%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL443-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n012.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 02:06:39 PM UTC 2026
% Result : Unsatisfiable 3.56s 1.06s
% Output : CNFRefutation 3.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 57 ( 47 unt; 0 def)
% Number of atoms : 77 ( 76 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 43 ( 23 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-4 aty)
% Number of variables : 95 ( 0 sgn 95 !; 0 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : ifeq(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
fof(f2,axiom,
! [X2,X3,X0,X1] : ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(X0,X1,X2),c_PropLog_Othms(X3,X2),tc_PropLog_Opl(X2)),true,ifeq(c_in(X0,c_PropLog_Othms(X3,X2),tc_PropLog_Opl(X2)),true,c_in(X1,c_PropLog_Othms(X3,X2),tc_PropLog_Opl(X2)),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Othms_OMP_0) ).
fof(f3,plain,
! [X2,X3,X0,X1] : true = ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(X0,X1,X2),c_PropLog_Othms(X3,X2),tc_PropLog_Opl(X2)),true,ifeq(c_in(X0,c_PropLog_Othms(X3,X2),tc_PropLog_Opl(X2)),true,c_in(X1,c_PropLog_Othms(X3,X2),tc_PropLog_Opl(X2)),true),true),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X3,X0,X1] : 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,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Odeduction_0) ).
fof(f5,plain,
! [X2,X3,X0,X1] : true = 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),
inference(reorient_equations,[],[f4]) ).
fof(f6,axiom,
! [X2,X0,X1] : ifeq(c_in(X0,X1,tc_PropLog_Opl(X2)),true,c_in(X0,c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2)),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Othms_OH_0) ).
fof(f7,plain,
! [X2,X0,X1] : true = ifeq(c_in(X0,X1,tc_PropLog_Opl(X2)),true,c_in(X0,c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2)),true),
inference(reorient_equations,[],[f6]) ).
fof(f8,axiom,
! [X2,X3,X0,X1] : ifeq(c_in(X0,c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2)),true,c_in(X0,c_PropLog_Othms(c_insert(X3,X1,tc_PropLog_Opl(X2)),X2),tc_PropLog_Opl(X2)),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Oweaken__left__insert_0) ).
fof(f9,plain,
! [X2,X3,X0,X1] : true = ifeq(c_in(X0,c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2)),true,c_in(X0,c_PropLog_Othms(c_insert(X3,X1,tc_PropLog_Opl(X2)),X2),tc_PropLog_Opl(X2)),true),
inference(reorient_equations,[],[f8]) ).
fof(f10,axiom,
! [X2,X0,X1] : c_in(X0,c_insert(X0,X1,X2),X2) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).
fof(f11,plain,
! [X2,X0,X1] : true = c_in(X0,c_insert(X0,X1,X2),X2),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f13,plain,
true = c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f15,plain,
true = c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(reorient_equations,[],[f14]) ).
fof(f16,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_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f17,plain,
true != 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_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(reorient_equations,[],[f16]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[],[f1]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(X0,X1,X2),c_PropLog_Othms(X3,X2),tc_PropLog_Opl(X2)),true,ifeq(c_in(X0,c_PropLog_Othms(X3,X2),tc_PropLog_Opl(X2)),true,c_in(X1,c_PropLog_Othms(X3,X2),tc_PropLog_Opl(X2)),true),true) = true,
inference(cnf_transformation,[],[f3]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : 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(cnf_transformation,[],[f5]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] : 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(cnf_transformation,[],[f7]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ifeq(c_in(X0,c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2)),true,c_in(X0,c_PropLog_Othms(c_insert(X3,X1,tc_PropLog_Opl(X2)),X2),tc_PropLog_Opl(X2)),true) = true,
inference(cnf_transformation,[],[f9]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] : c_in(X0,c_insert(X0,X1,X2),X2) = true,
inference(cnf_transformation,[],[f11]) ).
tcf(c_64,negated_conjecture,
c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) = true,
inference(cnf_transformation,[],[f13]) ).
tcf(c_65,negated_conjecture,
c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) = true,
inference(cnf_transformation,[],[f15]) ).
tcf(c_66,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_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) != true,
inference(cnf_transformation,[],[f17]) ).
tcf(c_99,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_100,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_113,plain,
true = true,
inference(instantiation,[status(thm)],[c_99]) ).
tcf(c_180,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(true,true,c_in(X0,c_PropLog_Othms(c_insert(X0,X1,tc_PropLog_Opl(X2)),X2),tc_PropLog_Opl(X2)),true) = true,
inference(superposition,[status(thm)],[c_63,c_61]) ).
tcf(c_186,plain,
! [X0: $i,X1: $i,X2: $i] : c_in(X0,c_PropLog_Othms(c_insert(X0,X1,tc_PropLog_Opl(X2)),X2),tc_PropLog_Opl(X2)) = true,
inference(demodulation,[status(thm)],[c_180,c_58]) ).
tcf(c_191,plain,
! [X0: $i] : ifeq(true,true,c_in(v_p,c_PropLog_Othms(c_insert(X0,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = true,
inference(superposition,[status(thm)],[c_64,c_62]) ).
tcf(c_192,plain,
! [X0: $i] : ifeq(true,true,c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X0,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = true,
inference(superposition,[status(thm)],[c_65,c_62]) ).
tcf(c_233,plain,
! [X0: $i] :
( ( 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_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) = true )
| ( true != X0 )
| ( 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_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) != X0 ) ),
inference(instantiation,[status(thm)],[c_100]) ).
tcf(c_235,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_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) = 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_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(instantiation,[status(thm)],[c_99]) ).
tcf(c_236,plain,
! [X0: $i,X1: $i] :
( ( 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_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) = X1 )
| ( X1 != X0 )
| ( 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_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) != X0 ) ),
inference(instantiation,[status(thm)],[c_100]) ).
tcf(c_265,plain,
! [X0: $i] : c_in(v_p,c_PropLog_Othms(c_insert(X0,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) = true,
inference(demodulation,[status(thm)],[c_191,c_58]) ).
tcf(c_266,plain,
! [X0: $i,X1: $i] : ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_p,X0,t_a),c_PropLog_Othms(c_insert(X1,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,ifeq(true,true,c_in(X0,c_PropLog_Othms(c_insert(X1,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true) = true,
inference(superposition,[status(thm)],[c_265,c_59]) ).
tcf(c_285,plain,
! [X0: $i] :
( ( 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_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) = X0 )
| ( X0 != 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_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) )
| ( 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_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) != 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_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) ) ),
inference(instantiation,[status(thm)],[c_236]) ).
tcf(c_314,plain,
! [X0: $i] : c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X0,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) = true,
inference(demodulation,[status(thm)],[c_192,c_58]) ).
tcf(c_315,plain,
! [X0: $i] : ifeq(true,true,ifeq(c_in(v_q,c_PropLog_Othms(c_insert(X0,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(X0,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true) = true,
inference(superposition,[status(thm)],[c_314,c_59]) ).
tcf(c_348,plain,
! [X0: $i,X1: $i] :
( ( 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_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) = ifeq(X0,X0,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_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),X1) )
| ( 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_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) != 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_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) )
| ( ifeq(X0,X0,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_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),X1) != 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_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) ) ),
inference(instantiation,[status(thm)],[c_285]) ).
tcf(c_349,plain,
! [X0: $i,X1: $i] : ifeq(X0,X0,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_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),X1) = 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_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_350,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_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) = ifeq(true,true,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_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true) )
| ( 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_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) != 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_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) )
| ( ifeq(true,true,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_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true) != 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_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) ) ),
inference(instantiation,[status(thm)],[c_348]) ).
tcf(c_351,plain,
ifeq(true,true,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_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true) = 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_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(instantiation,[status(thm)],[c_349]) ).
tcf(c_638,plain,
! [X0: $i,X1: $i] :
( ( 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_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) = true )
| ( true != ifeq(X0,X0,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_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),X1) )
| ( 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_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) != ifeq(X0,X0,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_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),X1) ) ),
inference(instantiation,[status(thm)],[c_233]) ).
tcf(c_639,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_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) = true )
| ( true != ifeq(true,true,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_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true) )
| ( 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_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) != ifeq(true,true,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_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true) ) ),
inference(instantiation,[status(thm)],[c_638]) ).
tcf(c_788,plain,
! [X0: $i] : ifeq(c_in(v_q,c_PropLog_Othms(c_insert(X0,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(X0,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = true,
inference(demodulation,[status(thm)],[c_315,c_58]) ).
tcf(c_890,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( true = ifeq(X0,X0,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_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),X1) )
| ( true != X2 )
| ( ifeq(X0,X0,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_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),X1) != X2 ) ),
inference(instantiation,[status(thm)],[c_100]) ).
tcf(c_891,plain,
( ( true = ifeq(true,true,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_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true) )
| ( true != true )
| ( ifeq(true,true,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_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true) != true ) ),
inference(instantiation,[status(thm)],[c_890]) ).
tcf(c_903,plain,
! [X0: $i,X1: $i] : ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_p,X0,t_a),c_PropLog_Othms(c_insert(X1,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(X0,c_PropLog_Othms(c_insert(X1,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = true,
inference(demodulation,[status(thm)],[c_266,c_58]) ).
tcf(c_904,plain,
! [X0: $i] : ifeq(true,true,c_in(X0,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,X0,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = true,
inference(superposition,[status(thm)],[c_186,c_903]) ).
tcf(c_940,plain,
! [X0: $i] : c_in(X0,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,X0,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) = true,
inference(demodulation,[status(thm)],[c_904,c_58]) ).
tcf(c_955,plain,
ifeq(true,true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = true,
inference(superposition,[status(thm)],[c_940,c_788]) ).
tcf(c_1013,plain,
c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) = true,
inference(demodulation,[status(thm)],[c_955,c_58]) ).
tcf(c_1016,plain,
ifeq(true,true,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_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true) = true,
inference(superposition,[status(thm)],[c_1013,c_60]) ).
tcf(c_1025,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1016,c_891,c_639,c_351,c_350,c_235,c_113,c_66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL443-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.04/0.29 % Computer : n012.cluster.edu
% 0.04/0.29 % Model : x86_64 x86_64
% 0.04/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.29 % Memory : 8046.5625MB
% 0.04/0.29 % OS : Linux 6.8.0-71-generic
% 0.04/0.29 % CPULimit : 300
% 0.04/0.29 % WCLimit : 300
% 0.04/0.29 % DateTime : Wed Sep 23 23:23:06 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.04/0.32 Running UEQ theorem proving
% 0.04/0.32 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.04/0.32
% 0.04/0.32 % ======== iProver multi-core TPTP/SMT =========
% 0.04/0.32
% 0.04/0.32 % Detected problem language: tptp
% 0.07/0.33 % Proving...
% 3.56/1.06 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 3.56/1.06 % SZS status Started for theBenchmark.p
% 3.56/1.06 % SZS status Unsatisfiable for theBenchmark.p
% 3.56/1.06
% 3.56/1.06 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.56/1.06
% 3.56/1.06 % ------ iProver source info
% 3.56/1.06
% 3.56/1.06 % git: date: 2026-07-19 20:42:38 +0200
% 3.56/1.06 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.56/1.06 % git: non_committed_changes: false
% 3.56/1.06
% 3.56/1.06 % ------ Parsing...% successful
% 3.56/1.06
% 3.56/1.06
% 3.56/1.06 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.56/1.06
% 3.56/1.06 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.56/1.06
% 3.56/1.06 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.56/1.06
% 3.56/1.06 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 3.56/1.06 % ------ Proving...
% 3.56/1.06 % ------ Problem Properties
% 3.56/1.06
% 3.56/1.06 %
% 3.56/1.06 % clauses 9
% 3.56/1.06 % conjectures 3
% 3.56/1.06 % EPR 0
% 3.56/1.06 % Horn 9
% 3.56/1.06 % unary 9
% 3.56/1.06 % binary 0
% 3.56/1.06 % lits 9
% 3.56/1.06 % lits eq 9
% 3.56/1.06 % fd_pure 0
% 3.56/1.06 % fd_pseudo 0
% 3.56/1.06 % fd_cond 0
% 3.56/1.06 % fd_pseudo_cond 0
% 3.56/1.06 % AC symbols 0
% 3.56/1.06
% 3.56/1.06 % ------ Input Options Time Limit: Unbounded
% 3.56/1.06
% 3.56/1.06
% 3.56/1.06 % ------
% 3.56/1.06 % Current options:
% 3.56/1.06 % ------
% 3.56/1.06
% 3.56/1.06
% 3.56/1.06 %
% 3.56/1.06
% 3.56/1.06 % ------ Proving...
% 3.56/1.06 %
% 3.56/1.06
% 3.56/1.06 % SZS status Unsatisfiable for theBenchmark.p
% 3.56/1.06
% 3.56/1.06 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.56/1.06
% 3.56/1.06
%------------------------------------------------------------------------------