%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV383+1 : TPTP v9.0.0. Released v3.3.0.
% 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 05:32:20 AM UTC 2025
% Result : Theorem 0.24s 0.42s
% Output : Proof 0.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.15 % Problem : SWV383+1 : TPTP v9.0.0. Released v3.3.0.
% 0.04/0.15 % Command : run_E %s %d THM
% 0.15/0.37 % Computer : n016.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Fri Jun 20 09:45:02 EDT 2025
% 0.15/0.37 % CPUTime :
% 0.24/0.42 % SZS status Theorem
% 0.24/0.42 % SZS output start Proof
% 0.24/0.42 tff(succ_cpq_type, type, (
% 0.24/0.42 succ_cpq: ( $i * $i ) > $o)).
% 0.24/0.42 tff(triple_type, type, (
% 0.24/0.42 triple: ( $i * $i * $i ) > $i)).
% 0.24/0.42 tff(tptp_fun_W_0_type, type, (
% 0.24/0.42 tptp_fun_W_0: $i)).
% 0.24/0.42 tff(tptp_fun_V_1_type, type, (
% 0.24/0.42 tptp_fun_V_1: $i)).
% 0.24/0.42 tff(tptp_fun_U_2_type, type, (
% 0.24/0.42 tptp_fun_U_2: $i)).
% 0.24/0.42 tff(check_cpq_type, type, (
% 0.24/0.42 check_cpq: $i > $o)).
% 0.24/0.42 tff(ok_type, type, (
% 0.24/0.42 ok: $i > $o)).
% 0.24/0.42 tff(tptp_fun_Z_3_type, type, (
% 0.24/0.42 tptp_fun_Z_3: $i)).
% 0.24/0.42 tff(tptp_fun_Y_4_type, type, (
% 0.24/0.42 tptp_fun_Y_4: $i)).
% 0.24/0.42 tff(tptp_fun_X_5_type, type, (
% 0.24/0.42 tptp_fun_X_5: $i)).
% 0.24/0.42 tff(1,plain,
% 0.24/0.42 ((~((~ok(triple(X!5, Y!4, Z!3))) | (~check_cpq(triple(X!5, Y!4, Z!3))) | (~succ_cpq(triple(U!2, V!1, W!0), triple(X!5, Y!4, Z!3))))) <=> (~((~ok(triple(X!5, Y!4, Z!3))) | (~check_cpq(triple(X!5, Y!4, Z!3))) | (~succ_cpq(triple(U!2, V!1, W!0), triple(X!5, Y!4, Z!3)))))),
% 0.24/0.42 inference(rewrite,[status(thm)],[])).
% 0.24/0.42 tff(2,plain,
% 0.24/0.42 (((~check_cpq(triple(U!2, V!1, W!0))) & (~((~ok(triple(X!5, Y!4, Z!3))) | (~check_cpq(triple(X!5, Y!4, Z!3))) | (~succ_cpq(triple(U!2, V!1, W!0), triple(X!5, Y!4, Z!3)))))) <=> ((~check_cpq(triple(U!2, V!1, W!0))) & (~((~ok(triple(X!5, Y!4, Z!3))) | (~check_cpq(triple(X!5, Y!4, Z!3))) | (~succ_cpq(triple(U!2, V!1, W!0), triple(X!5, Y!4, Z!3))))))),
% 0.24/0.42 inference(monotonicity,[status(thm)],[1])).
% 0.24/0.42 tff(3,plain,
% 0.24/0.42 ((~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z)))))) <=> (~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z))))))),
% 0.24/0.42 inference(rewrite,[status(thm)],[])).
% 0.24/0.42 tff(4,plain,
% 0.24/0.42 ((~![U: $i, V: $i, W: $i] : ((~check_cpq(triple(U, V, W))) => ![X: $i, Y: $i, Z: $i] : (succ_cpq(triple(U, V, W), triple(X, Y, Z)) => ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))))))) <=> (~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z))))))),
% 0.24/0.42 inference(rewrite,[status(thm)],[])).
% 0.24/0.42 tff(5,axiom,(~![U: $i, V: $i, W: $i] : ((~check_cpq(triple(U, V, W))) => ![X: $i, Y: $i, Z: $i] : (succ_cpq(triple(U, V, W), triple(X, Y, Z)) => ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l19_co')).
% 0.24/0.42 tff(6,plain,
% 0.24/0.42 (~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z)))))),
% 0.24/0.42 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.24/0.42 tff(7,plain,
% 0.24/0.42 (~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z)))))),
% 0.24/0.42 inference(modus_ponens,[status(thm)],[6, 3])).
% 0.24/0.42 tff(8,plain,
% 0.24/0.42 (~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z)))))),
% 0.24/0.42 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.24/0.42 tff(9,plain,
% 0.24/0.42 (~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z)))))),
% 0.24/0.42 inference(modus_ponens,[status(thm)],[8, 3])).
% 0.24/0.42 tff(10,plain,
% 0.24/0.42 ((~check_cpq(triple(U!2, V!1, W!0))) & (~((~ok(triple(X!5, Y!4, Z!3))) | (~check_cpq(triple(X!5, Y!4, Z!3))) | (~succ_cpq(triple(U!2, V!1, W!0), triple(X!5, Y!4, Z!3)))))),
% 0.24/0.42 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.24/0.42 tff(11,plain,
% 0.24/0.42 (~check_cpq(triple(U!2, V!1, W!0))),
% 0.24/0.42 inference(and_elim,[status(thm)],[10])).
% 0.24/0.42 tff(12,plain,
% 0.24/0.42 (((~check_cpq(triple(U!2, V!1, W!0))) | (~ok(triple(U!2, V!1, W!0)))) | check_cpq(triple(U!2, V!1, W!0))),
% 0.24/0.42 inference(tautology,[status(thm)],[])).
% 0.24/0.42 tff(13,plain,
% 0.24/0.42 ((~check_cpq(triple(U!2, V!1, W!0))) | (~ok(triple(U!2, V!1, W!0)))),
% 0.24/0.42 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.24/0.42 tff(14,plain,
% 0.24/0.42 (^[U: $i, V: $i, W: $i] : refl(((~((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W))))) | ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z))))) <=> ((~((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W))))) | ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z))))))),
% 0.24/0.42 inference(bind,[status(th)],[])).
% 0.24/0.42 tff(15,plain,
% 0.24/0.42 (![U: $i, V: $i, W: $i] : ((~((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W))))) | ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z))))) <=> ![U: $i, V: $i, W: $i] : ((~((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W))))) | ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z)))))),
% 0.24/0.42 inference(quant_intro,[status(thm)],[14])).
% 0.24/0.42 tff(16,plain,
% 0.24/0.42 (^[U: $i, V: $i, W: $i] : rewrite(((~((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W))))) | ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z))))) <=> ((~((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W))))) | ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z))))))),
% 0.24/0.42 inference(bind,[status(th)],[])).
% 0.24/0.42 tff(17,plain,
% 0.24/0.42 (![U: $i, V: $i, W: $i] : ((~((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W))))) | ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z))))) <=> ![U: $i, V: $i, W: $i] : ((~((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W))))) | ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z)))))),
% 0.24/0.42 inference(quant_intro,[status(thm)],[16])).
% 0.24/0.42 tff(18,plain,
% 0.24/0.42 (![U: $i, V: $i, W: $i] : ((~((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W))))) | ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z))))) <=> ![U: $i, V: $i, W: $i] : ((~((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W))))) | ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z)))))),
% 0.24/0.42 inference(transitivity,[status(thm)],[17, 15])).
% 0.24/0.42 tff(19,plain,
% 0.24/0.42 (![U: $i, V: $i, W: $i] : ((~((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W))))) | ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z))))) <=> ![U: $i, V: $i, W: $i] : ((~((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W))))) | ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z)))))),
% 0.24/0.42 inference(rewrite,[status(thm)],[])).
% 0.24/0.42 tff(20,plain,
% 0.24/0.42 (^[U: $i, V: $i, W: $i] : trans(monotonicity(quant_intro(proof_bind(^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite(((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z)))) <=> ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))))), ((succ_cpq(triple(U, V, W), triple(X, Y, Z)) => ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))))) <=> (succ_cpq(triple(U, V, W), triple(X, Y, Z)) => ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))))))), rewrite((succ_cpq(triple(U, V, W), triple(X, Y, Z)) => ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))))) <=> ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z))))), ((succ_cpq(triple(U, V, W), triple(X, Y, Z)) => ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))))) <=> ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z))))))), (![X: $i, Y: $i, Z: $i] : (succ_cpq(triple(U, V, W), triple(X, Y, Z)) => ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))))) <=> ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z)))))), ((((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W)))) => ![X: $i, Y: $i, Z: $i] : (succ_cpq(triple(U, V, W), triple(X, Y, Z)) => ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z)))))) <=> (((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W)))) => ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z))))))), rewrite((((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W)))) => ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z))))) <=> ((~((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W))))) | ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z)))))), ((((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W)))) => ![X: $i, Y: $i, Z: $i] : (succ_cpq(triple(U, V, W), triple(X, Y, Z)) => ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z)))))) <=> ((~((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W))))) | ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z)))))))),
% 0.24/0.42 inference(bind,[status(th)],[])).
% 0.24/0.42 tff(21,plain,
% 0.24/0.42 (![U: $i, V: $i, W: $i] : (((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W)))) => ![X: $i, Y: $i, Z: $i] : (succ_cpq(triple(U, V, W), triple(X, Y, Z)) => ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z)))))) <=> ![U: $i, V: $i, W: $i] : ((~((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W))))) | ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z)))))),
% 0.24/0.42 inference(quant_intro,[status(thm)],[20])).
% 0.24/0.42 tff(22,axiom,(![U: $i, V: $i, W: $i] : (((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W)))) => ![X: $i, Y: $i, Z: $i] : (succ_cpq(triple(U, V, W), triple(X, Y, Z)) => ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l19_l20')).
% 0.24/0.42 tff(23,plain,
% 0.24/0.42 (![U: $i, V: $i, W: $i] : ((~((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W))))) | ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z)))))),
% 0.24/0.42 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.24/0.42 tff(24,plain,
% 0.24/0.42 (![U: $i, V: $i, W: $i] : ((~((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W))))) | ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z)))))),
% 0.24/0.42 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.24/0.42 tff(25,plain,(
% 0.24/0.42 ![U: $i, V: $i, W: $i] : ((~((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W))))) | ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z)))))),
% 0.24/0.42 inference(skolemize,[status(sab)],[24])).
% 0.24/0.42 tff(26,plain,
% 0.24/0.42 (![U: $i, V: $i, W: $i] : ((~((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W))))) | ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z)))))),
% 0.24/0.42 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.24/0.42 tff(27,plain,
% 0.24/0.42 (((~![U: $i, V: $i, W: $i] : ((~((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W))))) | ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z)))))) | ((~((~check_cpq(triple(U!2, V!1, W!0))) | (~ok(triple(U!2, V!1, W!0))))) | ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U!2, V!1, W!0), triple(X, Y, Z)))))) <=> ((~![U: $i, V: $i, W: $i] : ((~((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W))))) | ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z)))))) | (~((~check_cpq(triple(U!2, V!1, W!0))) | (~ok(triple(U!2, V!1, W!0))))) | ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U!2, V!1, W!0), triple(X, Y, Z)))))),
% 0.24/0.43 inference(rewrite,[status(thm)],[])).
% 0.24/0.43 tff(28,plain,
% 0.24/0.43 ((~![U: $i, V: $i, W: $i] : ((~((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W))))) | ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z)))))) | ((~((~check_cpq(triple(U!2, V!1, W!0))) | (~ok(triple(U!2, V!1, W!0))))) | ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U!2, V!1, W!0), triple(X, Y, Z)))))),
% 0.24/0.43 inference(quant_inst,[status(thm)],[])).
% 0.24/0.43 tff(29,plain,
% 0.24/0.43 ((~![U: $i, V: $i, W: $i] : ((~((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W))))) | ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z)))))) | (~((~check_cpq(triple(U!2, V!1, W!0))) | (~ok(triple(U!2, V!1, W!0))))) | ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U!2, V!1, W!0), triple(X, Y, Z))))),
% 0.24/0.43 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.24/0.43 tff(30,plain,
% 0.24/0.43 (![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U!2, V!1, W!0), triple(X, Y, Z))))),
% 0.24/0.43 inference(unit_resolution,[status(thm)],[29, 26, 13])).
% 0.24/0.43 tff(31,plain,
% 0.24/0.43 (~((~ok(triple(X!5, Y!4, Z!3))) | (~check_cpq(triple(X!5, Y!4, Z!3))) | (~succ_cpq(triple(U!2, V!1, W!0), triple(X!5, Y!4, Z!3))))),
% 0.24/0.43 inference(and_elim,[status(thm)],[10])).
% 0.24/0.43 tff(32,plain,
% 0.24/0.43 (succ_cpq(triple(U!2, V!1, W!0), triple(X!5, Y!4, Z!3))),
% 0.24/0.43 inference(or_elim,[status(thm)],[31])).
% 0.24/0.43 tff(33,plain,
% 0.24/0.43 (check_cpq(triple(X!5, Y!4, Z!3))),
% 0.24/0.43 inference(or_elim,[status(thm)],[31])).
% 0.24/0.43 tff(34,plain,
% 0.24/0.43 (ok(triple(X!5, Y!4, Z!3))),
% 0.24/0.43 inference(or_elim,[status(thm)],[31])).
% 0.24/0.43 tff(35,plain,
% 0.24/0.43 (((~![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U!2, V!1, W!0), triple(X, Y, Z))))) | ((~ok(triple(X!5, Y!4, Z!3))) | (~check_cpq(triple(X!5, Y!4, Z!3))) | (~succ_cpq(triple(U!2, V!1, W!0), triple(X!5, Y!4, Z!3))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U!2, V!1, W!0), triple(X, Y, Z))))) | (~ok(triple(X!5, Y!4, Z!3))) | (~check_cpq(triple(X!5, Y!4, Z!3))) | (~succ_cpq(triple(U!2, V!1, W!0), triple(X!5, Y!4, Z!3))))),
% 0.24/0.43 inference(rewrite,[status(thm)],[])).
% 0.24/0.43 tff(36,plain,
% 0.24/0.43 ((~![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U!2, V!1, W!0), triple(X, Y, Z))))) | ((~ok(triple(X!5, Y!4, Z!3))) | (~check_cpq(triple(X!5, Y!4, Z!3))) | (~succ_cpq(triple(U!2, V!1, W!0), triple(X!5, Y!4, Z!3))))),
% 0.24/0.43 inference(quant_inst,[status(thm)],[])).
% 0.24/0.43 tff(37,plain,
% 0.24/0.43 ((~![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U!2, V!1, W!0), triple(X, Y, Z))))) | (~ok(triple(X!5, Y!4, Z!3))) | (~check_cpq(triple(X!5, Y!4, Z!3))) | (~succ_cpq(triple(U!2, V!1, W!0), triple(X!5, Y!4, Z!3)))),
% 0.24/0.43 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.24/0.43 tff(38,plain,
% 0.24/0.43 ($false),
% 0.24/0.43 inference(unit_resolution,[status(thm)],[37, 34, 33, 32, 30])).
% 0.24/0.43 % SZS output end Proof
% 0.24/0.43 % E exiting
%------------------------------------------------------------------------------