!9) | (~permitted_preference(X!12, Y!11)) | (~permitted_preference(Y!11, X!12)) | (~member(X!12, C!7)) | (~member(Y!11, C!7)) | (~member(X!12, A!9)) | (~((tptp_fun_Z_1(C!7, Y!11, X!12) = X!12) | (tptp_fun_Z_1(C!7, Y!11, X!12) = Y!11) | (~member(tptp_fun_Z_1(C!7, Y!11, X!12), C!7)))) | (~((~member(tptp_fun_Z_2(A!9, X!12), A!9)) | (tptp_fun_Z_2(A!9, X!12) = X!12))))) <=> ((~![X: option, Y: option, U: option_set, V: option_set] : (better(U, V) | (~permitted_preference(X, Y)) | (~permitted_preference(Y, X)) | (~member(X, U)) | (~member(Y, U)) | (~member(X, V)) | (~((tptp_fun_Z_1(U, Y, X) = X) | (tptp_fun_Z_1(U, Y, X) = Y) | (~member(tptp_fun_Z_1(U, Y, X), U)))) | (~((~member(tptp_fun_Z_2(V, X), V)) | (tptp_fun_Z_2(V, X) = X))))) | ((~permitted_preference(X!12, Y!11)) | (~permitted_preference(Y!11, X!12)) | (~member(X!12, A!9)) | (~((~member(tptp_fun_Z_2(A!9, X!12), A!9)) | (tptp_fun_Z_2(A!9, X!12) = X!12))) | (~member(Y!11, C!7)) | (~member(X!12, C!7)) | (~((tptp_fun_Z_1(C!7, Y!11, X!12) = X!12) | (tptp_fun_Z_1(C!7, Y!11, X!12) = Y!11) | (~member(tptp_fun_Z_1(C!7, Y!11, X!12), C!7)))) | better(C!7, A!9)))),
% 0.42/0.61 inference(monotonicity,[status(thm)],[76])).
% 0.42/0.61 tff(78,plain,
% 0.42/0.61 (((~![X: option, Y: option, U: option_set, V: option_set] : (better(U, V) | (~permitted_preference(X, Y)) | (~permitted_preference(Y, X)) | (~member(X, U)) | (~member(Y, U)) | (~member(X, V)) | (~((tptp_fun_Z_1(U, Y, X) = X) | (tptp_fun_Z_1(U, Y, X) = Y) | (~member(tptp_fun_Z_1(U, Y, X), U)))) | (~((~member(tptp_fun_Z_2(V, X), V)) | (tptp_fun_Z_2(V, X) = X))))) | (better(C!7, A!9) | (~permitted_preference(X!12, Y!11)) | (~permitted_preference(Y!11, X!12)) | (~member(X!12, C!7)) | (~member(Y!11, C!7)) | (~member(X!12, A!9)) | (~((tptp_fun_Z_1(C!7, Y!11, X!12) = X!12) | (tptp_fun_Z_1(C!7, Y!11, X!12) = Y!11) | (~member(tptp_fun_Z_1(C!7, Y!11, X!12), C!7)))) | (~((~member(tptp_fun_Z_2(A!9, X!12), A!9)) | (tptp_fun_Z_2(A!9, X!12) = X!12))))) <=> ((~![X: option, Y: option, U: option_set, V: option_set] : (better(U, V) | (~permitted_preference(X, Y)) | (~permitted_preference(Y, X)) | (~member(X, U)) | (~member(Y, U)) | (~member(X, V)) | (~((tptp_fun_Z_1(U, Y, X) = X) | (tptp_fun_Z_1(U, Y, X) = Y) | (~member(tptp_fun_Z_1(U, Y, X), U)))) | (~((~member(tptp_fun_Z_2(V, X), V)) | (tptp_fun_Z_2(V, X) = X))))) | (~permitted_preference(X!12, Y!11)) | (~permitted_preference(Y!11, X!12)) | (~member(X!12, A!9)) | (~((~member(tptp_fun_Z_2(A!9, X!12), A!9)) | (tptp_fun_Z_2(A!9, X!12) = X!12))) | (~member(Y!11, C!7)) | (~member(X!12, C!7)) | (~((tptp_fun_Z_1(C!7, Y!11, X!12) = X!12) | (tptp_fun_Z_1(C!7, Y!11, X!12) = Y!11) | (~member(tptp_fun_Z_1(C!7, Y!11, X!12), C!7)))) | better(C!7, A!9))),
% 0.42/0.61 inference(transitivity,[status(thm)],[77, 72])).
% 0.42/0.61 tff(79,plain,
% 0.42/0.61 ((~![X: option, Y: option, U: option_set, V: option_set] : (better(U, V) | (~permitted_preference(X, Y)) | (~permitted_preference(Y, X)) | (~member(X, U)) | (~member(Y, U)) | (~member(X, V)) | (~((tptp_fun_Z_1(U, Y, X) = X) | (tptp_fun_Z_1(U, Y, X) = Y) | (~member(tptp_fun_Z_1(U, Y, X), U)))) | (~((~member(tptp_fun_Z_2(V, X), V)) | (tptp_fun_Z_2(V, X) = X))))) | (better(C!7, A!9) | (~permitted_preference(X!12, Y!11)) | (~permitted_preference(Y!11, X!12)) | (~member(X!12, C!7)) | (~member(Y!11, C!7)) | (~member(X!12, A!9)) | (~((tptp_fun_Z_1(C!7, Y!11, X!12) = X!12) | (tptp_fun_Z_1(C!7, Y!11, X!12) = Y!11) | (~member(tptp_fun_Z_1(C!7, Y!11, X!12), C!7)))) | (~((~member(tptp_fun_Z_2(A!9, X!12), A!9)) | (tptp_fun_Z_2(A!9, X!12) = X!12))))),
% 0.42/0.61 inference(quant_inst,[status(thm)],[])).
% 0.42/0.61 tff(80,plain,
% 0.42/0.61 ((~![X: option, Y: option, U: option_set, V: option_set] : (better(U, V) | (~permitted_preference(X, Y)) | (~permitted_preference(Y, X)) | (~member(X, U)) | (~member(Y, U)) | (~member(X, V)) | (~((tptp_fun_Z_1(U, Y, X) = X) | (tptp_fun_Z_1(U, Y, X) = Y) | (~member(tptp_fun_Z_1(U, Y, X), U)))) | (~((~member(tptp_fun_Z_2(V, X), V)) | (tptp_fun_Z_2(V, X) = X))))) | (~permitted_preference(X!12, Y!11)) | (~permitted_preference(Y!11, X!12)) | (~member(X!12, A!9)) | (~((~member(tptp_fun_Z_2(A!9, X!12), A!9)) | (tptp_fun_Z_2(A!9, X!12) = X!12))) | (~member(Y!11, C!7)) | (~member(X!12, C!7)) | (~((tptp_fun_Z_1(C!7, Y!11, X!12) = X!12) | (tptp_fun_Z_1(C!7, Y!11, X!12) = Y!11) | (~member(tptp_fun_Z_1(C!7, Y!11, X!12), C!7)))) | better(C!7, A!9)),
% 0.42/0.61 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.42/0.61 tff(81,plain,
% 0.42/0.61 ((~((tptp_fun_Z_1(C!7, Y!11, X!12) = X!12) | (tptp_fun_Z_1(C!7, Y!11, X!12) = Y!11) | (~member(tptp_fun_Z_1(C!7, Y!11, X!12), C!7)))) | better(C!7, A!9)),
% 0.42/0.61 inference(unit_resolution,[status(thm)],[80, 71, 58, 57, 56, 55, 54, 53])).
% 0.42/0.61 tff(82,plain,
% 0.42/0.61 (better(C!7, A!9)),
% 0.42/0.61 inference(unit_resolution,[status(thm)],[81, 41])).
% 0.42/0.61 tff(83,plain,
% 0.42/0.61 (^[X: option_set, Y: option_set] : refl((~(((~weakly_better(X, Y)) | weakly_better(Y, X)) <=> better(X, Y))) <=> (~(((~weakly_better(X, Y)) | weakly_better(Y, X)) <=> better(X, Y))))),
% 0.42/0.61 inference(bind,[status(th)],[])).
% 0.42/0.61 tff(84,plain,
% 0.42/0.61 (![X: option_set, Y: option_set] : (~(((~weakly_better(X, Y)) | weakly_better(Y, X)) <=> better(X, Y))) <=> ![X: option_set, Y: option_set] : (~(((~weakly_better(X, Y)) | weakly_better(Y, X)) <=> better(X, Y)))),
% 0.42/0.61 inference(quant_intro,[status(thm)],[83])).
% 0.42/0.61 tff(85,plain,
% 0.42/0.61 (^[X: option_set, Y: option_set] : trans(trans(monotonicity(rewrite((weakly_better(X, Y) & (~weakly_better(Y, X))) <=> (~((~weakly_better(X, Y)) | weakly_better(Y, X)))), ((better(X, Y) <=> (weakly_better(X, Y) & (~weakly_better(Y, X)))) <=> (better(X, Y) <=> (~((~weakly_better(X, Y)) | weakly_better(Y, X)))))), rewrite((better(X, Y) <=> (~((~weakly_better(X, Y)) | weakly_better(Y, X)))) <=> (~(((~weakly_better(X, Y)) | weakly_better(Y, X)) <=> better(X, Y)))), ((better(X, Y) <=> (weakly_better(X, Y) & (~weakly_better(Y, X)))) <=> (~(((~weakly_better(X, Y)) | weakly_better(Y, X)) <=> better(X, Y))))), rewrite((~(((~weakly_better(X, Y)) | weakly_better(Y, X)) <=> better(X, Y))) <=> (~(((~weakly_better(X, Y)) | weakly_better(Y, X)) <=> better(X, Y)))), ((better(X, Y) <=> (weakly_better(X, Y) & (~weakly_better(Y, X)))) <=> (~(((~weakly_better(X, Y)) | weakly_better(Y, X)) <=> better(X, Y)))))),
% 0.42/0.61 inference(bind,[status(th)],[])).
% 0.42/0.61 tff(86,plain,
% 0.42/0.61 (![X: option_set, Y: option_set] : (better(X, Y) <=> (weakly_better(X, Y) & (~weakly_better(Y, X)))) <=> ![X: option_set, Y: option_set] : (~(((~weakly_better(X, Y)) | weakly_better(Y, X)) <=> better(X, Y)))),
% 0.42/0.61 inference(quant_intro,[status(thm)],[85])).
% 0.42/0.61 tff(87,plain,
% 0.42/0.61 (![X: option_set, Y: option_set] : (better(X, Y) <=> (weakly_better(X, Y) & (~weakly_better(Y, X)))) <=> ![X: option_set, Y: option_set] : (better(X, Y) <=> (weakly_better(X, Y) & (~weakly_better(Y, X))))),
% 0.42/0.61 inference(rewrite,[status(thm)],[])).
% 0.42/0.61 tff(88,axiom,(![X: option_set, Y: option_set] : (better(X, Y) <=> (weakly_better(X, Y) & (~weakly_better(Y, X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','better')).
% 0.42/0.61 tff(89,plain,
% 0.42/0.61 (![X: option_set, Y: option_set] : (better(X, Y) <=> (weakly_better(X, Y) & (~weakly_better(Y, X))))),
% 0.42/0.61 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.42/0.61 tff(90,plain,(
% 0.42/0.61 ![X: option_set, Y: option_set] : (better(X, Y) <=> (weakly_better(X, Y) & (~weakly_better(Y, X))))),
% 0.42/0.61 inference(skolemize,[status(sab)],[89])).
% 0.42/0.61 tff(91,plain,
% 0.42/0.61 (![X: option_set, Y: option_set] : (~(((~weakly_better(X, Y)) | weakly_better(Y, X)) <=> better(X, Y)))),
% 0.42/0.61 inference(modus_ponens,[status(thm)],[90, 86])).
% 0.42/0.61 tff(92,plain,
% 0.42/0.61 (![X: option_set, Y: option_set] : (~(((~weakly_better(X, Y)) | weakly_better(Y, X)) <=> better(X, Y)))),
% 0.42/0.61 inference(modus_ponens,[status(thm)],[91, 84])).
% 0.42/0.61 tff(93,plain,
% 0.42/0.61 ((~![X: option_set, Y: option_set] : (~(((~weakly_better(X, Y)) | weakly_better(Y, X)) <=> better(X, Y)))) | (~(((~weakly_better(C!7, A!9)) | weakly_better(A!9, C!7)) <=> better(C!7, A!9)))),
% 0.42/0.61 inference(quant_inst,[status(thm)],[])).
% 0.42/0.61 tff(94,plain,
% 0.42/0.61 (~(((~weakly_better(C!7, A!9)) | weakly_better(A!9, C!7)) <=> better(C!7, A!9))),
% 0.42/0.61 inference(unit_resolution,[status(thm)],[93, 92])).
% 0.42/0.61 tff(95,plain,
% 0.42/0.61 ((((~weakly_better(C!7, A!9)) | weakly_better(A!9, C!7)) <=> better(C!7, A!9)) | (~((~weakly_better(C!7, A!9)) | weakly_better(A!9, C!7))) | (~better(C!7, A!9))),
% 0.42/0.61 inference(tautology,[status(thm)],[])).
% 0.42/0.61 tff(96,plain,
% 0.42/0.61 ((~((~weakly_better(C!7, A!9)) | weakly_better(A!9, C!7))) | (~better(C!7, A!9))),
% 0.42/0.61 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.42/0.61 tff(97,plain,
% 0.42/0.61 (~((~weakly_better(C!7, A!9)) | weakly_better(A!9, C!7))),
% 0.42/0.61 inference(unit_resolution,[status(thm)],[96, 82])).
% 0.42/0.61 tff(98,plain,
% 0.42/0.61 (((~weakly_better(C!7, A!9)) | weakly_better(A!9, C!7)) | (~weakly_better(A!9, C!7))),
% 0.42/0.61 inference(tautology,[status(thm)],[])).
% 0.42/0.61 tff(99,plain,
% 0.42/0.61 (~weakly_better(A!9, C!7)),
% 0.42/0.61 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.42/0.61 tff(100,assumption,(~weakly_better(D!6, C!7)), introduced(assumption)).
% 0.42/0.61 tff(101,assumption,((~((~subset(C!7, D!6)) | ![X: option] : ((~member(X, C!7)) | member(X, D!6)))) | (~(subset(C!7, D!6) | (~((~member(tptp_fun_X_0(D!6, C!7), C!7)) | member(tptp_fun_X_0(D!6, C!7), D!6)))))), introduced(assumption)).
% 0.42/0.61 tff(102,plain,
% 0.42/0.61 (^[A: option_set, B: option_set] : refl((~((~((~subset(A, B)) | ![X: option] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: option] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.42/0.61 inference(bind,[status(th)],[])).
% 0.42/0.61 tff(103,plain,
% 0.42/0.61 (![A: option_set, B: option_set] : (~((~((~subset(A, B)) | ![X: option] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: option_set, B: option_set] : (~((~((~subset(A, B)) | ![X: option] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.42/0.61 inference(quant_intro,[status(thm)],[102])).
% 0.42/0.61 tff(104,plain,
% 0.42/0.61 (^[A: option_set, B: option_set] : rewrite((~((~((~subset(A, B)) | ![X: option] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: option] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.42/0.61 inference(bind,[status(th)],[])).
% 0.42/0.61 tff(105,plain,
% 0.42/0.61 (![A: option_set, B: option_set] : (~((~((~subset(A, B)) | ![X: option] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: option_set, B: option_set] : (~((~((~subset(A, B)) | ![X: option] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.42/0.62 inference(quant_intro,[status(thm)],[104])).
% 0.42/0.62 tff(106,plain,
% 0.42/0.62 (![A: option_set, B: option_set] : (~((~((~subset(A, B)) | ![X: option] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: option_set, B: option_set] : (~((~((~subset(A, B)) | ![X: option] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.42/0.62 inference(transitivity,[status(thm)],[105, 103])).
% 0.42/0.62 tff(107,plain,
% 0.42/0.62 (^[A: option_set, B: option_set] : trans(monotonicity(rewrite(((~subset(A, B)) | ![X: option] : ((~member(X, A)) | member(X, B))) <=> ((~subset(A, B)) | ![X: option] : ((~member(X, A)) | member(X, B)))), rewrite((subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))) <=> (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))), ((((~subset(A, B)) | ![X: option] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (((~subset(A, B)) | ![X: option] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![X: option] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: option] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))), ((((~subset(A, B)) | ![X: option] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: option] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))))),
% 0.42/0.62 inference(bind,[status(th)],[])).
% 0.42/0.62 tff(108,plain,
% 0.42/0.62 (![A: option_set, B: option_set] : (((~subset(A, B)) | ![X: option] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> ![A: option_set, B: option_set] : (~((~((~subset(A, B)) | ![X: option] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.42/0.62 inference(quant_intro,[status(thm)],[107])).
% 0.42/0.62 tff(109,plain,
% 0.42/0.62 (![A: option_set, B: option_set] : (subset(A, B) <=> ![X: option] : ((~member(X, A)) | member(X, B))) <=> ![A: option_set, B: option_set] : (subset(A, B) <=> ![X: option] : ((~member(X, A)) | member(X, B)))),
% 0.42/0.62 inference(rewrite,[status(thm)],[])).
% 0.42/0.62 tff(110,plain,
% 0.42/0.62 (^[A: option_set, B: option_set] : rewrite((subset(A, B) <=> ![X: option] : (member(X, A) => member(X, B))) <=> (subset(A, B) <=> ![X: option] : ((~member(X, A)) | member(X, B))))),
% 0.42/0.62 inference(bind,[status(th)],[])).
% 0.42/0.62 tff(111,plain,
% 0.42/0.62 (![A: option_set, B: option_set] : (subset(A, B) <=> ![X: option] : (member(X, A) => member(X, B))) <=> ![A: option_set, B: option_set] : (subset(A, B) <=> ![X: option] : ((~member(X, A)) | member(X, B)))),
% 0.42/0.62 inference(quant_intro,[status(thm)],[110])).
% 0.42/0.62 tff(112,axiom,(![A: option_set, B: option_set] : (subset(A, B) <=> ![X: option] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','subset')).
% 0.42/0.62 tff(113,plain,
% 0.42/0.62 (![A: option_set, B: option_set] : (subset(A, B) <=> ![X: option] : ((~member(X, A)) | member(X, B)))),
% 0.42/0.62 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.42/0.62 tff(114,plain,
% 0.42/0.62 (![A: option_set, B: option_set] : (subset(A, B) <=> ![X: option] : ((~member(X, A)) | member(X, B)))),
% 0.42/0.62 inference(modus_ponens,[status(thm)],[113, 109])).
% 0.42/0.62 tff(115,plain,(
% 0.42/0.62 ![A: option_set, B: option_set] : (((~subset(A, B)) | ![X: option] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))),
% 0.42/0.62 inference(skolemize,[status(sab)],[114])).
% 0.42/0.62 tff(116,plain,
% 0.42/0.62 (![A: option_set, B: option_set] : (~((~((~subset(A, B)) | ![X: option] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.42/0.62 inference(modus_ponens,[status(thm)],[115, 108])).
% 0.42/0.62 tff(117,plain,
% 0.42/0.62 (![A: option_set, B: option_set] : (~((~((~subset(A, B)) | ![X: option] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.42/0.62 inference(modus_ponens,[status(thm)],[116, 106])).
% 0.42/0.62 tff(118,plain,
% 0.42/0.62 ((~![A: option_set, B: option_set] : (~((~((~subset(A, B)) | ![X: option] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(C!7, D!6)) | ![X: option] : ((~member(X, C!7)) | member(X, D!6)))) | (~(subset(C!7, D!6) | (~((~member(tptp_fun_X_0(D!6, C!7), C!7)) | member(tptp_fun_X_0(D!6, C!7), D!6)))))))),
% 0.42/0.62 inference(quant_inst,[status(thm)],[])).
% 0.42/0.62 tff(119,plain,
% 0.42/0.62 ($false),
% 0.42/0.62 inference(unit_resolution,[status(thm)],[118, 117, 101])).
% 0.42/0.62 tff(120,plain,(~((~((~subset(C!7, D!6)) | ![X: option] : ((~member(X, C!7)) | member(X, D!6)))) | (~(subset(C!7, D!6) | (~((~member(tptp_fun_X_0(D!6, C!7), C!7)) | member(tptp_fun_X_0(D!6, C!7), D!6))))))), inference(lemma,lemma(discharge,[]))).
% 0.42/0.62 tff(121,plain,
% 0.42/0.62 (((~((~subset(C!7, D!6)) | ![X: option] : ((~member(X, C!7)) | member(X, D!6)))) | (~(subset(C!7, D!6) | (~((~member(tptp_fun_X_0(D!6, C!7), C!7)) | member(tptp_fun_X_0(D!6, C!7), D!6)))))) | (subset(C!7, D!6) | (~((~member(tptp_fun_X_0(D!6, C!7), C!7)) | member(tptp_fun_X_0(D!6, C!7), D!6))))),
% 0.42/0.62 inference(tautology,[status(thm)],[])).
% 0.42/0.62 tff(122,plain,
% 0.42/0.62 (subset(C!7, D!6) | (~((~member(tptp_fun_X_0(D!6, C!7), C!7)) | member(tptp_fun_X_0(D!6, C!7), D!6)))),
% 0.42/0.62 inference(unit_resolution,[status(thm)],[121, 120])).
% 0.42/0.62 tff(123,plain,
% 0.42/0.62 ((~![U: option] : (member(U, C!7) <=> ((U = Y!11) | (U = X!12)))) | (member(tptp_fun_X_0(D!6, C!7), C!7) <=> ((tptp_fun_X_0(D!6, C!7) = Y!11) | (tptp_fun_X_0(D!6, C!7) = X!12)))),
% 0.42/0.62 inference(quant_inst,[status(thm)],[])).
% 0.42/0.62 tff(124,plain,
% 0.42/0.62 (member(tptp_fun_X_0(D!6, C!7), C!7) <=> ((tptp_fun_X_0(D!6, C!7) = Y!11) | (tptp_fun_X_0(D!6, C!7) = X!12))),
% 0.42/0.62 inference(unit_resolution,[status(thm)],[123, 21])).
% 0.42/0.62 tff(125,assumption,(~((~member(tptp_fun_X_0(D!6, C!7), C!7)) | member(tptp_fun_X_0(D!6, C!7), D!6))), introduced(assumption)).
% 0.42/0.62 tff(126,plain,
% 0.42/0.62 (((~member(tptp_fun_X_0(D!6, C!7), C!7)) | member(tptp_fun_X_0(D!6, C!7), D!6)) | member(tptp_fun_X_0(D!6, C!7), C!7)),
% 0.42/0.62 inference(tautology,[status(thm)],[])).
% 0.42/0.62 tff(127,plain,
% 0.42/0.62 (member(tptp_fun_X_0(D!6, C!7), C!7)),
% 0.42/0.62 inference(unit_resolution,[status(thm)],[126, 125])).
% 0.42/0.62 tff(128,plain,
% 0.42/0.62 ((~(member(tptp_fun_X_0(D!6, C!7), C!7) <=> ((tptp_fun_X_0(D!6, C!7) = Y!11) | (tptp_fun_X_0(D!6, C!7) = X!12)))) | (~member(tptp_fun_X_0(D!6, C!7), C!7)) | ((tptp_fun_X_0(D!6, C!7) = Y!11) | (tptp_fun_X_0(D!6, C!7) = X!12))),
% 0.42/0.62 inference(tautology,[status(thm)],[])).
% 0.42/0.62 tff(129,plain,
% 0.42/0.62 ((~(member(tptp_fun_X_0(D!6, C!7), C!7) <=> ((tptp_fun_X_0(D!6, C!7) = Y!11) | (tptp_fun_X_0(D!6, C!7) = X!12)))) | ((tptp_fun_X_0(D!6, C!7) = Y!11) | (tptp_fun_X_0(D!6, C!7) = X!12))),
% 0.42/0.62 inference(unit_resolution,[status(thm)],[128, 127])).
% 0.42/0.62 tff(130,plain,
% 0.42/0.62 ((tptp_fun_X_0(D!6, C!7) = Y!11) | (tptp_fun_X_0(D!6, C!7) = X!12)),
% 0.42/0.62 inference(unit_resolution,[status(thm)],[129, 124])).
% 0.42/0.62 tff(131,plain,
% 0.42/0.62 (^[U: option] : refl((member(U, D!6) <=> ((U = Z!10) | (U = Y!11) | (U = X!12))) <=> (member(U, D!6) <=> ((U = Z!10) | (U = Y!11) | (U = X!12))))),
% 0.42/0.62 inference(bind,[status(th)],[])).
% 0.42/0.62 tff(132,plain,
% 0.42/0.62 (![U: option] : (member(U, D!6) <=> ((U = Z!10) | (U = Y!11) | (U = X!12))) <=> ![U: option] : (member(U, D!6) <=> ((U = Z!10) | (U = Y!11) | (U = X!12)))),
% 0.42/0.62 inference(quant_intro,[status(thm)],[131])).
% 0.42/0.62 tff(133,plain,
% 0.42/0.62 (![U: option] : (member(U, D!6) <=> ((U = Z!10) | (U = Y!11) | (U = X!12)))),
% 0.42/0.62 inference(and_elim,[status(thm)],[11])).
% 0.42/0.62 tff(134,plain,
% 0.42/0.62 (![U: option] : (member(U, D!6) <=> ((U = Z!10) | (U = Y!11) | (U = X!12)))),
% 0.42/0.62 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.42/0.62 tff(135,plain,
% 0.42/0.62 ((~![U: option] : (member(U, D!6) <=> ((U = Z!10) | (U = Y!11) | (U = X!12)))) | (member(tptp_fun_X_0(D!6, C!7), D!6) <=> ((tptp_fun_X_0(D!6, C!7) = Z!10) | (tptp_fun_X_0(D!6, C!7) = Y!11) | (tptp_fun_X_0(D!6, C!7) = X!12)))),
% 0.42/0.62 inference(quant_inst,[status(thm)],[])).
% 0.42/0.62 tff(136,plain,
% 0.42/0.62 (member(tptp_fun_X_0(D!6, C!7), D!6) <=> ((tptp_fun_X_0(D!6, C!7) = Z!10) | (tptp_fun_X_0(D!6, C!7) = Y!11) | (tptp_fun_X_0(D!6, C!7) = X!12))),
% 0.42/0.62 inference(unit_resolution,[status(thm)],[135, 134])).
% 0.42/0.62 tff(137,plain,
% 0.42/0.62 (((~member(tptp_fun_X_0(D!6, C!7), C!7)) | member(tptp_fun_X_0(D!6, C!7), D!6)) | (~member(tptp_fun_X_0(D!6, C!7), D!6))),
% 0.42/0.62 inference(tautology,[status(thm)],[])).
% 0.42/0.62 tff(138,plain,
% 0.42/0.62 (~member(tptp_fun_X_0(D!6, C!7), D!6)),
% 0.42/0.62 inference(unit_resolution,[status(thm)],[137, 125])).
% 0.42/0.62 tff(139,plain,
% 0.42/0.62 ((~(member(tptp_fun_X_0(D!6, C!7), D!6) <=> ((tptp_fun_X_0(D!6, C!7) = Z!10) | (tptp_fun_X_0(D!6, C!7) = Y!11) | (tptp_fun_X_0(D!6, C!7) = X!12)))) | member(tptp_fun_X_0(D!6, C!7), D!6) | (~((tptp_fun_X_0(D!6, C!7) = Z!10) | (tptp_fun_X_0(D!6, C!7) = Y!11) | (tptp_fun_X_0(D!6, C!7) = X!12)))),
% 0.42/0.62 inference(tautology,[status(thm)],[])).
% 0.42/0.62 tff(140,plain,
% 0.42/0.62 ((~(member(tptp_fun_X_0(D!6, C!7), D!6) <=> ((tptp_fun_X_0(D!6, C!7) = Z!10) | (tptp_fun_X_0(D!6, C!7) = Y!11) | (tptp_fun_X_0(D!6, C!7) = X!12)))) | (~((tptp_fun_X_0(D!6, C!7) = Z!10) | (tptp_fun_X_0(D!6, C!7) = Y!11) | (tptp_fun_X_0(D!6, C!7) = X!12)))),
% 0.42/0.62 inference(unit_resolution,[status(thm)],[139, 138])).
% 0.42/0.62 tff(141,plain,
% 0.42/0.62 (~((tptp_fun_X_0(D!6, C!7) = Z!10) | (tptp_fun_X_0(D!6, C!7) = Y!11) | (tptp_fun_X_0(D!6, C!7) = X!12))),
% 0.42/0.62 inference(unit_resolution,[status(thm)],[140, 136])).
% 0.42/0.62 tff(142,plain,
% 0.42/0.62 (((tptp_fun_X_0(D!6, C!7) = Z!10) | (tptp_fun_X_0(D!6, C!7) = Y!11) | (tptp_fun_X_0(D!6, C!7) = X!12)) | (~(tptp_fun_X_0(D!6, C!7) = Y!11))),
% 0.42/0.62 inference(tautology,[status(thm)],[])).
% 0.42/0.62 tff(143,plain,
% 0.42/0.62 (~(tptp_fun_X_0(D!6, C!7) = Y!11)),
% 0.42/0.62 inference(unit_resolution,[status(thm)],[142, 141])).
% 0.42/0.62 tff(144,plain,
% 0.42/0.62 (((tptp_fun_X_0(D!6, C!7) = Z!10) | (tptp_fun_X_0(D!6, C!7) = Y!11) | (tptp_fun_X_0(D!6, C!7) = X!12)) | (~(tptp_fun_X_0(D!6, C!7) = X!12))),
% 0.42/0.62 inference(tautology,[status(thm)],[])).
% 0.42/0.62 tff(145,plain,
% 0.42/0.62 (~(tptp_fun_X_0(D!6, C!7) = X!12)),
% 0.42/0.62 inference(unit_resolution,[status(thm)],[144, 141])).
% 0.42/0.62 tff(146,plain,
% 0.42/0.62 ((~((tptp_fun_X_0(D!6, C!7) = Y!11) | (tptp_fun_X_0(D!6, C!7) = X!12))) | (tptp_fun_X_0(D!6, C!7) = Y!11) | (tptp_fun_X_0(D!6, C!7) = X!12)),
% 0.42/0.62 inference(tautology,[status(thm)],[])).
% 0.42/0.62 tff(147,plain,
% 0.42/0.62 ($false),
% 0.42/0.62 inference(unit_resolution,[status(thm)],[146, 145, 143, 130])).
% 0.42/0.62 tff(148,plain,((~member(tptp_fun_X_0(D!6, C!7), C!7)) | member(tptp_fun_X_0(D!6, C!7), D!6)), inference(lemma,lemma(discharge,[]))).
% 0.42/0.62 tff(149,plain,
% 0.42/0.62 ((~(subset(C!7, D!6) | (~((~member(tptp_fun_X_0(D!6, C!7), C!7)) | member(tptp_fun_X_0(D!6, C!7), D!6))))) | subset(C!7, D!6) | (~((~member(tptp_fun_X_0(D!6, C!7), C!7)) | member(tptp_fun_X_0(D!6, C!7), D!6)))),
% 0.42/0.62 inference(tautology,[status(thm)],[])).
% 0.42/0.62 tff(150,plain,
% 0.42/0.62 ((~(subset(C!7, D!6) | (~((~member(tptp_fun_X_0(D!6, C!7), C!7)) | member(tptp_fun_X_0(D!6, C!7), D!6))))) | subset(C!7, D!6)),
% 0.42/0.62 inference(unit_resolution,[status(thm)],[149, 148])).
% 0.42/0.62 tff(151,plain,
% 0.42/0.62 (subset(C!7, D!6)),
% 0.42/0.62 inference(unit_resolution,[status(thm)],[150, 122])).
% 0.42/0.62 tff(152,plain,
% 0.42/0.62 (^[X: option_set, Y: option_set] : refl(((~subset(X, Y)) | weakly_better(Y, X)) <=> ((~subset(X, Y)) | weakly_better(Y, X)))),
% 0.42/0.62 inference(bind,[status(th)],[])).
% 0.42/0.62 tff(153,plain,
% 0.42/0.62 (![X: option_set, Y: option_set] : ((~subset(X, Y)) | weakly_better(Y, X)) <=> ![X: option_set, Y: option_set] : ((~subset(X, Y)) | weakly_better(Y, X))),
% 0.42/0.62 inference(quant_intro,[status(thm)],[152])).
% 0.42/0.62 tff(154,plain,
% 0.42/0.62 (![X: option_set, Y: option_set] : ((~subset(X, Y)) | weakly_better(Y, X)) <=> ![X: option_set, Y: option_set] : ((~subset(X, Y)) | weakly_better(Y, X))),
% 0.42/0.62 inference(rewrite,[status(thm)],[])).
% 0.42/0.62 tff(155,plain,
% 0.42/0.62 (^[X: option_set, Y: option_set] : rewrite((subset(X, Y) => weakly_better(Y, X)) <=> ((~subset(X, Y)) | weakly_better(Y, X)))),
% 0.42/0.62 inference(bind,[status(th)],[])).
% 0.42/0.62 tff(156,plain,
% 0.42/0.62 (![X: option_set, Y: option_set] : (subset(X, Y) => weakly_better(Y, X)) <=> ![X: option_set, Y: option_set] : ((~subset(X, Y)) | weakly_better(Y, X))),
% 0.42/0.62 inference(quant_intro,[status(thm)],[155])).
% 0.42/0.62 tff(157,axiom,(![X: option_set, Y: option_set] : (subset(X, Y) => weakly_better(Y, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','harmlessness_of_expansions')).
% 0.42/0.62 tff(158,plain,
% 0.42/0.62 (![X: option_set, Y: option_set] : ((~subset(X, Y)) | weakly_better(Y, X))),
% 0.42/0.62 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.42/0.62 tff(159,plain,
% 0.42/0.62 (![X: option_set, Y: option_set] : ((~subset(X, Y)) | weakly_better(Y, X))),
% 0.42/0.62 inference(modus_ponens,[status(thm)],[158, 154])).
% 0.42/0.62 tff(160,plain,(
% 0.42/0.62 ![X: option_set, Y: option_set] : ((~subset(X, Y)) | weakly_better(Y, X))),
% 0.42/0.62 inference(skolemize,[status(sab)],[159])).
% 0.42/0.62 tff(161,plain,
% 0.42/0.62 (![X: option_set, Y: option_set] : ((~subset(X, Y)) | weakly_better(Y, X))),
% 0.42/0.62 inference(modus_ponens,[status(thm)],[160, 153])).
% 0.42/0.62 tff(162,plain,
% 0.42/0.62 (((~![X: option_set, Y: option_set] : ((~subset(X, Y)) | weakly_better(Y, X))) | ((~subset(C!7, D!6)) | weakly_better(D!6, C!7))) <=> ((~![X: option_set, Y: option_set] : ((~subset(X, Y)) | weakly_better(Y, X))) | (~subset(C!7, D!6)) | weakly_better(D!6, C!7))),
% 0.42/0.62 inference(rewrite,[status(thm)],[])).
% 0.42/0.62 tff(163,plain,
% 0.42/0.62 ((~![X: option_set, Y: option_set] : ((~subset(X, Y)) | weakly_better(Y, X))) | ((~subset(C!7, D!6)) | weakly_better(D!6, C!7))),
% 0.42/0.62 inference(quant_inst,[status(thm)],[])).
% 0.42/0.62 tff(164,plain,
% 0.42/0.62 ((~![X: option_set, Y: option_set] : ((~subset(X, Y)) | weakly_better(Y, X))) | (~subset(C!7, D!6)) | weakly_better(D!6, C!7)),
% 0.42/0.62 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.42/0.62 tff(165,plain,
% 0.42/0.62 ($false),
% 0.42/0.62 inference(unit_resolution,[status(thm)],[164, 161, 151, 100])).
% 0.42/0.62 tff(166,plain,(weakly_better(D!6, C!7)), inference(lemma,lemma(discharge,[]))).
% 0.42/0.62 tff(167,assumption,(weakly_better(A!9, D!6)), introduced(assumption)).
% 0.42/0.62 tff(168,plain,
% 0.42/0.62 (![X: option_set, Y: option_set, Z: option_set] : (weakly_better(X, Z) | (~weakly_better(Y, Z)) | (~weakly_better(X, Y))) <=> ![X: option_set, Y: option_set, Z: option_set] : (weakly_better(X, Z) | (~weakly_better(Y, Z)) | (~weakly_better(X, Y)))),
% 0.42/0.62 inference(rewrite,[status(thm)],[])).
% 0.42/0.62 tff(169,plain,
% 0.42/0.62 (^[X: option_set, Y: option_set, Z: option_set] : trans(monotonicity(trans(monotonicity(rewrite((weakly_better(X, Y) & weakly_better(Y, Z)) <=> (~((~weakly_better(Y, Z)) | (~weakly_better(X, Y))))), ((~(weakly_better(X, Y) & weakly_better(Y, Z))) <=> (~(~((~weakly_better(Y, Z)) | (~weakly_better(X, Y))))))), rewrite((~(~((~weakly_better(Y, Z)) | (~weakly_better(X, Y))))) <=> ((~weakly_better(Y, Z)) | (~weakly_better(X, Y)))), ((~(weakly_better(X, Y) & weakly_better(Y, Z))) <=> ((~weakly_better(Y, Z)) | (~weakly_better(X, Y))))), (((~(weakly_better(X, Y) & weakly_better(Y, Z))) | weakly_better(X, Z)) <=> (((~weakly_better(Y, Z)) | (~weakly_better(X, Y))) | weakly_better(X, Z)))), rewrite((((~weakly_better(Y, Z)) | (~weakly_better(X, Y))) | weakly_better(X, Z)) <=> (weakly_better(X, Z) | (~weakly_better(Y, Z)) | (~weakly_better(X, Y)))), (((~(weakly_better(X, Y) & weakly_better(Y, Z))) | weakly_better(X, Z)) <=> (weakly_better(X, Z) | (~weakly_better(Y, Z)) | (~weakly_better(X, Y)))))),
% 0.42/0.62 inference(bind,[status(th)],[])).
% 0.42/0.62 tff(170,plain,
% 0.42/0.62 (![X: option_set, Y: option_set, Z: option_set] : ((~(weakly_better(X, Y) & weakly_better(Y, Z))) | weakly_better(X, Z)) <=> ![X: option_set, Y: option_set, Z: option_set] : (weakly_better(X, Z) | (~weakly_better(Y, Z)) | (~weakly_better(X, Y)))),
% 0.42/0.62 inference(quant_intro,[status(thm)],[169])).
% 0.42/0.62 tff(171,plain,
% 0.42/0.62 (![X: option_set, Y: option_set, Z: option_set] : ((~(weakly_better(X, Y) & weakly_better(Y, Z))) | weakly_better(X, Z)) <=> ![X: option_set, Y: option_set, Z: option_set] : ((~(weakly_better(X, Y) & weakly_better(Y, Z))) | weakly_better(X, Z))),
% 0.46/0.63 inference(rewrite,[status(thm)],[])).
% 0.46/0.63 tff(172,plain,
% 0.46/0.63 (^[X: option_set, Y: option_set, Z: option_set] : rewrite(((weakly_better(X, Y) & weakly_better(Y, Z)) => weakly_better(X, Z)) <=> ((~(weakly_better(X, Y) & weakly_better(Y, Z))) | weakly_better(X, Z)))),
% 0.46/0.63 inference(bind,[status(th)],[])).
% 0.46/0.63 tff(173,plain,
% 0.46/0.63 (![X: option_set, Y: option_set, Z: option_set] : ((weakly_better(X, Y) & weakly_better(Y, Z)) => weakly_better(X, Z)) <=> ![X: option_set, Y: option_set, Z: option_set] : ((~(weakly_better(X, Y) & weakly_better(Y, Z))) | weakly_better(X, Z))),
% 0.46/0.63 inference(quant_intro,[status(thm)],[172])).
% 0.46/0.63 tff(174,axiom,(![X: option_set, Y: option_set, Z: option_set] : ((weakly_better(X, Y) & weakly_better(Y, Z)) => weakly_better(X, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','transitivity_of_weakly_better_freedom_of_choice')).
% 0.46/0.63 tff(175,plain,
% 0.46/0.63 (![X: option_set, Y: option_set, Z: option_set] : ((~(weakly_better(X, Y) & weakly_better(Y, Z))) | weakly_better(X, Z))),
% 0.46/0.63 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.46/0.63 tff(176,plain,
% 0.46/0.63 (![X: option_set, Y: option_set, Z: option_set] : ((~(weakly_better(X, Y) & weakly_better(Y, Z))) | weakly_better(X, Z))),
% 0.46/0.63 inference(modus_ponens,[status(thm)],[175, 171])).
% 0.46/0.63 tff(177,plain,(
% 0.46/0.63 ![X: option_set, Y: option_set, Z: option_set] : ((~(weakly_better(X, Y) & weakly_better(Y, Z))) | weakly_better(X, Z))),
% 0.46/0.63 inference(skolemize,[status(sab)],[176])).
% 0.46/0.63 tff(178,plain,
% 0.46/0.63 (![X: option_set, Y: option_set, Z: option_set] : (weakly_better(X, Z) | (~weakly_better(Y, Z)) | (~weakly_better(X, Y)))),
% 0.46/0.63 inference(modus_ponens,[status(thm)],[177, 170])).
% 0.46/0.63 tff(179,plain,
% 0.46/0.63 (![X: option_set, Y: option_set, Z: option_set] : (weakly_better(X, Z) | (~weakly_better(Y, Z)) | (~weakly_better(X, Y)))),
% 0.46/0.63 inference(modus_ponens,[status(thm)],[178, 168])).
% 0.46/0.63 tff(180,plain,
% 0.46/0.63 (((~![X: option_set, Y: option_set, Z: option_set] : (weakly_better(X, Z) | (~weakly_better(Y, Z)) | (~weakly_better(X, Y)))) | ((~weakly_better(A!9, D!6)) | (~weakly_better(D!6, C!7)) | weakly_better(A!9, C!7))) <=> ((~![X: option_set, Y: option_set, Z: option_set] : (weakly_better(X, Z) | (~weakly_better(Y, Z)) | (~weakly_better(X, Y)))) | (~weakly_better(A!9, D!6)) | (~weakly_better(D!6, C!7)) | weakly_better(A!9, C!7))),
% 0.46/0.63 inference(rewrite,[status(thm)],[])).
% 0.46/0.63 tff(181,plain,
% 0.46/0.63 ((weakly_better(A!9, C!7) | (~weakly_better(D!6, C!7)) | (~weakly_better(A!9, D!6))) <=> ((~weakly_better(A!9, D!6)) | (~weakly_better(D!6, C!7)) | weakly_better(A!9, C!7))),
% 0.46/0.63 inference(rewrite,[status(thm)],[])).
% 0.46/0.63 tff(182,plain,
% 0.46/0.63 (((~![X: option_set, Y: option_set, Z: option_set] : (weakly_better(X, Z) | (~weakly_better(Y, Z)) | (~weakly_better(X, Y)))) | (weakly_better(A!9, C!7) | (~weakly_better(D!6, C!7)) | (~weakly_better(A!9, D!6)))) <=> ((~![X: option_set, Y: option_set, Z: option_set] : (weakly_better(X, Z) | (~weakly_better(Y, Z)) | (~weakly_better(X, Y)))) | ((~weakly_better(A!9, D!6)) | (~weakly_better(D!6, C!7)) | weakly_better(A!9, C!7)))),
% 0.46/0.63 inference(monotonicity,[status(thm)],[181])).
% 0.46/0.63 tff(183,plain,
% 0.46/0.63 (((~![X: option_set, Y: option_set, Z: option_set] : (weakly_better(X, Z) | (~weakly_better(Y, Z)) | (~weakly_better(X, Y)))) | (weakly_better(A!9, C!7) | (~weakly_better(D!6, C!7)) | (~weakly_better(A!9, D!6)))) <=> ((~![X: option_set, Y: option_set, Z: option_set] : (weakly_better(X, Z) | (~weakly_better(Y, Z)) | (~weakly_better(X, Y)))) | (~weakly_better(A!9, D!6)) | (~weakly_better(D!6, C!7)) | weakly_better(A!9, C!7))),
% 0.46/0.63 inference(transitivity,[status(thm)],[182, 180])).
% 0.46/0.63 tff(184,plain,
% 0.46/0.63 ((~![X: option_set, Y: option_set, Z: option_set] : (weakly_better(X, Z) | (~weakly_better(Y, Z)) | (~weakly_better(X, Y)))) | (weakly_better(A!9, C!7) | (~weakly_better(D!6, C!7)) | (~weakly_better(A!9, D!6)))),
% 0.46/0.63 inference(quant_inst,[status(thm)],[])).
% 0.46/0.63 tff(185,plain,
% 0.46/0.63 ((~![X: option_set, Y: option_set, Z: option_set] : (weakly_better(X, Z) | (~weakly_better(Y, Z)) | (~weakly_better(X, Y)))) | (~weakly_better(A!9, D!6)) | (~weakly_better(D!6, C!7)) | weakly_better(A!9, C!7)),
% 0.46/0.63 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.46/0.63 tff(186,plain,
% 0.46/0.63 ($false),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[185, 179, 167, 166, 99])).
% 0.46/0.63 tff(187,plain,(~weakly_better(A!9, D!6)), inference(lemma,lemma(discharge,[]))).
% 0.46/0.63 tff(188,assumption,(weakly_better(A!9, B!8)), introduced(assumption)).
% 0.46/0.63 tff(189,plain,
% 0.46/0.63 ((~![U: option] : (member(U, D!6) <=> ((U = Z!10) | (U = Y!11) | (U = X!12)))) | (member(tptp_fun_V_3(Z!10, D!6, B!8), D!6) <=> ((tptp_fun_V_3(Z!10, D!6, B!8) = Z!10) | (tptp_fun_V_3(Z!10, D!6, B!8) = Y!11) | (tptp_fun_V_3(Z!10, D!6, B!8) = X!12)))),
% 0.46/0.63 inference(quant_inst,[status(thm)],[])).
% 0.46/0.63 tff(190,plain,
% 0.46/0.63 (member(tptp_fun_V_3(Z!10, D!6, B!8), D!6) <=> ((tptp_fun_V_3(Z!10, D!6, B!8) = Z!10) | (tptp_fun_V_3(Z!10, D!6, B!8) = Y!11) | (tptp_fun_V_3(Z!10, D!6, B!8) = X!12))),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[189, 134])).
% 0.46/0.63 tff(191,assumption,(~((~member(tptp_fun_V_3(Z!10, D!6, B!8), D!6)) | member(tptp_fun_V_3(Z!10, D!6, B!8), B!8) | required_preference(Z!10, tptp_fun_V_3(Z!10, D!6, B!8)))), introduced(assumption)).
% 0.46/0.63 tff(192,plain,
% 0.46/0.63 (((~member(tptp_fun_V_3(Z!10, D!6, B!8), D!6)) | member(tptp_fun_V_3(Z!10, D!6, B!8), B!8) | required_preference(Z!10, tptp_fun_V_3(Z!10, D!6, B!8))) | member(tptp_fun_V_3(Z!10, D!6, B!8), D!6)),
% 0.46/0.63 inference(tautology,[status(thm)],[])).
% 0.46/0.63 tff(193,plain,
% 0.46/0.63 (member(tptp_fun_V_3(Z!10, D!6, B!8), D!6)),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[192, 191])).
% 0.46/0.63 tff(194,plain,
% 0.46/0.63 ((~(member(tptp_fun_V_3(Z!10, D!6, B!8), D!6) <=> ((tptp_fun_V_3(Z!10, D!6, B!8) = Z!10) | (tptp_fun_V_3(Z!10, D!6, B!8) = Y!11) | (tptp_fun_V_3(Z!10, D!6, B!8) = X!12)))) | (~member(tptp_fun_V_3(Z!10, D!6, B!8), D!6)) | ((tptp_fun_V_3(Z!10, D!6, B!8) = Z!10) | (tptp_fun_V_3(Z!10, D!6, B!8) = Y!11) | (tptp_fun_V_3(Z!10, D!6, B!8) = X!12))),
% 0.46/0.63 inference(tautology,[status(thm)],[])).
% 0.46/0.63 tff(195,plain,
% 0.46/0.63 ((~(member(tptp_fun_V_3(Z!10, D!6, B!8), D!6) <=> ((tptp_fun_V_3(Z!10, D!6, B!8) = Z!10) | (tptp_fun_V_3(Z!10, D!6, B!8) = Y!11) | (tptp_fun_V_3(Z!10, D!6, B!8) = X!12)))) | ((tptp_fun_V_3(Z!10, D!6, B!8) = Z!10) | (tptp_fun_V_3(Z!10, D!6, B!8) = Y!11) | (tptp_fun_V_3(Z!10, D!6, B!8) = X!12))),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[194, 193])).
% 0.46/0.63 tff(196,plain,
% 0.46/0.63 ((tptp_fun_V_3(Z!10, D!6, B!8) = Z!10) | (tptp_fun_V_3(Z!10, D!6, B!8) = Y!11) | (tptp_fun_V_3(Z!10, D!6, B!8) = X!12)),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[195, 190])).
% 0.46/0.63 tff(197,plain,
% 0.46/0.63 (^[U: option] : refl((member(U, B!8) <=> (U = Z!10)) <=> (member(U, B!8) <=> (U = Z!10)))),
% 0.46/0.63 inference(bind,[status(th)],[])).
% 0.46/0.63 tff(198,plain,
% 0.46/0.63 (![U: option] : (member(U, B!8) <=> (U = Z!10)) <=> ![U: option] : (member(U, B!8) <=> (U = Z!10))),
% 0.46/0.63 inference(quant_intro,[status(thm)],[197])).
% 0.46/0.63 tff(199,plain,
% 0.46/0.63 (![U: option] : (member(U, B!8) <=> (U = Z!10))),
% 0.46/0.63 inference(and_elim,[status(thm)],[11])).
% 0.46/0.63 tff(200,plain,
% 0.46/0.63 (![U: option] : (member(U, B!8) <=> (U = Z!10))),
% 0.46/0.63 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.46/0.63 tff(201,plain,
% 0.46/0.63 ((~![U: option] : (member(U, B!8) <=> (U = Z!10))) | (member(tptp_fun_V_3(Z!10, D!6, B!8), B!8) <=> (tptp_fun_V_3(Z!10, D!6, B!8) = Z!10))),
% 0.46/0.63 inference(quant_inst,[status(thm)],[])).
% 0.46/0.63 tff(202,plain,
% 0.46/0.63 (member(tptp_fun_V_3(Z!10, D!6, B!8), B!8) <=> (tptp_fun_V_3(Z!10, D!6, B!8) = Z!10)),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[201, 200])).
% 0.46/0.63 tff(203,plain,
% 0.46/0.63 (((~member(tptp_fun_V_3(Z!10, D!6, B!8), D!6)) | member(tptp_fun_V_3(Z!10, D!6, B!8), B!8) | required_preference(Z!10, tptp_fun_V_3(Z!10, D!6, B!8))) | (~member(tptp_fun_V_3(Z!10, D!6, B!8), B!8))),
% 0.46/0.63 inference(tautology,[status(thm)],[])).
% 0.46/0.63 tff(204,plain,
% 0.46/0.63 (~member(tptp_fun_V_3(Z!10, D!6, B!8), B!8)),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[203, 191])).
% 0.46/0.63 tff(205,plain,
% 0.46/0.63 ((~(member(tptp_fun_V_3(Z!10, D!6, B!8), B!8) <=> (tptp_fun_V_3(Z!10, D!6, B!8) = Z!10))) | member(tptp_fun_V_3(Z!10, D!6, B!8), B!8) | (~(tptp_fun_V_3(Z!10, D!6, B!8) = Z!10))),
% 0.46/0.63 inference(tautology,[status(thm)],[])).
% 0.46/0.63 tff(206,plain,
% 0.46/0.63 ((~(member(tptp_fun_V_3(Z!10, D!6, B!8), B!8) <=> (tptp_fun_V_3(Z!10, D!6, B!8) = Z!10))) | (~(tptp_fun_V_3(Z!10, D!6, B!8) = Z!10))),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[205, 204])).
% 0.46/0.63 tff(207,plain,
% 0.46/0.63 (~(tptp_fun_V_3(Z!10, D!6, B!8) = Z!10)),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[206, 202])).
% 0.46/0.63 tff(208,plain,
% 0.46/0.63 (((~member(tptp_fun_V_3(Z!10, D!6, B!8), D!6)) | member(tptp_fun_V_3(Z!10, D!6, B!8), B!8) | required_preference(Z!10, tptp_fun_V_3(Z!10, D!6, B!8))) | (~required_preference(Z!10, tptp_fun_V_3(Z!10, D!6, B!8)))),
% 0.46/0.63 inference(tautology,[status(thm)],[])).
% 0.46/0.63 tff(209,plain,
% 0.46/0.63 (~required_preference(Z!10, tptp_fun_V_3(Z!10, D!6, B!8))),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[208, 191])).
% 0.46/0.63 tff(210,assumption,(tptp_fun_V_3(Z!10, D!6, B!8) = Y!11), introduced(assumption)).
% 0.46/0.63 tff(211,plain,
% 0.46/0.63 (required_preference(Z!10, tptp_fun_V_3(Z!10, D!6, B!8)) <=> required_preference(Z!10, Y!11)),
% 0.46/0.63 inference(monotonicity,[status(thm)],[210])).
% 0.46/0.63 tff(212,plain,
% 0.46/0.63 (required_preference(Z!10, Y!11) <=> required_preference(Z!10, tptp_fun_V_3(Z!10, D!6, B!8))),
% 0.46/0.63 inference(symmetry,[status(thm)],[211])).
% 0.46/0.63 tff(213,plain,
% 0.46/0.63 (required_preference(Z!10, Y!11)),
% 0.46/0.63 inference(and_elim,[status(thm)],[11])).
% 0.46/0.63 tff(214,plain,
% 0.46/0.63 (required_preference(Z!10, tptp_fun_V_3(Z!10, D!6, B!8))),
% 0.46/0.63 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.46/0.63 tff(215,assumption,(~required_preference(Z!10, tptp_fun_V_3(Z!10, D!6, B!8))), introduced(assumption)).
% 0.46/0.63 tff(216,plain,
% 0.46/0.63 ($false),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[215, 214])).
% 0.46/0.63 tff(217,plain,((~(tptp_fun_V_3(Z!10, D!6, B!8) = Y!11)) | required_preference(Z!10, tptp_fun_V_3(Z!10, D!6, B!8))), inference(lemma,lemma(discharge,[]))).
% 0.46/0.63 tff(218,plain,
% 0.46/0.63 (~(tptp_fun_V_3(Z!10, D!6, B!8) = Y!11)),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[217, 209])).
% 0.46/0.63 tff(219,plain,
% 0.46/0.63 ((~((tptp_fun_V_3(Z!10, D!6, B!8) = Z!10) | (tptp_fun_V_3(Z!10, D!6, B!8) = Y!11) | (tptp_fun_V_3(Z!10, D!6, B!8) = X!12))) | (tptp_fun_V_3(Z!10, D!6, B!8) = Z!10) | (tptp_fun_V_3(Z!10, D!6, B!8) = Y!11) | (tptp_fun_V_3(Z!10, D!6, B!8) = X!12)),
% 0.46/0.63 inference(tautology,[status(thm)],[])).
% 0.46/0.63 tff(220,plain,
% 0.46/0.63 (tptp_fun_V_3(Z!10, D!6, B!8) = X!12),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[219, 218, 207, 196])).
% 0.46/0.63 tff(221,plain,
% 0.46/0.63 (required_preference(Z!10, tptp_fun_V_3(Z!10, D!6, B!8)) <=> required_preference(Z!10, X!12)),
% 0.46/0.63 inference(monotonicity,[status(thm)],[220])).
% 0.46/0.63 tff(222,plain,
% 0.46/0.63 (required_preference(Z!10, X!12) <=> required_preference(Z!10, tptp_fun_V_3(Z!10, D!6, B!8))),
% 0.46/0.63 inference(symmetry,[status(thm)],[221])).
% 0.46/0.63 tff(223,plain,
% 0.46/0.63 (required_preference(Z!10, X!12)),
% 0.46/0.63 inference(and_elim,[status(thm)],[11])).
% 0.46/0.63 tff(224,plain,
% 0.46/0.63 (required_preference(Z!10, tptp_fun_V_3(Z!10, D!6, B!8))),
% 0.46/0.63 inference(modus_ponens,[status(thm)],[223, 222])).
% 0.46/0.63 tff(225,plain,
% 0.46/0.63 ($false),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[209, 224])).
% 0.46/0.63 tff(226,plain,((~member(tptp_fun_V_3(Z!10, D!6, B!8), D!6)) | member(tptp_fun_V_3(Z!10, D!6, B!8), B!8) | required_preference(Z!10, tptp_fun_V_3(Z!10, D!6, B!8))), inference(lemma,lemma(discharge,[]))).
% 0.46/0.63 tff(227,assumption,(![U: option] : ((~member(U, B!8)) | (~(member(tptp_fun_V_3(U, D!6, B!8), B!8) | required_preference(U, tptp_fun_V_3(U, D!6, B!8)) | (~member(tptp_fun_V_3(U, D!6, B!8), D!6)))))), introduced(assumption)).
% 0.46/0.63 tff(228,plain,
% 0.46/0.63 (member(Z!10, B!8)),
% 0.46/0.63 inference(and_elim,[status(thm)],[11])).
% 0.46/0.63 tff(229,plain,
% 0.46/0.63 (((~![U: option] : ((~member(U, B!8)) | (~(member(tptp_fun_V_3(U, D!6, B!8), B!8) | required_preference(U, tptp_fun_V_3(U, D!6, B!8)) | (~member(tptp_fun_V_3(U, D!6, B!8), D!6)))))) | ((~member(Z!10, B!8)) | (~((~member(tptp_fun_V_3(Z!10, D!6, B!8), D!6)) | member(tptp_fun_V_3(Z!10, D!6, B!8), B!8) | required_preference(Z!10, tptp_fun_V_3(Z!10, D!6, B!8)))))) <=> ((~![U: option] : ((~member(U, B!8)) | (~(member(tptp_fun_V_3(U, D!6, B!8), B!8) | required_preference(U, tptp_fun_V_3(U, D!6, B!8)) | (~member(tptp_fun_V_3(U, D!6, B!8), D!6)))))) | (~member(Z!10, B!8)) | (~((~member(tptp_fun_V_3(Z!10, D!6, B!8), D!6)) | member(tptp_fun_V_3(Z!10, D!6, B!8), B!8) | required_preference(Z!10, tptp_fun_V_3(Z!10, D!6, B!8)))))),
% 0.46/0.64 inference(rewrite,[status(thm)],[])).
% 0.46/0.64 tff(230,plain,
% 0.46/0.64 (((~member(Z!10, B!8)) | (~(member(tptp_fun_V_3(Z!10, D!6, B!8), B!8) | required_preference(Z!10, tptp_fun_V_3(Z!10, D!6, B!8)) | (~member(tptp_fun_V_3(Z!10, D!6, B!8), D!6))))) <=> ((~member(Z!10, B!8)) | (~((~member(tptp_fun_V_3(Z!10, D!6, B!8), D!6)) | member(tptp_fun_V_3(Z!10, D!6, B!8), B!8) | required_preference(Z!10, tptp_fun_V_3(Z!10, D!6, B!8)))))),
% 0.46/0.64 inference(rewrite,[status(thm)],[])).
% 0.46/0.64 tff(231,plain,
% 0.46/0.64 (((~![U: option] : ((~member(U, B!8)) | (~(member(tptp_fun_V_3(U, D!6, B!8), B!8) | required_preference(U, tptp_fun_V_3(U, D!6, B!8)) | (~member(tptp_fun_V_3(U, D!6, B!8), D!6)))))) | ((~member(Z!10, B!8)) | (~(member(tptp_fun_V_3(Z!10, D!6, B!8), B!8) | required_preference(Z!10, tptp_fun_V_3(Z!10, D!6, B!8)) | (~member(tptp_fun_V_3(Z!10, D!6, B!8), D!6)))))) <=> ((~![U: option] : ((~member(U, B!8)) | (~(member(tptp_fun_V_3(U, D!6, B!8), B!8) | required_preference(U, tptp_fun_V_3(U, D!6, B!8)) | (~member(tptp_fun_V_3(U, D!6, B!8), D!6)))))) | ((~member(Z!10, B!8)) | (~((~member(tptp_fun_V_3(Z!10, D!6, B!8), D!6)) | member(tptp_fun_V_3(Z!10, D!6, B!8), B!8) | required_preference(Z!10, tptp_fun_V_3(Z!10, D!6, B!8))))))),
% 0.46/0.64 inference(monotonicity,[status(thm)],[230])).
% 0.46/0.64 tff(232,plain,
% 0.46/0.64 (((~![U: option] : ((~member(U, B!8)) | (~(member(tptp_fun_V_3(U, D!6, B!8), B!8) | required_preference(U, tptp_fun_V_3(U, D!6, B!8)) | (~member(tptp_fun_V_3(U, D!6, B!8), D!6)))))) | ((~member(Z!10, B!8)) | (~(member(tptp_fun_V_3(Z!10, D!6, B!8), B!8) | required_preference(Z!10, tptp_fun_V_3(Z!10, D!6, B!8)) | (~member(tptp_fun_V_3(Z!10, D!6, B!8), D!6)))))) <=> ((~![U: option] : ((~member(U, B!8)) | (~(member(tptp_fun_V_3(U, D!6, B!8), B!8) | required_preference(U, tptp_fun_V_3(U, D!6, B!8)) | (~member(tptp_fun_V_3(U, D!6, B!8), D!6)))))) | (~member(Z!10, B!8)) | (~((~member(tptp_fun_V_3(Z!10, D!6, B!8), D!6)) | member(tptp_fun_V_3(Z!10, D!6, B!8), B!8) | required_preference(Z!10, tptp_fun_V_3(Z!10, D!6, B!8)))))),
% 0.46/0.64 inference(transitivity,[status(thm)],[231, 229])).
% 0.46/0.64 tff(233,plain,
% 0.46/0.64 ((~![U: option] : ((~member(U, B!8)) | (~(member(tptp_fun_V_3(U, D!6, B!8), B!8) | required_preference(U, tptp_fun_V_3(U, D!6, B!8)) | (~member(tptp_fun_V_3(U, D!6, B!8), D!6)))))) | ((~member(Z!10, B!8)) | (~(member(tptp_fun_V_3(Z!10, D!6, B!8), B!8) | required_preference(Z!10, tptp_fun_V_3(Z!10, D!6, B!8)) | (~member(tptp_fun_V_3(Z!10, D!6, B!8), D!6)))))),
% 0.46/0.64 inference(quant_inst,[status(thm)],[])).
% 0.46/0.64 tff(234,plain,
% 0.46/0.64 ((~![U: option] : ((~member(U, B!8)) | (~(member(tptp_fun_V_3(U, D!6, B!8), B!8) | required_preference(U, tptp_fun_V_3(U, D!6, B!8)) | (~member(tptp_fun_V_3(U, D!6, B!8), D!6)))))) | (~member(Z!10, B!8)) | (~((~member(tptp_fun_V_3(Z!10, D!6, B!8), D!6)) | member(tptp_fun_V_3(Z!10, D!6, B!8), B!8) | required_preference(Z!10, tptp_fun_V_3(Z!10, D!6, B!8))))),
% 0.46/0.64 inference(modus_ponens,[status(thm)],[233, 232])).
% 0.46/0.64 tff(235,plain,
% 0.46/0.64 ($false),
% 0.46/0.64 inference(unit_resolution,[status(thm)],[234, 228, 227, 226])).
% 0.46/0.64 tff(236,plain,(~![U: option] : ((~member(U, B!8)) | (~(member(tptp_fun_V_3(U, D!6, B!8), B!8) | required_preference(U, tptp_fun_V_3(U, D!6, B!8)) | (~member(tptp_fun_V_3(U, D!6, B!8), D!6)))))), inference(lemma,lemma(discharge,[]))).
% 0.46/0.64 tff(237,assumption,((~((~subset(B!8, D!6)) | ![X: option] : ((~member(X, B!8)) | member(X, D!6)))) | (~(subset(B!8, D!6) | (~((~member(tptp_fun_X_0(D!6, B!8), B!8)) | member(tptp_fun_X_0(D!6, B!8), D!6)))))), introduced(assumption)).
% 0.46/0.64 tff(238,plain,
% 0.46/0.64 ((~![A: option_set, B: option_set] : (~((~((~subset(A, B)) | ![X: option] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(B!8, D!6)) | ![X: option] : ((~member(X, B!8)) | member(X, D!6)))) | (~(subset(B!8, D!6) | (~((~member(tptp_fun_X_0(D!6, B!8), B!8)) | member(tptp_fun_X_0(D!6, B!8), D!6)))))))),
% 0.46/0.64 inference(quant_inst,[status(thm)],[])).
% 0.46/0.64 tff(239,plain,
% 0.46/0.64 ($false),
% 0.46/0.64 inference(unit_resolution,[status(thm)],[238, 117, 237])).
% 0.47/0.64 tff(240,plain,(~((~((~subset(B!8, D!6)) | ![X: option] : ((~member(X, B!8)) | member(X, D!6)))) | (~(subset(B!8, D!6) | (~((~member(tptp_fun_X_0(D!6, B!8), B!8)) | member(tptp_fun_X_0(D!6, B!8), D!6))))))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.64 tff(241,plain,
% 0.47/0.64 (((~((~subset(B!8, D!6)) | ![X: option] : ((~member(X, B!8)) | member(X, D!6)))) | (~(subset(B!8, D!6) | (~((~member(tptp_fun_X_0(D!6, B!8), B!8)) | member(tptp_fun_X_0(D!6, B!8), D!6)))))) | (subset(B!8, D!6) | (~((~member(tptp_fun_X_0(D!6, B!8), B!8)) | member(tptp_fun_X_0(D!6, B!8), D!6))))),
% 0.47/0.64 inference(tautology,[status(thm)],[])).
% 0.47/0.64 tff(242,plain,
% 0.47/0.64 (subset(B!8, D!6) | (~((~member(tptp_fun_X_0(D!6, B!8), B!8)) | member(tptp_fun_X_0(D!6, B!8), D!6)))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[241, 240])).
% 0.47/0.64 tff(243,plain,
% 0.47/0.64 ((~![U: option] : (member(U, D!6) <=> ((U = Z!10) | (U = Y!11) | (U = X!12)))) | (member(tptp_fun_X_0(D!6, B!8), D!6) <=> ((tptp_fun_X_0(D!6, B!8) = Z!10) | (tptp_fun_X_0(D!6, B!8) = Y!11) | (tptp_fun_X_0(D!6, B!8) = X!12)))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(244,plain,
% 0.47/0.64 (member(tptp_fun_X_0(D!6, B!8), D!6) <=> ((tptp_fun_X_0(D!6, B!8) = Z!10) | (tptp_fun_X_0(D!6, B!8) = Y!11) | (tptp_fun_X_0(D!6, B!8) = X!12))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[243, 134])).
% 0.47/0.64 tff(245,assumption,(~((~member(tptp_fun_X_0(D!6, B!8), B!8)) | member(tptp_fun_X_0(D!6, B!8), D!6))), introduced(assumption)).
% 0.47/0.64 tff(246,plain,
% 0.47/0.64 (((~member(tptp_fun_X_0(D!6, B!8), B!8)) | member(tptp_fun_X_0(D!6, B!8), D!6)) | (~member(tptp_fun_X_0(D!6, B!8), D!6))),
% 0.47/0.64 inference(tautology,[status(thm)],[])).
% 0.47/0.64 tff(247,plain,
% 0.47/0.64 (~member(tptp_fun_X_0(D!6, B!8), D!6)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[246, 245])).
% 0.47/0.64 tff(248,plain,
% 0.47/0.64 ((~(member(tptp_fun_X_0(D!6, B!8), D!6) <=> ((tptp_fun_X_0(D!6, B!8) = Z!10) | (tptp_fun_X_0(D!6, B!8) = Y!11) | (tptp_fun_X_0(D!6, B!8) = X!12)))) | member(tptp_fun_X_0(D!6, B!8), D!6) | (~((tptp_fun_X_0(D!6, B!8) = Z!10) | (tptp_fun_X_0(D!6, B!8) = Y!11) | (tptp_fun_X_0(D!6, B!8) = X!12)))),
% 0.47/0.64 inference(tautology,[status(thm)],[])).
% 0.47/0.64 tff(249,plain,
% 0.47/0.64 ((~(member(tptp_fun_X_0(D!6, B!8), D!6) <=> ((tptp_fun_X_0(D!6, B!8) = Z!10) | (tptp_fun_X_0(D!6, B!8) = Y!11) | (tptp_fun_X_0(D!6, B!8) = X!12)))) | (~((tptp_fun_X_0(D!6, B!8) = Z!10) | (tptp_fun_X_0(D!6, B!8) = Y!11) | (tptp_fun_X_0(D!6, B!8) = X!12)))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[248, 247])).
% 0.47/0.64 tff(250,plain,
% 0.47/0.64 (~((tptp_fun_X_0(D!6, B!8) = Z!10) | (tptp_fun_X_0(D!6, B!8) = Y!11) | (tptp_fun_X_0(D!6, B!8) = X!12))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[249, 244])).
% 0.47/0.64 tff(251,plain,
% 0.47/0.64 ((~![U: option] : (member(U, B!8) <=> (U = Z!10))) | (member(tptp_fun_X_0(D!6, B!8), B!8) <=> (tptp_fun_X_0(D!6, B!8) = Z!10))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(252,plain,
% 0.47/0.64 (member(tptp_fun_X_0(D!6, B!8), B!8) <=> (tptp_fun_X_0(D!6, B!8) = Z!10)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[251, 200])).
% 0.47/0.64 tff(253,plain,
% 0.47/0.64 (((~member(tptp_fun_X_0(D!6, B!8), B!8)) | member(tptp_fun_X_0(D!6, B!8), D!6)) | member(tptp_fun_X_0(D!6, B!8), B!8)),
% 0.47/0.64 inference(tautology,[status(thm)],[])).
% 0.47/0.64 tff(254,plain,
% 0.47/0.64 (member(tptp_fun_X_0(D!6, B!8), B!8)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[253, 245])).
% 0.47/0.64 tff(255,plain,
% 0.47/0.64 ((~(member(tptp_fun_X_0(D!6, B!8), B!8) <=> (tptp_fun_X_0(D!6, B!8) = Z!10))) | (~member(tptp_fun_X_0(D!6, B!8), B!8)) | (tptp_fun_X_0(D!6, B!8) = Z!10)),
% 0.47/0.64 inference(tautology,[status(thm)],[])).
% 0.47/0.64 tff(256,plain,
% 0.47/0.64 ((~(member(tptp_fun_X_0(D!6, B!8), B!8) <=> (tptp_fun_X_0(D!6, B!8) = Z!10))) | (tptp_fun_X_0(D!6, B!8) = Z!10)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[255, 254])).
% 0.47/0.64 tff(257,plain,
% 0.47/0.64 (tptp_fun_X_0(D!6, B!8) = Z!10),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[256, 252])).
% 0.47/0.64 tff(258,plain,
% 0.47/0.64 (((tptp_fun_X_0(D!6, B!8) = Z!10) | (tptp_fun_X_0(D!6, B!8) = Y!11) | (tptp_fun_X_0(D!6, B!8) = X!12)) | (~(tptp_fun_X_0(D!6, B!8) = Z!10))),
% 0.47/0.64 inference(tautology,[status(thm)],[])).
% 0.47/0.64 tff(259,plain,
% 0.47/0.64 ($false),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[258, 257, 250])).
% 0.47/0.64 tff(260,plain,((~member(tptp_fun_X_0(D!6, B!8), B!8)) | member(tptp_fun_X_0(D!6, B!8), D!6)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.64 tff(261,plain,
% 0.47/0.64 ((~(subset(B!8, D!6) | (~((~member(tptp_fun_X_0(D!6, B!8), B!8)) | member(tptp_fun_X_0(D!6, B!8), D!6))))) | subset(B!8, D!6) | (~((~member(tptp_fun_X_0(D!6, B!8), B!8)) | member(tptp_fun_X_0(D!6, B!8), D!6)))),
% 0.47/0.64 inference(tautology,[status(thm)],[])).
% 0.47/0.64 tff(262,plain,
% 0.47/0.64 ((~(subset(B!8, D!6) | (~((~member(tptp_fun_X_0(D!6, B!8), B!8)) | member(tptp_fun_X_0(D!6, B!8), D!6))))) | subset(B!8, D!6)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[261, 260])).
% 0.47/0.64 tff(263,plain,
% 0.47/0.64 (subset(B!8, D!6)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[262, 242])).
% 0.47/0.64 tff(264,plain,
% 0.47/0.64 (^[X: option_set, Y: option_set] : refl(((~better(Y, X)) | (~subset(X, Y)) | ![U: option] : ((~member(U, X)) | (~(member(tptp_fun_V_3(U, Y, X), X) | required_preference(U, tptp_fun_V_3(U, Y, X)) | (~member(tptp_fun_V_3(U, Y, X), Y)))))) <=> ((~better(Y, X)) | (~subset(X, Y)) | ![U: option] : ((~member(U, X)) | (~(member(tptp_fun_V_3(U, Y, X), X) | required_preference(U, tptp_fun_V_3(U, Y, X)) | (~member(tptp_fun_V_3(U, Y, X), Y)))))))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(265,plain,
% 0.47/0.64 (![X: option_set, Y: option_set] : ((~better(Y, X)) | (~subset(X, Y)) | ![U: option] : ((~member(U, X)) | (~(member(tptp_fun_V_3(U, Y, X), X) | required_preference(U, tptp_fun_V_3(U, Y, X)) | (~member(tptp_fun_V_3(U, Y, X), Y)))))) <=> ![X: option_set, Y: option_set] : ((~better(Y, X)) | (~subset(X, Y)) | ![U: option] : ((~member(U, X)) | (~(member(tptp_fun_V_3(U, Y, X), X) | required_preference(U, tptp_fun_V_3(U, Y, X)) | (~member(tptp_fun_V_3(U, Y, X), Y))))))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[264])).
% 0.47/0.64 tff(266,plain,
% 0.47/0.64 (^[X: option_set, Y: option_set] : rewrite(((~better(Y, X)) | (~subset(X, Y)) | ![U: option] : ((~member(U, X)) | (~(member(tptp_fun_V_3(U, Y, X), X) | required_preference(U, tptp_fun_V_3(U, Y, X)) | (~member(tptp_fun_V_3(U, Y, X), Y)))))) <=> ((~better(Y, X)) | (~subset(X, Y)) | ![U: option] : ((~member(U, X)) | (~(member(tptp_fun_V_3(U, Y, X), X) | required_preference(U, tptp_fun_V_3(U, Y, X)) | (~member(tptp_fun_V_3(U, Y, X), Y)))))))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(267,plain,
% 0.47/0.64 (![X: option_set, Y: option_set] : ((~better(Y, X)) | (~subset(X, Y)) | ![U: option] : ((~member(U, X)) | (~(member(tptp_fun_V_3(U, Y, X), X) | required_preference(U, tptp_fun_V_3(U, Y, X)) | (~member(tptp_fun_V_3(U, Y, X), Y)))))) <=> ![X: option_set, Y: option_set] : ((~better(Y, X)) | (~subset(X, Y)) | ![U: option] : ((~member(U, X)) | (~(member(tptp_fun_V_3(U, Y, X), X) | required_preference(U, tptp_fun_V_3(U, Y, X)) | (~member(tptp_fun_V_3(U, Y, X), Y))))))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[266])).
% 0.47/0.64 tff(268,plain,
% 0.47/0.64 (![X: option_set, Y: option_set] : ((~better(Y, X)) | (~subset(X, Y)) | ![U: option] : ((~member(U, X)) | (~(member(tptp_fun_V_3(U, Y, X), X) | required_preference(U, tptp_fun_V_3(U, Y, X)) | (~member(tptp_fun_V_3(U, Y, X), Y)))))) <=> ![X: option_set, Y: option_set] : ((~better(Y, X)) | (~subset(X, Y)) | ![U: option] : ((~member(U, X)) | (~(member(tptp_fun_V_3(U, Y, X), X) | required_preference(U, tptp_fun_V_3(U, Y, X)) | (~member(tptp_fun_V_3(U, Y, X), Y))))))),
% 0.47/0.64 inference(transitivity,[status(thm)],[267, 265])).
% 0.47/0.64 tff(269,plain,
% 0.47/0.64 (^[X: option_set, Y: option_set] : rewrite(((~better(Y, X)) | (~subset(X, Y)) | ![U: option] : ((~member(U, X)) | (~((~(member(tptp_fun_V_3(U, Y, X), Y) & (~member(tptp_fun_V_3(U, Y, X), X)))) | required_preference(U, tptp_fun_V_3(U, Y, X)))))) <=> ((~better(Y, X)) | (~subset(X, Y)) | ![U: option] : ((~member(U, X)) | (~(member(tptp_fun_V_3(U, Y, X), X) | required_preference(U, tptp_fun_V_3(U, Y, X)) | (~member(tptp_fun_V_3(U, Y, X), Y)))))))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(270,plain,
% 0.47/0.64 (![X: option_set, Y: option_set] : ((~better(Y, X)) | (~subset(X, Y)) | ![U: option] : ((~member(U, X)) | (~((~(member(tptp_fun_V_3(U, Y, X), Y) & (~member(tptp_fun_V_3(U, Y, X), X)))) | required_preference(U, tptp_fun_V_3(U, Y, X)))))) <=> ![X: option_set, Y: option_set] : ((~better(Y, X)) | (~subset(X, Y)) | ![U: option] : ((~member(U, X)) | (~(member(tptp_fun_V_3(U, Y, X), X) | required_preference(U, tptp_fun_V_3(U, Y, X)) | (~member(tptp_fun_V_3(U, Y, X), Y))))))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[269])).
% 0.47/0.64 tff(271,plain,
% 0.47/0.64 (^[X: option_set, Y: option_set] : trans(monotonicity(rewrite(((~subset(X, Y)) | ![U: option] : ((~member(U, X)) | (~((~(member(tptp_fun_V_3(U, Y, X), Y) & (~member(tptp_fun_V_3(U, Y, X), X)))) | required_preference(U, tptp_fun_V_3(U, Y, X)))))) <=> ((~subset(X, Y)) | ![U: option] : ((~member(U, X)) | (~((~(member(tptp_fun_V_3(U, Y, X), Y) & (~member(tptp_fun_V_3(U, Y, X), X)))) | required_preference(U, tptp_fun_V_3(U, Y, X))))))), (((~better(Y, X)) | ((~subset(X, Y)) | ![U: option] : ((~member(U, X)) | (~((~(member(tptp_fun_V_3(U, Y, X), Y) & (~member(tptp_fun_V_3(U, Y, X), X)))) | required_preference(U, tptp_fun_V_3(U, Y, X))))))) <=> ((~better(Y, X)) | ((~subset(X, Y)) | ![U: option] : ((~member(U, X)) | (~((~(member(tptp_fun_V_3(U, Y, X), Y) & (~member(tptp_fun_V_3(U, Y, X), X)))) | required_preference(U, tptp_fun_V_3(U, Y, X))))))))), rewrite(((~better(Y, X)) | ((~subset(X, Y)) | ![U: option] : ((~member(U, X)) | (~((~(member(tptp_fun_V_3(U, Y, X), Y) & (~member(tptp_fun_V_3(U, Y, X), X)))) | required_preference(U, tptp_fun_V_3(U, Y, X))))))) <=> ((~better(Y, X)) | (~subset(X, Y)) | ![U: option] : ((~member(U, X)) | (~((~(member(tptp_fun_V_3(U, Y, X), Y) & (~member(tptp_fun_V_3(U, Y, X), X)))) | required_preference(U, tptp_fun_V_3(U, Y, X))))))), (((~better(Y, X)) | ((~subset(X, Y)) | ![U: option] : ((~member(U, X)) | (~((~(member(tptp_fun_V_3(U, Y, X), Y) & (~member(tptp_fun_V_3(U, Y, X), X)))) | required_preference(U, tptp_fun_V_3(U, Y, X))))))) <=> ((~better(Y, X)) | (~subset(X, Y)) | ![U: option] : ((~member(U, X)) | (~((~(member(tptp_fun_V_3(U, Y, X), Y) & (~member(tptp_fun_V_3(U, Y, X), X)))) | required_preference(U, tptp_fun_V_3(U, Y, X))))))))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(272,plain,
% 0.47/0.64 (![X: option_set, Y: option_set] : ((~better(Y, X)) | ((~subset(X, Y)) | ![U: option] : ((~member(U, X)) | (~((~(member(tptp_fun_V_3(U, Y, X), Y) & (~member(tptp_fun_V_3(U, Y, X), X)))) | required_preference(U, tptp_fun_V_3(U, Y, X))))))) <=> ![X: option_set, Y: option_set] : ((~better(Y, X)) | (~subset(X, Y)) | ![U: option] : ((~member(U, X)) | (~((~(member(tptp_fun_V_3(U, Y, X), Y) & (~member(tptp_fun_V_3(U, Y, X), X)))) | required_preference(U, tptp_fun_V_3(U, Y, X))))))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[271])).
% 0.47/0.64 tff(273,plain,
% 0.47/0.64 (![X: option_set, Y: option_set] : ((~better(Y, X)) | (~(subset(X, Y) & ?[U: option] : (member(U, X) & ![V: option] : ((~(member(V, Y) & (~member(V, X)))) | required_preference(U, V)))))) <=> ![X: option_set, Y: option_set] : ((~better(Y, X)) | (~(subset(X, Y) & ?[U: option] : (member(U, X) & ![V: option] : ((~(member(V, Y) & (~member(V, X)))) | required_preference(U, V))))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(274,plain,
% 0.47/0.64 (^[X: option_set, Y: option_set] : trans(monotonicity(rewrite((subset(X, Y) & ?[U: option] : (member(U, X) & ![V: option] : ((member(V, Y) & (~member(V, X))) => required_preference(U, V)))) <=> (subset(X, Y) & ?[U: option] : (member(U, X) & ![V: option] : ((~(member(V, Y) & (~member(V, X)))) | required_preference(U, V))))), (((subset(X, Y) & ?[U: option] : (member(U, X) & ![V: option] : ((member(V, Y) & (~member(V, X))) => required_preference(U, V)))) => (~better(Y, X))) <=> ((subset(X, Y) & ?[U: option] : (member(U, X) & ![V: option] : ((~(member(V, Y) & (~member(V, X)))) | required_preference(U, V)))) => (~better(Y, X))))), rewrite(((subset(X, Y) & ?[U: option] : (member(U, X) & ![V: option] : ((~(member(V, Y) & (~member(V, X)))) | required_preference(U, V)))) => (~better(Y, X))) <=> ((~better(Y, X)) | (~(subset(X, Y) & ?[U: option] : (member(U, X) & ![V: option] : ((~(member(V, Y) & (~member(V, X)))) | required_preference(U, V))))))), (((subset(X, Y) & ?[U: option] : (member(U, X) & ![V: option] : ((member(V, Y) & (~member(V, X))) => required_preference(U, V)))) => (~better(Y, X))) <=> ((~better(Y, X)) | (~(subset(X, Y) & ?[U: option] : (member(U, X) & ![V: option] : ((~(member(V, Y) & (~member(V, X)))) | required_preference(U, V))))))))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(275,plain,
% 0.47/0.65 (![X: option_set, Y: option_set] : ((subset(X, Y) & ?[U: option] : (member(U, X) & ![V: option] : ((member(V, Y) & (~member(V, X))) => required_preference(U, V)))) => (~better(Y, X))) <=> ![X: option_set, Y: option_set] : ((~better(Y, X)) | (~(subset(X, Y) & ?[U: option] : (member(U, X) & ![V: option] : ((~(member(V, Y) & (~member(V, X)))) | required_preference(U, V))))))),
% 0.47/0.65 inference(quant_intro,[status(thm)],[274])).
% 0.47/0.65 tff(276,axiom,(![X: option_set, Y: option_set] : ((subset(X, Y) & ?[U: option] : (member(U, X) & ![V: option] : ((member(V, Y) & (~member(V, X))) => required_preference(U, V)))) => (~better(Y, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','insignificance_of_dominated_options')).
% 0.47/0.65 tff(277,plain,
% 0.47/0.65 (![X: option_set, Y: option_set] : ((~better(Y, X)) | (~(subset(X, Y) & ?[U: option] : (member(U, X) & ![V: option] : ((~(member(V, Y) & (~member(V, X)))) | required_preference(U, V))))))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[276, 275])).
% 0.47/0.65 tff(278,plain,
% 0.47/0.65 (![X: option_set, Y: option_set] : ((~better(Y, X)) | (~(subset(X, Y) & ?[U: option] : (member(U, X) & ![V: option] : ((~(member(V, Y) & (~member(V, X)))) | required_preference(U, V))))))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[277, 273])).
% 0.47/0.65 tff(279,plain,(
% 0.47/0.65 ![X: option_set, Y: option_set] : ((~better(Y, X)) | ((~subset(X, Y)) | ![U: option] : ((~member(U, X)) | (~((~(member(tptp_fun_V_3(U, Y, X), Y) & (~member(tptp_fun_V_3(U, Y, X), X)))) | required_preference(U, tptp_fun_V_3(U, Y, X)))))))),
% 0.47/0.65 inference(skolemize,[status(sab)],[278])).
% 0.47/0.65 tff(280,plain,
% 0.47/0.65 (![X: option_set, Y: option_set] : ((~better(Y, X)) | (~subset(X, Y)) | ![U: option] : ((~member(U, X)) | (~((~(member(tptp_fun_V_3(U, Y, X), Y) & (~member(tptp_fun_V_3(U, Y, X), X)))) | required_preference(U, tptp_fun_V_3(U, Y, X))))))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[279, 272])).
% 0.47/0.65 tff(281,plain,
% 0.47/0.65 (![X: option_set, Y: option_set] : ((~better(Y, X)) | (~subset(X, Y)) | ![U: option] : ((~member(U, X)) | (~(member(tptp_fun_V_3(U, Y, X), X) | required_preference(U, tptp_fun_V_3(U, Y, X)) | (~member(tptp_fun_V_3(U, Y, X), Y))))))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[280, 270])).
% 0.47/0.65 tff(282,plain,
% 0.47/0.65 (![X: option_set, Y: option_set] : ((~better(Y, X)) | (~subset(X, Y)) | ![U: option] : ((~member(U, X)) | (~(member(tptp_fun_V_3(U, Y, X), X) | required_preference(U, tptp_fun_V_3(U, Y, X)) | (~member(tptp_fun_V_3(U, Y, X), Y))))))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[281, 268])).
% 0.47/0.65 tff(283,plain,
% 0.47/0.65 (((~![X: option_set, Y: option_set] : ((~better(Y, X)) | (~subset(X, Y)) | ![U: option] : ((~member(U, X)) | (~(member(tptp_fun_V_3(U, Y, X), X) | required_preference(U, tptp_fun_V_3(U, Y, X)) | (~member(tptp_fun_V_3(U, Y, X), Y))))))) | ((~better(D!6, B!8)) | (~subset(B!8, D!6)) | ![U: option] : ((~member(U, B!8)) | (~(member(tptp_fun_V_3(U, D!6, B!8), B!8) | required_preference(U, tptp_fun_V_3(U, D!6, B!8)) | (~member(tptp_fun_V_3(U, D!6, B!8), D!6))))))) <=> ((~![X: option_set, Y: option_set] : ((~better(Y, X)) | (~subset(X, Y)) | ![U: option] : ((~member(U, X)) | (~(member(tptp_fun_V_3(U, Y, X), X) | required_preference(U, tptp_fun_V_3(U, Y, X)) | (~member(tptp_fun_V_3(U, Y, X), Y))))))) | (~better(D!6, B!8)) | (~subset(B!8, D!6)) | ![U: option] : ((~member(U, B!8)) | (~(member(tptp_fun_V_3(U, D!6, B!8), B!8) | required_preference(U, tptp_fun_V_3(U, D!6, B!8)) | (~member(tptp_fun_V_3(U, D!6, B!8), D!6))))))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(284,plain,
% 0.47/0.65 ((~![X: option_set, Y: option_set] : ((~better(Y, X)) | (~subset(X, Y)) | ![U: option] : ((~member(U, X)) | (~(member(tptp_fun_V_3(U, Y, X), X) | required_preference(U, tptp_fun_V_3(U, Y, X)) | (~member(tptp_fun_V_3(U, Y, X), Y))))))) | ((~better(D!6, B!8)) | (~subset(B!8, D!6)) | ![U: option] : ((~member(U, B!8)) | (~(member(tptp_fun_V_3(U, D!6, B!8), B!8) | required_preference(U, tptp_fun_V_3(U, D!6, B!8)) | (~member(tptp_fun_V_3(U, D!6, B!8), D!6))))))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(285,plain,
% 0.47/0.65 ((~![X: option_set, Y: option_set] : ((~better(Y, X)) | (~subset(X, Y)) | ![U: option] : ((~member(U, X)) | (~(member(tptp_fun_V_3(U, Y, X), X) | required_preference(U, tptp_fun_V_3(U, Y, X)) | (~member(tptp_fun_V_3(U, Y, X), Y))))))) | (~better(D!6, B!8)) | (~subset(B!8, D!6)) | ![U: option] : ((~member(U, B!8)) | (~(member(tptp_fun_V_3(U, D!6, B!8), B!8) | required_preference(U, tptp_fun_V_3(U, D!6, B!8)) | (~member(tptp_fun_V_3(U, D!6, B!8), D!6)))))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[284, 283])).
% 0.47/0.65 tff(286,plain,
% 0.47/0.65 ((~better(D!6, B!8)) | ![U: option] : ((~member(U, B!8)) | (~(member(tptp_fun_V_3(U, D!6, B!8), B!8) | required_preference(U, tptp_fun_V_3(U, D!6, B!8)) | (~member(tptp_fun_V_3(U, D!6, B!8), D!6)))))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[285, 282, 263])).
% 0.47/0.65 tff(287,plain,
% 0.47/0.65 (~better(D!6, B!8)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[286, 236])).
% 0.47/0.65 tff(288,plain,
% 0.47/0.65 ((~![X: option_set, Y: option_set] : (~(((~weakly_better(X, Y)) | weakly_better(Y, X)) <=> better(X, Y)))) | (~(((~weakly_better(D!6, B!8)) | weakly_better(B!8, D!6)) <=> better(D!6, B!8)))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(289,plain,
% 0.47/0.65 (~(((~weakly_better(D!6, B!8)) | weakly_better(B!8, D!6)) <=> better(D!6, B!8))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[288, 92])).
% 0.47/0.65 tff(290,plain,
% 0.47/0.65 ((((~weakly_better(D!6, B!8)) | weakly_better(B!8, D!6)) <=> better(D!6, B!8)) | ((~weakly_better(D!6, B!8)) | weakly_better(B!8, D!6)) | better(D!6, B!8)),
% 0.47/0.65 inference(tautology,[status(thm)],[])).
% 0.47/0.65 tff(291,plain,
% 0.47/0.65 (((~weakly_better(D!6, B!8)) | weakly_better(B!8, D!6)) | better(D!6, B!8)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[290, 289])).
% 0.47/0.65 tff(292,plain,
% 0.47/0.65 ((~weakly_better(D!6, B!8)) | weakly_better(B!8, D!6)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[291, 287])).
% 0.47/0.65 tff(293,assumption,(~weakly_better(D!6, B!8)), introduced(assumption)).
% 0.47/0.65 tff(294,plain,
% 0.47/0.65 (((~![X: option_set, Y: option_set] : ((~subset(X, Y)) | weakly_better(Y, X))) | ((~subset(B!8, D!6)) | weakly_better(D!6, B!8))) <=> ((~![X: option_set, Y: option_set] : ((~subset(X, Y)) | weakly_better(Y, X))) | (~subset(B!8, D!6)) | weakly_better(D!6, B!8))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(295,plain,
% 0.47/0.65 ((~![X: option_set, Y: option_set] : ((~subset(X, Y)) | weakly_better(Y, X))) | ((~subset(B!8, D!6)) | weakly_better(D!6, B!8))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(296,plain,
% 0.47/0.65 ((~![X: option_set, Y: option_set] : ((~subset(X, Y)) | weakly_better(Y, X))) | (~subset(B!8, D!6)) | weakly_better(D!6, B!8)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[295, 294])).
% 0.47/0.65 tff(297,plain,
% 0.47/0.65 ($false),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[296, 161, 263, 293])).
% 0.47/0.65 tff(298,plain,(weakly_better(D!6, B!8)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.65 tff(299,plain,
% 0.47/0.65 ((~((~weakly_better(D!6, B!8)) | weakly_better(B!8, D!6))) | (~weakly_better(D!6, B!8)) | weakly_better(B!8, D!6)),
% 0.47/0.65 inference(tautology,[status(thm)],[])).
% 0.47/0.65 tff(300,plain,
% 0.47/0.65 ((~((~weakly_better(D!6, B!8)) | weakly_better(B!8, D!6))) | weakly_better(B!8, D!6)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[299, 298])).
% 0.47/0.65 tff(301,plain,
% 0.47/0.65 (weakly_better(B!8, D!6)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[300, 292])).
% 0.47/0.65 tff(302,assumption,(~weakly_better(A!9, D!6)), introduced(assumption)).
% 0.47/0.65 tff(303,plain,
% 0.47/0.65 (((~![X: option_set, Y: option_set, Z: option_set] : (weakly_better(X, Z) | (~weakly_better(Y, Z)) | (~weakly_better(X, Y)))) | (weakly_better(A!9, D!6) | (~weakly_better(B!8, D!6)) | (~weakly_better(A!9, B!8)))) <=> ((~![X: option_set, Y: option_set, Z: option_set] : (weakly_better(X, Z) | (~weakly_better(Y, Z)) | (~weakly_better(X, Y)))) | weakly_better(A!9, D!6) | (~weakly_better(B!8, D!6)) | (~weakly_better(A!9, B!8)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(304,plain,
% 0.47/0.65 ((~![X: option_set, Y: option_set, Z: option_set] : (weakly_better(X, Z) | (~weakly_better(Y, Z)) | (~weakly_better(X, Y)))) | (weakly_better(A!9, D!6) | (~weakly_better(B!8, D!6)) | (~weakly_better(A!9, B!8)))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(305,plain,
% 0.47/0.65 ((~![X: option_set, Y: option_set, Z: option_set] : (weakly_better(X, Z) | (~weakly_better(Y, Z)) | (~weakly_better(X, Y)))) | weakly_better(A!9, D!6) | (~weakly_better(B!8, D!6)) | (~weakly_better(A!9, B!8))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[304, 303])).
% 0.47/0.65 tff(306,plain,
% 0.47/0.65 ($false),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[305, 179, 302, 301, 188])).
% 0.47/0.65 tff(307,plain,((~weakly_better(A!9, B!8)) | weakly_better(A!9, D!6)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.65 tff(308,plain,
% 0.47/0.65 (~weakly_better(A!9, B!8)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[307, 187])).
% 0.47/0.65 tff(309,assumption,((~((~subset(A!9, D!6)) | ![X: option] : ((~member(X, A!9)) | member(X, D!6)))) | (~(subset(A!9, D!6) | (~((~member(tptp_fun_X_0(D!6, A!9), A!9)) | member(tptp_fun_X_0(D!6, A!9), D!6)))))), introduced(assumption)).
% 0.47/0.65 tff(310,plain,
% 0.47/0.65 ((~![A: option_set, B: option_set] : (~((~((~subset(A, B)) | ![X: option] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(A!9, D!6)) | ![X: option] : ((~member(X, A!9)) | member(X, D!6)))) | (~(subset(A!9, D!6) | (~((~member(tptp_fun_X_0(D!6, A!9), A!9)) | member(tptp_fun_X_0(D!6, A!9), D!6)))))))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(311,plain,
% 0.47/0.65 ($false),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[310, 117, 309])).
% 0.47/0.65 tff(312,plain,(~((~((~subset(A!9, D!6)) | ![X: option] : ((~member(X, A!9)) | member(X, D!6)))) | (~(subset(A!9, D!6) | (~((~member(tptp_fun_X_0(D!6, A!9), A!9)) | member(tptp_fun_X_0(D!6, A!9), D!6))))))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.65 tff(313,plain,
% 0.47/0.65 (((~((~subset(A!9, D!6)) | ![X: option] : ((~member(X, A!9)) | member(X, D!6)))) | (~(subset(A!9, D!6) | (~((~member(tptp_fun_X_0(D!6, A!9), A!9)) | member(tptp_fun_X_0(D!6, A!9), D!6)))))) | (subset(A!9, D!6) | (~((~member(tptp_fun_X_0(D!6, A!9), A!9)) | member(tptp_fun_X_0(D!6, A!9), D!6))))),
% 0.47/0.65 inference(tautology,[status(thm)],[])).
% 0.47/0.65 tff(314,plain,
% 0.47/0.65 (subset(A!9, D!6) | (~((~member(tptp_fun_X_0(D!6, A!9), A!9)) | member(tptp_fun_X_0(D!6, A!9), D!6)))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[313, 312])).
% 0.47/0.65 tff(315,plain,
% 0.47/0.65 ((~![U: option] : (member(U, D!6) <=> ((U = Z!10) | (U = Y!11) | (U = X!12)))) | (member(tptp_fun_X_0(D!6, A!9), D!6) <=> ((tptp_fun_X_0(D!6, A!9) = Z!10) | (tptp_fun_X_0(D!6, A!9) = Y!11) | (tptp_fun_X_0(D!6, A!9) = X!12)))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(316,plain,
% 0.47/0.65 (member(tptp_fun_X_0(D!6, A!9), D!6) <=> ((tptp_fun_X_0(D!6, A!9) = Z!10) | (tptp_fun_X_0(D!6, A!9) = Y!11) | (tptp_fun_X_0(D!6, A!9) = X!12))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[315, 134])).
% 0.47/0.65 tff(317,assumption,(~((~member(tptp_fun_X_0(D!6, A!9), A!9)) | member(tptp_fun_X_0(D!6, A!9), D!6))), introduced(assumption)).
% 0.47/0.65 tff(318,plain,
% 0.47/0.65 (((~member(tptp_fun_X_0(D!6, A!9), A!9)) | member(tptp_fun_X_0(D!6, A!9), D!6)) | (~member(tptp_fun_X_0(D!6, A!9), D!6))),
% 0.47/0.65 inference(tautology,[status(thm)],[])).
% 0.47/0.65 tff(319,plain,
% 0.47/0.65 (~member(tptp_fun_X_0(D!6, A!9), D!6)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[318, 317])).
% 0.47/0.65 tff(320,plain,
% 0.47/0.65 ((~(member(tptp_fun_X_0(D!6, A!9), D!6) <=> ((tptp_fun_X_0(D!6, A!9) = Z!10) | (tptp_fun_X_0(D!6, A!9) = Y!11) | (tptp_fun_X_0(D!6, A!9) = X!12)))) | member(tptp_fun_X_0(D!6, A!9), D!6) | (~((tptp_fun_X_0(D!6, A!9) = Z!10) | (tptp_fun_X_0(D!6, A!9) = Y!11) | (tptp_fun_X_0(D!6, A!9) = X!12)))),
% 0.47/0.65 inference(tautology,[status(thm)],[])).
% 0.47/0.65 tff(321,plain,
% 0.47/0.65 ((~(member(tptp_fun_X_0(D!6, A!9), D!6) <=> ((tptp_fun_X_0(D!6, A!9) = Z!10) | (tptp_fun_X_0(D!6, A!9) = Y!11) | (tptp_fun_X_0(D!6, A!9) = X!12)))) | (~((tptp_fun_X_0(D!6, A!9) = Z!10) | (tptp_fun_X_0(D!6, A!9) = Y!11) | (tptp_fun_X_0(D!6, A!9) = X!12)))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[320, 319])).
% 0.47/0.65 tff(322,plain,
% 0.47/0.65 (~((tptp_fun_X_0(D!6, A!9) = Z!10) | (tptp_fun_X_0(D!6, A!9) = Y!11) | (tptp_fun_X_0(D!6, A!9) = X!12))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[321, 316])).
% 0.47/0.66 tff(323,plain,
% 0.47/0.66 ((~![U: option] : (member(U, A!9) <=> (U = X!12))) | (member(tptp_fun_X_0(D!6, A!9), A!9) <=> (tptp_fun_X_0(D!6, A!9) = X!12))),
% 0.47/0.66 inference(quant_inst,[status(thm)],[])).
% 0.47/0.66 tff(324,plain,
% 0.47/0.66 (member(tptp_fun_X_0(D!6, A!9), A!9) <=> (tptp_fun_X_0(D!6, A!9) = X!12)),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[323, 13])).
% 0.47/0.66 tff(325,plain,
% 0.47/0.66 (((~member(tptp_fun_X_0(D!6, A!9), A!9)) | member(tptp_fun_X_0(D!6, A!9), D!6)) | member(tptp_fun_X_0(D!6, A!9), A!9)),
% 0.47/0.66 inference(tautology,[status(thm)],[])).
% 0.47/0.66 tff(326,plain,
% 0.47/0.66 (member(tptp_fun_X_0(D!6, A!9), A!9)),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[325, 317])).
% 0.47/0.66 tff(327,plain,
% 0.47/0.66 ((~(member(tptp_fun_X_0(D!6, A!9), A!9) <=> (tptp_fun_X_0(D!6, A!9) = X!12))) | (~member(tptp_fun_X_0(D!6, A!9), A!9)) | (tptp_fun_X_0(D!6, A!9) = X!12)),
% 0.47/0.66 inference(tautology,[status(thm)],[])).
% 0.47/0.66 tff(328,plain,
% 0.47/0.66 ((~(member(tptp_fun_X_0(D!6, A!9), A!9) <=> (tptp_fun_X_0(D!6, A!9) = X!12))) | (tptp_fun_X_0(D!6, A!9) = X!12)),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[327, 326])).
% 0.47/0.66 tff(329,plain,
% 0.47/0.66 (tptp_fun_X_0(D!6, A!9) = X!12),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[328, 324])).
% 0.47/0.66 tff(330,plain,
% 0.47/0.66 (((tptp_fun_X_0(D!6, A!9) = Z!10) | (tptp_fun_X_0(D!6, A!9) = Y!11) | (tptp_fun_X_0(D!6, A!9) = X!12)) | (~(tptp_fun_X_0(D!6, A!9) = X!12))),
% 0.47/0.66 inference(tautology,[status(thm)],[])).
% 0.47/0.66 tff(331,plain,
% 0.47/0.66 ($false),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[330, 329, 322])).
% 0.47/0.66 tff(332,plain,((~member(tptp_fun_X_0(D!6, A!9), A!9)) | member(tptp_fun_X_0(D!6, A!9), D!6)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.66 tff(333,plain,
% 0.47/0.66 ((~(subset(A!9, D!6) | (~((~member(tptp_fun_X_0(D!6, A!9), A!9)) | member(tptp_fun_X_0(D!6, A!9), D!6))))) | subset(A!9, D!6) | (~((~member(tptp_fun_X_0(D!6, A!9), A!9)) | member(tptp_fun_X_0(D!6, A!9), D!6)))),
% 0.47/0.66 inference(tautology,[status(thm)],[])).
% 0.47/0.66 tff(334,plain,
% 0.47/0.66 ((~(subset(A!9, D!6) | (~((~member(tptp_fun_X_0(D!6, A!9), A!9)) | member(tptp_fun_X_0(D!6, A!9), D!6))))) | subset(A!9, D!6)),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[333, 332])).
% 0.47/0.66 tff(335,plain,
% 0.47/0.66 (subset(A!9, D!6)),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[334, 314])).
% 0.47/0.66 tff(336,assumption,(~weakly_better(D!6, A!9)), introduced(assumption)).
% 0.47/0.66 tff(337,plain,
% 0.47/0.66 (((~![X: option_set, Y: option_set] : ((~subset(X, Y)) | weakly_better(Y, X))) | ((~subset(A!9, D!6)) | weakly_better(D!6, A!9))) <=> ((~![X: option_set, Y: option_set] : ((~subset(X, Y)) | weakly_better(Y, X))) | (~subset(A!9, D!6)) | weakly_better(D!6, A!9))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(338,plain,
% 0.47/0.66 ((~![X: option_set, Y: option_set] : ((~subset(X, Y)) | weakly_better(Y, X))) | ((~subset(A!9, D!6)) | weakly_better(D!6, A!9))),
% 0.47/0.66 inference(quant_inst,[status(thm)],[])).
% 0.47/0.66 tff(339,plain,
% 0.47/0.66 ((~![X: option_set, Y: option_set] : ((~subset(X, Y)) | weakly_better(Y, X))) | (~subset(A!9, D!6)) | weakly_better(D!6, A!9)),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[338, 337])).
% 0.47/0.66 tff(340,plain,
% 0.47/0.66 ($false),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[339, 161, 336, 335])).
% 0.47/0.66 tff(341,plain,(weakly_better(D!6, A!9)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.66 tff(342,plain,
% 0.47/0.66 (((~![X: option_set, Y: option_set, Z: option_set] : (weakly_better(X, Z) | (~weakly_better(Y, Z)) | (~weakly_better(X, Y)))) | ((~weakly_better(D!6, A!9)) | (~weakly_better(B!8, D!6)) | weakly_better(B!8, A!9))) <=> ((~![X: option_set, Y: option_set, Z: option_set] : (weakly_better(X, Z) | (~weakly_better(Y, Z)) | (~weakly_better(X, Y)))) | (~weakly_better(D!6, A!9)) | (~weakly_better(B!8, D!6)) | weakly_better(B!8, A!9))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(343,plain,
% 0.47/0.66 ((weakly_better(B!8, A!9) | (~weakly_better(D!6, A!9)) | (~weakly_better(B!8, D!6))) <=> ((~weakly_better(D!6, A!9)) | (~weakly_better(B!8, D!6)) | weakly_better(B!8, A!9))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(344,plain,
% 0.47/0.66 (((~![X: option_set, Y: option_set, Z: option_set] : (weakly_better(X, Z) | (~weakly_better(Y, Z)) | (~weakly_better(X, Y)))) | (weakly_better(B!8, A!9) | (~weakly_better(D!6, A!9)) | (~weakly_better(B!8, D!6)))) <=> ((~![X: option_set, Y: option_set, Z: option_set] : (weakly_better(X, Z) | (~weakly_better(Y, Z)) | (~weakly_better(X, Y)))) | ((~weakly_better(D!6, A!9)) | (~weakly_better(B!8, D!6)) | weakly_better(B!8, A!9)))),
% 0.47/0.66 inference(monotonicity,[status(thm)],[343])).
% 0.47/0.66 tff(345,plain,
% 0.47/0.66 (((~![X: option_set, Y: option_set, Z: option_set] : (weakly_better(X, Z) | (~weakly_better(Y, Z)) | (~weakly_better(X, Y)))) | (weakly_better(B!8, A!9) | (~weakly_better(D!6, A!9)) | (~weakly_better(B!8, D!6)))) <=> ((~![X: option_set, Y: option_set, Z: option_set] : (weakly_better(X, Z) | (~weakly_better(Y, Z)) | (~weakly_better(X, Y)))) | (~weakly_better(D!6, A!9)) | (~weakly_better(B!8, D!6)) | weakly_better(B!8, A!9))),
% 0.47/0.66 inference(transitivity,[status(thm)],[344, 342])).
% 0.47/0.66 tff(346,plain,
% 0.47/0.66 ((~![X: option_set, Y: option_set, Z: option_set] : (weakly_better(X, Z) | (~weakly_better(Y, Z)) | (~weakly_better(X, Y)))) | (weakly_better(B!8, A!9) | (~weakly_better(D!6, A!9)) | (~weakly_better(B!8, D!6)))),
% 0.47/0.66 inference(quant_inst,[status(thm)],[])).
% 0.47/0.66 tff(347,plain,
% 0.47/0.66 ((~![X: option_set, Y: option_set, Z: option_set] : (weakly_better(X, Z) | (~weakly_better(Y, Z)) | (~weakly_better(X, Y)))) | (~weakly_better(D!6, A!9)) | (~weakly_better(B!8, D!6)) | weakly_better(B!8, A!9)),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[346, 345])).
% 0.47/0.66 tff(348,plain,
% 0.47/0.66 (weakly_better(B!8, A!9)),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[347, 179, 341, 301])).
% 0.47/0.66 tff(349,plain,
% 0.47/0.66 ((~((~weakly_better(B!8, A!9)) | weakly_better(A!9, B!8))) | (~weakly_better(B!8, A!9)) | weakly_better(A!9, B!8)),
% 0.47/0.66 inference(tautology,[status(thm)],[])).
% 0.47/0.66 tff(350,plain,
% 0.47/0.66 ((~((~weakly_better(B!8, A!9)) | weakly_better(A!9, B!8))) | weakly_better(A!9, B!8)),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[349, 348])).
% 0.47/0.66 tff(351,plain,
% 0.47/0.66 (~((~weakly_better(B!8, A!9)) | weakly_better(A!9, B!8))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[350, 308])).
% 0.47/0.66 tff(352,plain,
% 0.47/0.66 ((~![X: option_set, Y: option_set] : (~(((~weakly_better(X, Y)) | weakly_better(Y, X)) <=> better(X, Y)))) | (~(((~weakly_better(B!8, A!9)) | weakly_better(A!9, B!8)) <=> better(B!8, A!9)))),
% 0.47/0.66 inference(quant_inst,[status(thm)],[])).
% 0.47/0.66 tff(353,plain,
% 0.47/0.66 (~(((~weakly_better(B!8, A!9)) | weakly_better(A!9, B!8)) <=> better(B!8, A!9))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[352, 92])).
% 0.47/0.66 tff(354,plain,
% 0.47/0.66 ((((~weakly_better(B!8, A!9)) | weakly_better(A!9, B!8)) <=> better(B!8, A!9)) | ((~weakly_better(B!8, A!9)) | weakly_better(A!9, B!8)) | better(B!8, A!9)),
% 0.47/0.66 inference(tautology,[status(thm)],[])).
% 0.47/0.66 tff(355,plain,
% 0.47/0.66 (((~weakly_better(B!8, A!9)) | weakly_better(A!9, B!8)) | better(B!8, A!9)),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[354, 353])).
% 0.47/0.66 tff(356,plain,
% 0.47/0.66 (better(B!8, A!9)),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[355, 351])).
% 0.47/0.66 tff(357,plain,
% 0.47/0.66 (^[X: option, Y: option, U: option_set, V: option_set] : trans(monotonicity(rewrite(((~(member(tptp_fun_Z_4(U, X), U) <=> (tptp_fun_Z_4(U, X) = X))) | (~(member(tptp_fun_Z_5(V, Y), V) <=> (tptp_fun_Z_5(V, Y) = Y)))) <=> ((~(member(tptp_fun_Z_4(U, X), U) <=> (tptp_fun_Z_4(U, X) = X))) | (~(member(tptp_fun_Z_5(V, Y), V) <=> (tptp_fun_Z_5(V, Y) = Y))))), (((~better(U, V)) | ((~(member(tptp_fun_Z_4(U, X), U) <=> (tptp_fun_Z_4(U, X) = X))) | (~(member(tptp_fun_Z_5(V, Y), V) <=> (tptp_fun_Z_5(V, Y) = Y))))) <=> ((~better(U, V)) | ((~(member(tptp_fun_Z_4(U, X), U) <=> (tptp_fun_Z_4(U, X) = X))) | (~(member(tptp_fun_Z_5(V, Y), V) <=> (tptp_fun_Z_5(V, Y) = Y))))))), rewrite(((~better(U, V)) | ((~(member(tptp_fun_Z_4(U, X), U) <=> (tptp_fun_Z_4(U, X) = X))) | (~(member(tptp_fun_Z_5(V, Y), V) <=> (tptp_fun_Z_5(V, Y) = Y))))) <=> ((~better(U, V)) | (~(member(tptp_fun_Z_4(U, X), U) <=> (tptp_fun_Z_4(U, X) = X))) | (~(member(tptp_fun_Z_5(V, Y), V) <=> (tptp_fun_Z_5(V, Y) = Y))))), (((~better(U, V)) | ((~(member(tptp_fun_Z_4(U, X), U) <=> (tptp_fun_Z_4(U, X) = X))) | (~(member(tptp_fun_Z_5(V, Y), V) <=> (tptp_fun_Z_5(V, Y) = Y))))) <=> ((~better(U, V)) | (~(member(tptp_fun_Z_4(U, X), U) <=> (tptp_fun_Z_4(U, X) = X))) | (~(member(tptp_fun_Z_5(V, Y), V) <=> (tptp_fun_Z_5(V, Y) = Y))))))),
% 0.47/0.66 inference(bind,[status(th)],[])).
% 0.47/0.66 tff(358,plain,
% 0.47/0.66 (![X: option, Y: option, U: option_set, V: option_set] : ((~better(U, V)) | ((~(member(tptp_fun_Z_4(U, X), U) <=> (tptp_fun_Z_4(U, X) = X))) | (~(member(tptp_fun_Z_5(V, Y), V) <=> (tptp_fun_Z_5(V, Y) = Y))))) <=> ![X: option, Y: option, U: option_set, V: option_set] : ((~better(U, V)) | (~(member(tptp_fun_Z_4(U, X), U) <=> (tptp_fun_Z_4(U, X) = X))) | (~(member(tptp_fun_Z_5(V, Y), V) <=> (tptp_fun_Z_5(V, Y) = Y))))),
% 0.47/0.66 inference(quant_intro,[status(thm)],[357])).
% 0.47/0.66 tff(359,plain,
% 0.47/0.66 (![X: option, Y: option, U: option_set, V: option_set] : ((~better(U, V)) | (~(![Z: option] : (member(Z, U) <=> (Z = X)) & ![Z: option] : (member(Z, V) <=> (Z = Y))))) <=> ![X: option, Y: option, U: option_set, V: option_set] : ((~better(U, V)) | (~(![Z: option] : (member(Z, U) <=> (Z = X)) & ![Z: option] : (member(Z, V) <=> (Z = Y)))))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(360,plain,
% 0.47/0.66 (^[X: option, Y: option, U: option_set, V: option_set] : trans(monotonicity(rewrite((![Z: option] : (member(Z, U) <=> (Z = X)) & ![Z: option] : (member(Z, V) <=> (Z = Y))) <=> (![Z: option] : (member(Z, U) <=> (Z = X)) & ![Z: option] : (member(Z, V) <=> (Z = Y)))), (((![Z: option] : (member(Z, U) <=> (Z = X)) & ![Z: option] : (member(Z, V) <=> (Z = Y))) => (~better(U, V))) <=> ((![Z: option] : (member(Z, U) <=> (Z = X)) & ![Z: option] : (member(Z, V) <=> (Z = Y))) => (~better(U, V))))), rewrite(((![Z: option] : (member(Z, U) <=> (Z = X)) & ![Z: option] : (member(Z, V) <=> (Z = Y))) => (~better(U, V))) <=> ((~better(U, V)) | (~(![Z: option] : (member(Z, U) <=> (Z = X)) & ![Z: option] : (member(Z, V) <=> (Z = Y)))))), (((![Z: option] : (member(Z, U) <=> (Z = X)) & ![Z: option] : (member(Z, V) <=> (Z = Y))) => (~better(U, V))) <=> ((~better(U, V)) | (~(![Z: option] : (member(Z, U) <=> (Z = X)) & ![Z: option] : (member(Z, V) <=> (Z = Y)))))))),
% 0.47/0.66 inference(bind,[status(th)],[])).
% 0.47/0.66 tff(361,plain,
% 0.47/0.66 (![X: option, Y: option, U: option_set, V: option_set] : ((![Z: option] : (member(Z, U) <=> (Z = X)) & ![Z: option] : (member(Z, V) <=> (Z = Y))) => (~better(U, V))) <=> ![X: option, Y: option, U: option_set, V: option_set] : ((~better(U, V)) | (~(![Z: option] : (member(Z, U) <=> (Z = X)) & ![Z: option] : (member(Z, V) <=> (Z = Y)))))),
% 0.47/0.66 inference(quant_intro,[status(thm)],[360])).
% 0.47/0.66 tff(362,axiom,(![X: option, Y: option, U: option_set, V: option_set] : ((![Z: option] : (member(Z, U) <=> (Z = X)) & ![Z: option] : (member(Z, V) <=> (Z = Y))) => (~better(U, V)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','parity_of_no_choice_situations')).
% 0.47/0.66 tff(363,plain,
% 0.47/0.66 (![X: option, Y: option, U: option_set, V: option_set] : ((~better(U, V)) | (~(![Z: option] : (member(Z, U) <=> (Z = X)) & ![Z: option] : (member(Z, V) <=> (Z = Y)))))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[362, 361])).
% 0.47/0.66 tff(364,plain,
% 0.47/0.66 (![X: option, Y: option, U: option_set, V: option_set] : ((~better(U, V)) | (~(![Z: option] : (member(Z, U) <=> (Z = X)) & ![Z: option] : (member(Z, V) <=> (Z = Y)))))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[363, 359])).
% 0.47/0.66 tff(365,plain,(
% 0.47/0.66 ![X: option, Y: option, U: option_set, V: option_set] : ((~better(U, V)) | ((~(member(tptp_fun_Z_4(U, X), U) <=> (tptp_fun_Z_4(U, X) = X))) | (~(member(tptp_fun_Z_5(V, Y), V) <=> (tptp_fun_Z_5(V, Y) = Y)))))),
% 0.47/0.66 inference(skolemize,[status(sab)],[364])).
% 0.47/0.66 tff(366,plain,
% 0.47/0.66 (![X: option, Y: option, U: option_set, V: option_set] : ((~better(U, V)) | (~(member(tptp_fun_Z_4(U, X), U) <=> (tptp_fun_Z_4(U, X) = X))) | (~(member(tptp_fun_Z_5(V, Y), V) <=> (tptp_fun_Z_5(V, Y) = Y))))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[365, 358])).
% 0.47/0.66 tff(367,plain,
% 0.47/0.66 (((~![X: option, Y: option, U: option_set, V: option_set] : ((~better(U, V)) | (~(member(tptp_fun_Z_4(U, X), U) <=> (tptp_fun_Z_4(U, X) = X))) | (~(member(tptp_fun_Z_5(V, Y), V) <=> (tptp_fun_Z_5(V, Y) = Y))))) | ((~better(B!8, A!9)) | (~(member(tptp_fun_Z_4(B!8, Z!10), B!8) <=> (tptp_fun_Z_4(B!8, Z!10) = Z!10))) | (~(member(tptp_fun_Z_5(A!9, X!12), A!9) <=> (tptp_fun_Z_5(A!9, X!12) = X!12))))) <=> ((~![X: option, Y: option, U: option_set, V: option_set] : ((~better(U, V)) | (~(member(tptp_fun_Z_4(U, X), U) <=> (tptp_fun_Z_4(U, X) = X))) | (~(member(tptp_fun_Z_5(V, Y), V) <=> (tptp_fun_Z_5(V, Y) = Y))))) | (~better(B!8, A!9)) | (~(member(tptp_fun_Z_4(B!8, Z!10), B!8) <=> (tptp_fun_Z_4(B!8, Z!10) = Z!10))) | (~(member(tptp_fun_Z_5(A!9, X!12), A!9) <=> (tptp_fun_Z_5(A!9, X!12) = X!12))))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(368,plain,
% 0.47/0.66 ((~![X: option, Y: option, U: option_set, V: option_set] : ((~better(U, V)) | (~(member(tptp_fun_Z_4(U, X), U) <=> (tptp_fun_Z_4(U, X) = X))) | (~(member(tptp_fun_Z_5(V, Y), V) <=> (tptp_fun_Z_5(V, Y) = Y))))) | ((~better(B!8, A!9)) | (~(member(tptp_fun_Z_4(B!8, Z!10), B!8) <=> (tptp_fun_Z_4(B!8, Z!10) = Z!10))) | (~(member(tptp_fun_Z_5(A!9, X!12), A!9) <=> (tptp_fun_Z_5(A!9, X!12) = X!12))))),
% 0.47/0.66 inference(quant_inst,[status(thm)],[])).
% 0.47/0.66 tff(369,plain,
% 0.47/0.66 ((~![X: option, Y: option, U: option_set, V: option_set] : ((~better(U, V)) | (~(member(tptp_fun_Z_4(U, X), U) <=> (tptp_fun_Z_4(U, X) = X))) | (~(member(tptp_fun_Z_5(V, Y), V) <=> (tptp_fun_Z_5(V, Y) = Y))))) | (~better(B!8, A!9)) | (~(member(tptp_fun_Z_4(B!8, Z!10), B!8) <=> (tptp_fun_Z_4(B!8, Z!10) = Z!10))) | (~(member(tptp_fun_Z_5(A!9, X!12), A!9) <=> (tptp_fun_Z_5(A!9, X!12) = X!12)))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[368, 367])).
% 0.47/0.66 tff(370,plain,
% 0.47/0.66 (~(member(tptp_fun_Z_4(B!8, Z!10), B!8) <=> (tptp_fun_Z_4(B!8, Z!10) = Z!10))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[369, 366, 356, 16])).
% 0.47/0.66 tff(371,plain,
% 0.47/0.66 ((~![U: option] : (member(U, B!8) <=> (U = Z!10))) | (member(tptp_fun_Z_4(B!8, Z!10), B!8) <=> (tptp_fun_Z_4(B!8, Z!10) = Z!10))),
% 0.47/0.66 inference(quant_inst,[status(thm)],[])).
% 0.47/0.66 tff(372,plain,
% 0.47/0.66 ($false),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[371, 200, 370])).
% 0.47/0.66 % SZS output end Proof
% 0.47/0.67 % E exiting
%------------------------------------------------------------------------------