%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL447-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 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 : Fri Sep 25 02:02:04 PM UTC 2026
% Result : Unsatisfiable 6.21s 6.27s
% Output : Proof 6.21s
% Verified :
% Comments :
%------------------------------------------------------------------------------
cnf(t4,axiom,
sFlat0 = c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),
introduced(definition) ).
cnf(t29,plain,
c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a) = sFlat0,
inference(orient,[status(thm)],[t4]) ).
cnf(t5,axiom,
sFlat1 = c_PropLog_Othms(v_H,t_a),
introduced(definition) ).
cnf(t23,plain,
c_PropLog_Othms(v_H,t_a) = sFlat1,
inference(orient,[status(thm)],[t5]) ).
cnf(t6,axiom,
sFlat2 = tc_PropLog_Opl(t_a),
introduced(definition) ).
cnf(t17,plain,
tc_PropLog_Opl(t_a) = sFlat2,
inference(orient,[status(thm)],[t6]) ).
cnf(t7,axiom,
sFlat3 = c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
introduced(definition) ).
cnf(t73,plain,
sFlat3 = c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),sFlat1,tc_PropLog_Opl(t_a)),
inference(step,[status(thm)],[t7,t23]) ).
cnf(t74,plain,
sFlat3 = c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),sFlat1,sFlat2),
inference(step,[status(thm)],[t73,t17]) ).
cnf(t28,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),sFlat1,sFlat2) = sFlat3,
inference(orient,[status(thm)],[t74]) ).
cnf(t75,plain,
c_in(sFlat0,sFlat1,sFlat2) = sFlat3,
inference(step,[status(thm)],[t28,t29]) ).
cnf(t32,plain,
c_in(sFlat0,sFlat1,sFlat2) = sFlat3,
inference(rw,[status(thm)],[t75]) ).
cnf(t33,plain,
c_in(sFlat0,sFlat1,sFlat2) = sFlat3,
inference(orient,[status(thm)],[t32]) ).
cnf(f3,axiom,
( c_in(V_q,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(V_p,V_q,T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
| ~ c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Othms_OMP_0) ).
fof(f3_nnf,plain,
! [V_p,V_H,T_a,V_q] :
( c_in(V_q,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(V_p,V_q,T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
| ~ c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [V_p,V_H,T_a,V_q] :
( c_in(V_q,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(V_p,V_q,T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
| ~ c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( c_in(X3,c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(X0,X3,X2),c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2))
| ~ c_in(X0,c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2)) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t3,plain,
ifeq(c_in(X1,c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3)),true,ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(X1,X4,X3),c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3)),true,c_in(X4,c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3)),true),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t11,plain,
ifeq(c_in(X1,c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3)),true,ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(X1,X4,X3),c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3)),true,c_in(X4,c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3)),true),true) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(f2,axiom,
c_in(c_PropLog_Opl_Oop_A_N_62(V_p,c_PropLog_Opl_Oop_A_N_62(V_q,V_p,T_a),T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Othms_OK_0) ).
fof(f2_nnf,plain,
! [V_p,V_q,T_a,V_H] : c_in(c_PropLog_Opl_Oop_A_N_62(V_p,c_PropLog_Opl_Oop_A_N_62(V_q,V_p,T_a),T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [V_p,V_q,T_a,V_H] : c_in(c_PropLog_Opl_Oop_A_N_62(V_p,c_PropLog_Opl_Oop_A_N_62(V_q,V_p,T_a),T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(X0,c_PropLog_Opl_Oop_A_N_62(X1,X0,X2),X2),c_PropLog_Othms(X3,X2),tc_PropLog_Opl(X2)),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t2,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(X1,c_PropLog_Opl_Oop_A_N_62(X2,X1,X3),X3),c_PropLog_Othms(X4,X3),tc_PropLog_Opl(X3)) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t9,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(X1,c_PropLog_Opl_Oop_A_N_62(X2,X1,X3),X3),c_PropLog_Othms(X4,X3),tc_PropLog_Opl(X3)) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(t14,plain,
true = ifeq(c_in(X1,c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3)),true,ifeq(true,true,c_in(c_PropLog_Opl_Oop_A_N_62(X4,X1,X3),c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3)),true),true),
inference(cp,[status(thm)],[t11,t9]) ).
cnf(t0,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t8,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t0]) ).
cnf(t79,plain,
true = ifeq(c_in(X1,c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3)),true,c_in(c_PropLog_Opl_Oop_A_N_62(X4,X1,X3),c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3)),true),
inference(step,[status(thm)],[t14,t8]) ).
cnf(t40,plain,
ifeq(c_in(X1,c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3)),true,c_in(c_PropLog_Opl_Oop_A_N_62(X4,X1,X3),c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3)),true) = true,
inference(orient,[status(thm)],[t79]) ).
cnf(t42,plain,
true = ifeq(c_in(X1,sFlat1,tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Oop_A_N_62(X2,X1,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true),
inference(cp,[status(thm)],[t40,t23]) ).
cnf(t80,plain,
true = ifeq(c_in(X1,sFlat1,sFlat2),true,c_in(c_PropLog_Opl_Oop_A_N_62(X2,X1,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true),
inference(step,[status(thm)],[t42,t17]) ).
cnf(t81,plain,
true = ifeq(c_in(X1,sFlat1,sFlat2),true,c_in(c_PropLog_Opl_Oop_A_N_62(X2,X1,t_a),sFlat1,tc_PropLog_Opl(t_a)),true),
inference(step,[status(thm)],[t80,t23]) ).
cnf(t82,plain,
true = ifeq(c_in(X1,sFlat1,sFlat2),true,c_in(c_PropLog_Opl_Oop_A_N_62(X2,X1,t_a),sFlat1,sFlat2),true),
inference(step,[status(thm)],[t81,t17]) ).
cnf(t48,plain,
ifeq(c_in(X1,sFlat1,sFlat2),true,c_in(c_PropLog_Opl_Oop_A_N_62(X2,X1,t_a),sFlat1,sFlat2),true) = true,
inference(orient,[status(thm)],[t82]) ).
cnf(t55,plain,
true = ifeq(c_in(v_q,sFlat1,sFlat2),true,c_in(sFlat0,sFlat1,sFlat2),true),
inference(cp,[status(thm)],[t48,t29]) ).
cnf(f0,negated_conjecture,
c_in(v_q,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f0_nnf,plain,
c_in(v_q,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(nnf_transformation,[status(thm)],[f0]) ).
cnf(c0,plain,
c_in(v_q,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(cnf_transformation,[status(esa)],[f0_nnf]) ).
cnf(t1,plain,
c_in(v_q,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t10,plain,
c_in(v_q,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(t72,plain,
c_in(v_q,c_PropLog_Othms(v_H,t_a),sFlat2) = true,
inference(step,[status(thm)],[t10,t17]) ).
cnf(t22,plain,
c_in(v_q,c_PropLog_Othms(v_H,t_a),sFlat2) = true,
inference(rw,[status(thm)],[t72]) ).
cnf(t76,plain,
c_in(v_q,sFlat1,sFlat2) = true,
inference(step,[status(thm)],[t22,t23]) ).
cnf(t34,plain,
c_in(v_q,sFlat1,sFlat2) = true,
inference(orient,[status(thm)],[t76]) ).
cnf(t83,plain,
true = ifeq(true,true,c_in(sFlat0,sFlat1,sFlat2),true),
inference(step,[status(thm)],[t55,t34]) ).
cnf(t84,plain,
true = c_in(sFlat0,sFlat1,sFlat2),
inference(step,[status(thm)],[t83,t8]) ).
cnf(t85,plain,
true = sFlat3,
inference(step,[status(thm)],[t84,t33]) ).
cnf(t56,plain,
true = sFlat3,
inference(orient,[status(thm)],[t85]) ).
cnf(f1,negated_conjecture,
~ c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f1_nnf,plain,
~ c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
~ c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
~ c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(goal_0,negated_conjecture,
c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) != true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(g0_0,plain,
c_in(sFlat0,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) != true,
inference(rw,[status(thm)],[goal_0,t29]) ).
cnf(g0_1,plain,
c_in(sFlat0,sFlat1,tc_PropLog_Opl(t_a)) != true,
inference(rw,[status(thm)],[g0_0,t23]) ).
cnf(g0_2,plain,
c_in(sFlat0,sFlat1,sFlat2) != true,
inference(rw,[status(thm)],[g0_1,t17]) ).
cnf(g0_3,plain,
sFlat3 != true,
inference(rw,[status(thm)],[g0_2,t33]) ).
cnf(g0_4,plain,
sFlat3 != sFlat3,
inference(rw,[status(thm)],[g0_3,t56]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL447-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/5.39 % Computer : n017.cluster.edu
% 0.11/5.39 % Model : x86_64 x86_64
% 0.11/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.39 % Memory : 8046.5625MB
% 0.11/5.39 % OS : Linux 6.8.0-71-generic
% 0.11/5.39 % CPULimit : 300
% 0.11/5.39 % WCLimit : 300
% 0.11/5.39 % DateTime : Wed Sep 23 23:20:37 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.39 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.21/6.27 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.21/6.27 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------