%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL444-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n013.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 02:02:03 PM UTC 2026
% Result : Unsatisfiable 148.39s 29.58s
% Output : Proof 148.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 7
% Syntax : Number of formulae : 92 ( 76 unt; 0 def)
% Number of atoms : 112 ( 63 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 46 ( 26 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-4 aty)
% Number of variables : 353 ( 105 sgn 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f4,axiom,
( c_in(V_a,c_insert(V_b,V_B,T_a),T_a)
| ~ c_in(V_a,V_B,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertCI_0) ).
fof(f4_nnf,plain,
! [V_a,V_B,T_a,V_b] :
( c_in(V_a,c_insert(V_b,V_B,T_a),T_a)
| ~ c_in(V_a,V_B,T_a) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [V_a,V_B,T_a,V_b] :
( c_in(V_a,c_insert(V_b,V_B,T_a),T_a)
| ~ c_in(V_a,V_B,T_a) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( c_in(X0,c_insert(X3,X1,X2),X2)
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi4,axiom,
ifeq(c_in(X0,X1,X2),true,c_in(X0,c_insert(X3,X1,X2),X2),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(f5,axiom,
c_in(V_x,c_insert(V_x,V_B,T_a),T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).
fof(f5_nnf,plain,
! [V_x,V_B,T_a] : c_in(V_x,c_insert(V_x,V_B,T_a),T_a),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [V_x,V_B,T_a] : c_in(V_x,c_insert(V_x,V_B,T_a),T_a),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
c_in(X0,c_insert(X0,X1,X2),X2),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi5,axiom,
c_in(X0,c_insert(X0,X1,X2),X2) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(h0,plain,
c_in(V0,c_insert(V1,c_insert(V0,V2,V3),V3),V3) = true,
inference(hyper_resolution,[status(thm)],[hi4,hi5]) ).
cnf(f2,axiom,
( c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
| ~ c_in(V_p,V_H,tc_PropLog_Opl(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Othms_OH_0) ).
fof(f2_nnf,plain,
! [V_p,V_H,T_a] :
( c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
| ~ c_in(V_p,V_H,tc_PropLog_Opl(T_a)) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [V_p,V_H,T_a] :
( c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
| ~ c_in(V_p,V_H,tc_PropLog_Opl(T_a)) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( c_in(X0,c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2))
| ~ c_in(X0,X1,tc_PropLog_Opl(X2)) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
ifeq(c_in(X0,X1,tc_PropLog_Opl(X2)),true,c_in(X0,c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2)),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h3,plain,
c_in(V0,c_PropLog_Othms(c_insert(V1,c_insert(V0,V2,tc_PropLog_Opl(V3)),tc_PropLog_Opl(V3)),V3),tc_PropLog_Opl(V3)) = true,
inference(hyper_resolution,[status(thm)],[hi2,h0]) ).
cnf(h1,plain,
c_in(V0,c_PropLog_Othms(c_insert(V0,V1,tc_PropLog_Opl(V2)),V2),tc_PropLog_Opl(V2)) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi5]) ).
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(hi3,axiom,
ifeq(c_in(X0,c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2)),true,ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(X0,X3,X2),c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2)),true,c_in(X3,c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2)),true),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(h16,plain,
c_in(V0,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(V1,V0,V2),c_insert(V1,V3,tc_PropLog_Opl(V2)),tc_PropLog_Opl(V2)),V2),tc_PropLog_Opl(V2)) = true,
inference(hyper_resolution,[status(thm)],[hi3,h3,h1]) ).
cnf(f0,axiom,
( 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_q,c_PropLog_Othms(c_insert(V_p,V_H,tc_PropLog_Opl(T_a)),T_a),tc_PropLog_Opl(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Odeduction_0) ).
fof(f0_nnf,plain,
! [V_q,V_p,V_H,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_q,c_PropLog_Othms(c_insert(V_p,V_H,tc_PropLog_Opl(T_a)),T_a),tc_PropLog_Opl(T_a)) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [V_q,V_p,V_H,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_q,c_PropLog_Othms(c_insert(V_p,V_H,tc_PropLog_Opl(T_a)),T_a),tc_PropLog_Opl(T_a)) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( c_in(c_PropLog_Opl_Oop_A_N_62(X1,X0,X3),c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3))
| ~ c_in(X0,c_PropLog_Othms(c_insert(X1,X2,tc_PropLog_Opl(X3)),X3),tc_PropLog_Opl(X3)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(c_in(X0,c_PropLog_Othms(c_insert(X1,X2,tc_PropLog_Opl(X3)),X3),tc_PropLog_Opl(X3)),true,c_in(c_PropLog_Opl_Oop_A_N_62(X1,X0,X3),c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3)),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h55,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V0,V1,V2),V1,V2),c_PropLog_Othms(c_insert(V0,V3,tc_PropLog_Opl(V2)),V2),tc_PropLog_Opl(V2)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h16]) ).
cnf(h397,plain,
c_in(V0,c_PropLog_Othms(c_insert(V1,c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V1,V2,V3),V2,V3),V0,V3),V4,tc_PropLog_Opl(V3)),tc_PropLog_Opl(V3)),V3),tc_PropLog_Opl(V3)) = true,
inference(hyper_resolution,[status(thm)],[hi3,h55,h3]) ).
cnf(h1593,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(V0,V1,V2),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V0,V3,V2),V3,V2),V1,V2),V4,tc_PropLog_Opl(V2)),V2),tc_PropLog_Opl(V2)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h397]) ).
cnf(h18,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(V0,V1,V2),c_PropLog_Othms(c_insert(V1,V3,tc_PropLog_Opl(V2)),V2),tc_PropLog_Opl(V2)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h3]) ).
cnf(f1,axiom,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p,c_PropLog_Opl_Ofalse,T_a),c_PropLog_Opl_Ofalse,T_a),V_p,T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Othms_ODN_0) ).
fof(f1_nnf,plain,
! [V_p,T_a,V_H] : c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p,c_PropLog_Opl_Ofalse,T_a),c_PropLog_Opl_Ofalse,T_a),V_p,T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [V_p,T_a,V_H] : c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p,c_PropLog_Opl_Ofalse,T_a),c_PropLog_Opl_Ofalse,T_a),V_p,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(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X0,c_PropLog_Opl_Ofalse,X1),c_PropLog_Opl_Ofalse,X1),X0,X1),c_PropLog_Othms(X2,X1),tc_PropLog_Opl(X1)),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X0,c_PropLog_Opl_Ofalse,X1),c_PropLog_Opl_Ofalse,X1),X0,X1),c_PropLog_Othms(X2,X1),tc_PropLog_Opl(X1)) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h29,plain,
c_in(V0,c_PropLog_Othms(c_insert(c_PropLog_Opl_Ofalse,V1,tc_PropLog_Opl(V2)),V2),tc_PropLog_Opl(V2)) = true,
inference(hyper_resolution,[status(thm)],[hi3,h18,hi1]) ).
cnf(h33,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ofalse,V0,V1),c_PropLog_Othms(V2,V1),tc_PropLog_Opl(V1)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h29]) ).
cnf(h15,plain,
c_in(V0,c_PropLog_Othms(c_insert(V1,c_insert(c_PropLog_Opl_Oop_A_N_62(V1,V0,V2),V3,tc_PropLog_Opl(V2)),tc_PropLog_Opl(V2)),V2),tc_PropLog_Opl(V2)) = true,
inference(hyper_resolution,[status(thm)],[hi3,h1,h3]) ).
cnf(h53,plain,
c_in(V0,c_PropLog_Othms(c_insert(V1,c_insert(c_PropLog_Opl_Oop_A_N_62(V1,c_PropLog_Opl_Ofalse,V2),V3,tc_PropLog_Opl(V2)),tc_PropLog_Opl(V2)),V2),tc_PropLog_Opl(V2)) = true,
inference(hyper_resolution,[status(thm)],[hi3,h15,h33]) ).
cnf(h57,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(V0,V1,V2),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(V0,c_PropLog_Opl_Ofalse,V2),V3,tc_PropLog_Opl(V2)),V2),tc_PropLog_Opl(V2)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h53]) ).
cnf(h58,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V0,c_PropLog_Opl_Ofalse,V1),c_PropLog_Opl_Oop_A_N_62(V0,V2,V1),V1),c_PropLog_Othms(V3,V1),tc_PropLog_Opl(V1)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h57]) ).
cnf(h72,plain,
c_in(V0,c_PropLog_Othms(c_insert(V1,c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V2,V1,V3),V0,V3),V4,tc_PropLog_Opl(V3)),tc_PropLog_Opl(V3)),V3),tc_PropLog_Opl(V3)) = true,
inference(hyper_resolution,[status(thm)],[hi3,h18,h3]) ).
cnf(h259,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(V0,V1,V2),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V3,V0,V2),V1,V2),V4,tc_PropLog_Opl(V2)),V2),tc_PropLog_Opl(V2)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h72]) ).
cnf(h260,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(V0,V1,V2),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V3,V0,V2),c_PropLog_Opl_Ofalse,V2),V4,tc_PropLog_Opl(V2)),V2),tc_PropLog_Opl(V2)) = true,
inference(hyper_resolution,[status(thm)],[hi3,h259,h58]) ).
cnf(h1594,plain,
c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V0,V1,V2),V0,V2),V0,V2),c_PropLog_Opl_Ofalse,V2),V3,tc_PropLog_Opl(V2)),V2),tc_PropLog_Opl(V2)) = true,
inference(hyper_resolution,[status(thm)],[hi3,h260,h1593]) ).
cnf(h1607,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V0,V1,V2),V0,V2),V0,V2),c_PropLog_Opl_Ofalse,V2),c_PropLog_Opl_Ofalse,V2),c_PropLog_Othms(V3,V2),tc_PropLog_Opl(V2)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1594]) ).
cnf(h1621,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V0,V1,V2),V0,V2),V0,V2),c_PropLog_Othms(V3,V2),tc_PropLog_Opl(V2)) = true,
inference(hyper_resolution,[status(thm)],[hi3,h1607,hi1]) ).
cnf(h1623,plain,
c_in(V0,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V0,V1,V2),V3,V2),V3,V2),V0,V2),V4,tc_PropLog_Opl(V2)),V2),tc_PropLog_Opl(V2)) = true,
inference(hyper_resolution,[status(thm)],[hi3,h1593,h1621]) ).
cnf(h1800,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V0,V1,V2),V3,V2),V3,V2),V0,V2),V0,V2),c_PropLog_Othms(V4,V2),tc_PropLog_Opl(V2)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1623]) ).
cnf(h2,plain,
c_in(V0,c_insert(V1,c_insert(V2,c_insert(V0,V3,V4),V4),V4),V4) = true,
inference(hyper_resolution,[status(thm)],[hi4,h0]) ).
cnf(h61,plain,
c_in(V0,c_PropLog_Othms(c_insert(V1,c_insert(V2,c_insert(V0,V3,tc_PropLog_Opl(V4)),tc_PropLog_Opl(V4)),tc_PropLog_Opl(V4)),V4),tc_PropLog_Opl(V4)) = true,
inference(hyper_resolution,[status(thm)],[hi2,h2]) ).
cnf(h437,plain,
c_in(V0,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(V1,V2,V3),c_insert(V1,c_insert(c_PropLog_Opl_Oop_A_N_62(V2,V0,V3),V4,tc_PropLog_Opl(V3)),tc_PropLog_Opl(V3)),tc_PropLog_Opl(V3)),V3),tc_PropLog_Opl(V3)) = true,
inference(hyper_resolution,[status(thm)],[hi3,h16,h61]) ).
cnf(h2506,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V0,V1,V2),V3,V2),c_PropLog_Othms(c_insert(V0,c_insert(c_PropLog_Opl_Oop_A_N_62(V1,V3,V2),V4,tc_PropLog_Opl(V2)),tc_PropLog_Opl(V2)),V2),tc_PropLog_Opl(V2)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h437]) ).
cnf(h2510,plain,
c_in(V0,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V0,V1,V2),V3,V2),c_insert(c_PropLog_Opl_Oop_A_N_62(V3,V0,V2),V4,tc_PropLog_Opl(V2)),tc_PropLog_Opl(V2)),V2),tc_PropLog_Opl(V2)) = true,
inference(hyper_resolution,[status(thm)],[hi3,h2506,h1800]) ).
cnf(h2722,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V0,V1,V2),V3,V2),V0,V2),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(V3,V0,V2),V4,tc_PropLog_Opl(V2)),V2),tc_PropLog_Opl(V2)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h2510]) ).
cnf(h188,plain,
c_in(V0,c_PropLog_Othms(c_insert(V1,c_insert(c_PropLog_Opl_Oop_A_N_62(V1,c_PropLog_Opl_Oop_A_N_62(V1,V0,V2),V2),V3,tc_PropLog_Opl(V2)),tc_PropLog_Opl(V2)),V2),tc_PropLog_Opl(V2)) = true,
inference(hyper_resolution,[status(thm)],[hi3,h1,h15]) ).
cnf(h273,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(V0,V1,V2),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(V0,c_PropLog_Opl_Oop_A_N_62(V0,V1,V2),V2),V3,tc_PropLog_Opl(V2)),V2),tc_PropLog_Opl(V2)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h188]) ).
cnf(h276,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V0,c_PropLog_Opl_Oop_A_N_62(V0,V1,V2),V2),c_PropLog_Opl_Oop_A_N_62(V0,V1,V2),V2),c_PropLog_Othms(V3,V2),tc_PropLog_Opl(V2)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h273]) ).
cnf(h752,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(V0,V1,V2),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V3,V0,V2),c_PropLog_Opl_Oop_A_N_62(V0,V1,V2),V2),V4,tc_PropLog_Opl(V2)),V2),tc_PropLog_Opl(V2)) = true,
inference(hyper_resolution,[status(thm)],[hi3,h259,h276]) ).
cnf(h1172,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V0,V1,V2),c_PropLog_Opl_Oop_A_N_62(V1,V3,V2),V2),c_PropLog_Opl_Oop_A_N_62(V1,V3,V2),V2),c_PropLog_Othms(V4,V2),tc_PropLog_Opl(V2)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h752]) ).
cnf(h2730,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(V0,V1,V2),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V1,V3,V2),c_PropLog_Opl_Oop_A_N_62(V0,V1,V2),V2),V4,tc_PropLog_Opl(V2)),V2),tc_PropLog_Opl(V2)) = true,
inference(hyper_resolution,[status(thm)],[hi3,h1172,h2722]) ).
cnf(h4420,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V0,V1,V2),c_PropLog_Opl_Oop_A_N_62(V3,V0,V2),V2),c_PropLog_Opl_Oop_A_N_62(V3,V0,V2),V2),c_PropLog_Othms(V4,V2),tc_PropLog_Opl(V2)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h2730]) ).
cnf(h56,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(V0,c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V0,V1,V2),V1,V2),V2),c_PropLog_Othms(V3,V2),tc_PropLog_Opl(V2)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h55]) ).
cnf(h420,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V0,V1,V2),V1,V2),c_PropLog_Othms(c_insert(V3,c_insert(c_PropLog_Opl_Oop_A_N_62(V3,V0,V2),V4,tc_PropLog_Opl(V2)),tc_PropLog_Opl(V2)),V2),tc_PropLog_Opl(V2)) = true,
inference(hyper_resolution,[status(thm)],[hi3,h15,h56]) ).
cnf(h2125,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(V0,c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V1,V2,V3),V2,V3),V3),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(V0,V1,V3),V4,tc_PropLog_Opl(V3)),V3),tc_PropLog_Opl(V3)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h420]) ).
cnf(h4424,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V0,V1,V2),V1,V2),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V1,V3,V2),V0,V2),V4,tc_PropLog_Opl(V2)),V2),tc_PropLog_Opl(V2)) = true,
inference(hyper_resolution,[status(thm)],[hi3,h2125,h4420]) ).
cnf(h4440,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V0,V1,V2),V3,V2),c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V3,V0,V2),V0,V2),V2),c_PropLog_Othms(V4,V2),tc_PropLog_Opl(V2)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h4424]) ).
cnf(h4441,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V0,V1,V2),V1,V2),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V0,V3,V2),V1,V2),V4,tc_PropLog_Opl(V2)),V2),tc_PropLog_Opl(V2)) = true,
inference(hyper_resolution,[status(thm)],[hi3,h4424,h4440]) ).
cnf(h4489,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V0,V1,V2),V3,V2),c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V0,V3,V2),V3,V2),V2),c_PropLog_Othms(V4,V2),tc_PropLog_Opl(V2)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h4441]) ).
cnf(h409,plain,
c_in(V0,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(V1,c_PropLog_Opl_Ofalse,V2),c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V1,V3,V2),V0,V2),V4,tc_PropLog_Opl(V2)),tc_PropLog_Opl(V2)),V2),tc_PropLog_Opl(V2)) = true,
inference(hyper_resolution,[status(thm)],[hi3,h57,h3]) ).
cnf(h1857,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V0,c_PropLog_Opl_Ofalse,V1),V2,V1),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V0,V3,V1),V2,V1),V4,tc_PropLog_Opl(V1)),V1),tc_PropLog_Opl(V1)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h409]) ).
cnf(h1863,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V0,V1,V2),V3,V2),c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V0,c_PropLog_Opl_Ofalse,V2),V3,V2),V2),c_PropLog_Othms(V4,V2),tc_PropLog_Opl(V2)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1857]) ).
cnf(h30,plain,
c_in(V0,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V0,c_PropLog_Opl_Ofalse,V1),c_PropLog_Opl_Ofalse,V1),V2,tc_PropLog_Opl(V1)),V1),tc_PropLog_Opl(V1)) = true,
inference(hyper_resolution,[status(thm)],[hi3,h1,hi1]) ).
cnf(h373,plain,
c_in(V0,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V1,V0,V2),c_PropLog_Opl_Ofalse,V2),c_PropLog_Opl_Ofalse,V2),c_insert(V1,V3,tc_PropLog_Opl(V2)),tc_PropLog_Opl(V2)),V2),tc_PropLog_Opl(V2)) = true,
inference(hyper_resolution,[status(thm)],[hi3,h3,h30]) ).
cnf(h1309,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V0,V1,V2),c_PropLog_Opl_Ofalse,V2),c_PropLog_Opl_Ofalse,V2),V1,V2),c_PropLog_Othms(c_insert(V0,V3,tc_PropLog_Opl(V2)),V2),tc_PropLog_Opl(V2)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h373]) ).
cnf(h1614,plain,
c_in(V0,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V0,V1,V2),V0,V2),V3,tc_PropLog_Opl(V2)),V2),tc_PropLog_Opl(V2)) = true,
inference(hyper_resolution,[status(thm)],[hi3,h1607,h1309]) ).
cnf(h1682,plain,
c_in(V0,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V1,V2,V3),V1,V3),c_insert(c_PropLog_Opl_Oop_A_N_62(V1,V0,V3),V4,tc_PropLog_Opl(V3)),tc_PropLog_Opl(V3)),V3),tc_PropLog_Opl(V3)) = true,
inference(hyper_resolution,[status(thm)],[hi3,h1614,h3]) ).
cnf(h2335,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V0,V1,V2),V0,V2),V3,V2),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(V0,V3,V2),V4,tc_PropLog_Opl(V2)),V2),tc_PropLog_Opl(V2)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1682]) ).
cnf(h2336,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V0,V1,V2),c_PropLog_Opl_Ofalse,V2),V3,V2),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(V0,V3,V2),V4,tc_PropLog_Opl(V2)),V2),tc_PropLog_Opl(V2)) = true,
inference(hyper_resolution,[status(thm)],[hi3,h2335,h1863]) ).
cnf(h4490,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V0,V1,V2),V3,V2),V3,V2),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(V0,V3,V2),V4,tc_PropLog_Opl(V2)),V2),tc_PropLog_Opl(V2)) = true,
inference(hyper_resolution,[status(thm)],[hi3,h2336,h4489]) ).
cnf(t5,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X1,X2,X3),c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X1,X4,X3),X2,X3),X2,X3),X3),c_PropLog_Othms(X5,X3),tc_PropLog_Opl(X3)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h4490]) ).
cnf(t258,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X1,X2,X3),c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X1,X4,X3),X2,X3),X2,X3),X3),c_PropLog_Othms(X5,X3),tc_PropLog_Opl(X3)) = true,
inference(orient,[status(thm)],[t5]) ).
cnf(f6,negated_conjecture,
~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),v_q,t_a),v_q,t_a),t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f6_nnf,plain,
~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),v_q,t_a),v_q,t_a),t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),v_q,t_a),v_q,t_a),t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),v_q,t_a),v_q,t_a),t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(goal_0,negated_conjecture,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),v_q,t_a),v_q,t_a),t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) != true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t258]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL444-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/10.79 % Computer : n013.cluster.edu
% 0.10/10.79 % Model : x86_64 x86_64
% 0.10/10.79 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.79 % Memory : 8046.5625MB
% 0.10/10.79 % OS : Linux 6.8.0-71-generic
% 0.10/10.79 % CPULimit : 300
% 0.10/10.79 % WCLimit : 300
% 0.10/10.79 % DateTime : Wed Sep 23 23:24:06 UTC 2026
% 0.13/10.80 % CPUTime :
% 0.13/10.80 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 148.39/29.58 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 148.39/29.58 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------