%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL430-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:49:50 AM UTC 2026
% Result : Unsatisfiable 0.18s 0.48s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL430-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.39 % Computer : n017.cluster.edu
% 0.09/0.39 % Model : x86_64 x86_64
% 0.09/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.39 % Memory : 8046.5625MB
% 0.09/0.39 % OS : Linux 6.8.0-71-generic
% 0.09/0.39 % CPULimit : 300
% 0.09/0.39 % WCLimit : 300
% 0.09/0.39 % DateTime : Sun Sep 27 15:38:04 UTC 2026
% 0.09/0.39 % CPUTime :
% 0.09/0.39 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.48 Command-line arguments: --no-flatten-goal
% 0.18/0.48
% 0.18/0.48 % SZS status Unsatisfiable
% 0.18/0.48
% 0.18/0.50 % SZS output start Proof
% 0.18/0.50 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.18/0.50 Axiom 2 (cls_conjecture_3): c_in(v_p, c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p, X, t_a), v_F, tc_set(tc_PropLog_Opl(t_a))), t_a), tc_PropLog_Opl(t_a)) = true.
% 0.18/0.50 Axiom 3 (cls_PropLog_Oinsert__Diff__same_0): c_lessequals(c_minus(X, Y, tc_set(Z)), c_insert(W, c_minus(X, c_insert(W, Y, Z), tc_set(Z)), Z), tc_set(Z)) = true.
% 0.18/0.50 Axiom 4 (cls_PropLog_Oweaken__left_0): ifeq(c_lessequals(X, Y, tc_set(tc_PropLog_Opl(Z))), true, ifeq(c_in(W, c_PropLog_Othms(X, Z), tc_PropLog_Opl(Z)), true, c_in(W, c_PropLog_Othms(Y, Z), tc_PropLog_Opl(Z)), true), true) = true.
% 0.18/0.50 Axiom 5 (cls_PropLog_Oinsert__Diff__subset2_0): c_lessequals(c_minus(c_insert(X, c_minus(Y, c_insert(Z, c_emptyset, W), tc_set(W)), W), V, tc_set(W)), c_insert(X, c_minus(Y, c_insert(Z, V, W), tc_set(W)), W), tc_set(W)) = true.
% 0.18/0.50 Axiom 6 (cls_PropLog_Ohyps__insert_0): c_lessequals(c_PropLog_Ohyps(X, c_insert(Y, Z, W), W), c_insert(c_PropLog_Opl_Ovar(Y, W), c_minus(c_PropLog_Ohyps(X, Z, W), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(Y, W), c_PropLog_Opl_Ofalse, W), c_emptyset, tc_PropLog_Opl(W)), tc_set(tc_PropLog_Opl(W))), tc_PropLog_Opl(W)), tc_set(tc_PropLog_Opl(W))) = true.
% 0.18/0.50 Axiom 7 (cls_PropLog_ODiff__weaken__left_0): ifeq(c_lessequals(X, Y, tc_set(tc_PropLog_Opl(Z))), true, ifeq(c_in(W, c_PropLog_Othms(c_minus(X, V, tc_set(tc_PropLog_Opl(Z))), Z), tc_PropLog_Opl(Z)), true, c_in(W, c_PropLog_Othms(c_minus(Y, V, tc_set(tc_PropLog_Opl(Z))), Z), tc_PropLog_Opl(Z)), true), true) = true.
% 0.18/0.50 Axiom 8 (cls_PropLog_Othms__excluded__middle__rule_0): ifeq(c_in(X, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(Y, c_PropLog_Opl_Ofalse, Z), W, tc_PropLog_Opl(Z)), Z), tc_PropLog_Opl(Z)), true, ifeq(c_in(X, c_PropLog_Othms(c_insert(Y, W, tc_PropLog_Opl(Z)), Z), tc_PropLog_Opl(Z)), true, c_in(X, c_PropLog_Othms(W, Z), tc_PropLog_Opl(Z)), true), true) = true.
% 0.18/0.50
% 0.18/0.50 Goal 1 (cls_conjecture_5): c_in(v_p, c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), t_a), tc_PropLog_Opl(t_a)) = true.
% 0.18/0.50 Proof:
% 0.18/0.50 c_in(v_p, c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), t_a), tc_PropLog_Opl(t_a))
% 0.18/0.50 = { by axiom 1 (ifeq_axiom) R->L }
% 0.18/0.50 ifeq(true, true, c_in(v_p, c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), t_a), tc_PropLog_Opl(t_a)), true)
% 0.18/0.50 = { by axiom 1 (ifeq_axiom) R->L }
% 0.18/0.50 ifeq(true, true, ifeq(true, true, c_in(v_p, c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), t_a), tc_PropLog_Opl(t_a)), true), true)
% 0.18/0.50 = { by axiom 4 (cls_PropLog_Oweaken__left_0) R->L }
% 0.18/0.50 ifeq(ifeq(c_lessequals(c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), v_F, tc_set(tc_PropLog_Opl(t_a))), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), true, ifeq(c_in(v_p, c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), v_F, tc_set(tc_PropLog_Opl(t_a))), t_a), tc_PropLog_Opl(t_a)), true, c_in(v_p, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true), true), true, ifeq(true, true, c_in(v_p, c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), t_a), tc_PropLog_Opl(t_a)), true), true)
% 0.18/0.50 = { by axiom 2 (cls_conjecture_3) }
% 0.18/0.50 ifeq(ifeq(c_lessequals(c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), v_F, tc_set(tc_PropLog_Opl(t_a))), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), true, ifeq(true, true, c_in(v_p, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true), true), true, ifeq(true, true, c_in(v_p, c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), t_a), tc_PropLog_Opl(t_a)), true), true)
% 0.18/0.50 = { by axiom 1 (ifeq_axiom) }
% 0.18/0.50 ifeq(ifeq(c_lessequals(c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), v_F, tc_set(tc_PropLog_Opl(t_a))), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), true, c_in(v_p, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true), true, ifeq(true, true, c_in(v_p, c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), t_a), tc_PropLog_Opl(t_a)), true), true)
% 0.18/0.50 = { by axiom 3 (cls_PropLog_Oinsert__Diff__same_0) }
% 0.18/0.50 ifeq(ifeq(true, true, c_in(v_p, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true), true, ifeq(true, true, c_in(v_p, c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), t_a), tc_PropLog_Opl(t_a)), true), true)
% 0.18/0.50 = { by axiom 1 (ifeq_axiom) }
% 0.18/0.50 ifeq(c_in(v_p, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true, ifeq(true, true, c_in(v_p, c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), t_a), tc_PropLog_Opl(t_a)), true), true)
% 0.18/0.50 = { by axiom 4 (cls_PropLog_Oweaken__left_0) R->L }
% 0.18/0.50 ifeq(c_in(v_p, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true, ifeq(ifeq(c_lessequals(c_minus(c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), c_emptyset, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), v_F, tc_set(tc_PropLog_Opl(t_a))), c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), true, ifeq(c_in(v_p, c_PropLog_Othms(c_minus(c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), c_emptyset, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), v_F, tc_set(tc_PropLog_Opl(t_a))), t_a), tc_PropLog_Opl(t_a)), true, c_in(v_p, c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true), true), true, c_in(v_p, c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), t_a), tc_PropLog_Opl(t_a)), true), true)
% 0.18/0.50 = { by axiom 1 (ifeq_axiom) R->L }
% 0.18/0.50 ifeq(c_in(v_p, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true, ifeq(ifeq(c_lessequals(c_minus(c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), c_emptyset, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), v_F, tc_set(tc_PropLog_Opl(t_a))), c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), true, ifeq(ifeq(true, true, c_in(v_p, c_PropLog_Othms(c_minus(c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), c_emptyset, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), v_F, tc_set(tc_PropLog_Opl(t_a))), t_a), tc_PropLog_Opl(t_a)), true), true, c_in(v_p, c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true), true), true, c_in(v_p, c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), t_a), tc_PropLog_Opl(t_a)), true), true)
% 0.18/0.51 = { by axiom 6 (cls_PropLog_Ohyps__insert_0) R->L }
% 0.18/0.51 ifeq(c_in(v_p, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true, ifeq(ifeq(c_lessequals(c_minus(c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), c_emptyset, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), v_F, tc_set(tc_PropLog_Opl(t_a))), c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), true, ifeq(ifeq(c_lessequals(c_PropLog_Ohyps(v_p, c_insert(v_v, v_t, t_a), t_a), c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), c_emptyset, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), true, c_in(v_p, c_PropLog_Othms(c_minus(c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), c_emptyset, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), v_F, tc_set(tc_PropLog_Opl(t_a))), t_a), tc_PropLog_Opl(t_a)), true), true, c_in(v_p, c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true), true), true, c_in(v_p, c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), t_a), tc_PropLog_Opl(t_a)), true), true)
% 0.18/0.51 = { by axiom 1 (ifeq_axiom) R->L }
% 0.18/0.51 ifeq(c_in(v_p, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true, ifeq(ifeq(c_lessequals(c_minus(c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), c_emptyset, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), v_F, tc_set(tc_PropLog_Opl(t_a))), c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), true, ifeq(ifeq(c_lessequals(c_PropLog_Ohyps(v_p, c_insert(v_v, v_t, t_a), t_a), c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), c_emptyset, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), true, ifeq(true, true, c_in(v_p, c_PropLog_Othms(c_minus(c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), c_emptyset, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), v_F, tc_set(tc_PropLog_Opl(t_a))), t_a), tc_PropLog_Opl(t_a)), true), true), true, c_in(v_p, c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true), true), true, c_in(v_p, c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), t_a), tc_PropLog_Opl(t_a)), true), true)
% 0.18/0.51 = { by axiom 2 (cls_conjecture_3) R->L }
% 0.18/0.51 ifeq(c_in(v_p, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true, ifeq(ifeq(c_lessequals(c_minus(c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), c_emptyset, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), v_F, tc_set(tc_PropLog_Opl(t_a))), c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), true, ifeq(ifeq(c_lessequals(c_PropLog_Ohyps(v_p, c_insert(v_v, v_t, t_a), t_a), c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), c_emptyset, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), true, ifeq(c_in(v_p, c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p, c_insert(v_v, v_t, t_a), t_a), v_F, tc_set(tc_PropLog_Opl(t_a))), t_a), tc_PropLog_Opl(t_a)), true, c_in(v_p, c_PropLog_Othms(c_minus(c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), c_emptyset, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), v_F, tc_set(tc_PropLog_Opl(t_a))), t_a), tc_PropLog_Opl(t_a)), true), true), true, c_in(v_p, c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true), true), true, c_in(v_p, c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), t_a), tc_PropLog_Opl(t_a)), true), true)
% 0.18/0.51 = { by axiom 7 (cls_PropLog_ODiff__weaken__left_0) }
% 0.18/0.51 ifeq(c_in(v_p, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true, ifeq(ifeq(c_lessequals(c_minus(c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), c_emptyset, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), v_F, tc_set(tc_PropLog_Opl(t_a))), c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), true, ifeq(true, true, c_in(v_p, c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true), true), true, c_in(v_p, c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), t_a), tc_PropLog_Opl(t_a)), true), true)
% 0.18/0.51 = { by axiom 1 (ifeq_axiom) }
% 0.18/0.51 ifeq(c_in(v_p, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true, ifeq(ifeq(c_lessequals(c_minus(c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), c_emptyset, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), v_F, tc_set(tc_PropLog_Opl(t_a))), c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), true, c_in(v_p, c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true), true, c_in(v_p, c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), t_a), tc_PropLog_Opl(t_a)), true), true)
% 0.18/0.51 = { by axiom 5 (cls_PropLog_Oinsert__Diff__subset2_0) }
% 0.18/0.51 ifeq(c_in(v_p, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true, ifeq(ifeq(true, true, c_in(v_p, c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true), true, c_in(v_p, c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), t_a), tc_PropLog_Opl(t_a)), true), true)
% 0.18/0.51 = { by axiom 1 (ifeq_axiom) }
% 0.18/0.51 ifeq(c_in(v_p, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true, ifeq(c_in(v_p, c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(v_v, t_a), c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true, c_in(v_p, c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p, v_t, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v, t_a), c_PropLog_Opl_Ofalse, t_a), v_F, tc_PropLog_Opl(t_a)), tc_set(tc_PropLog_Opl(t_a))), t_a), tc_PropLog_Opl(t_a)), true), true)
% 0.18/0.51 = { by axiom 8 (cls_PropLog_Othms__excluded__middle__rule_0) }
% 0.18/0.51 true
% 0.18/0.51 % SZS output end Proof
% 0.18/0.51
% 0.18/0.51 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------