%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL443-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n016.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 : Sun Sep 27 07:51:51 AM UTC 2026
% Result : Unsatisfiable 10.83s 8.85s
% Output : Refutation 9.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 102 ( 40 unt; 0 typ; 0 def)
% Number of atoms : 282 ( 78 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 1704 ( 141 ~; 92 |; 0 &;1471 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 7 con; 0-3 aty)
% Number of variables : 171 ( 0 ^; 171 !; 0 ?; 171 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_in_decl,type,
c_in: $i > $i > $i > $o ).
thf(v_p_decl,type,
v_p: $i ).
thf(c_PropLog_Othms_decl,type,
c_PropLog_Othms: $i > $i > $i ).
thf(v_H_decl,type,
v_H: $i ).
thf(t_a_decl,type,
t_a: $i ).
thf(tc_PropLog_Opl_decl,type,
tc_PropLog_Opl: $i > $i ).
thf(c_PropLog_Opl_Oop_A_N_62_decl,type,
c_PropLog_Opl_Oop_A_N_62: $i > $i > $i > $i ).
thf(v_q_decl,type,
v_q: $i ).
thf(c_PropLog_Opl_Ofalse_decl,type,
c_PropLog_Opl_Ofalse: $i ).
thf(c_insert_decl,type,
c_insert: $i > $i > $i > $i ).
thf(2,negated_conjecture,
t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( t_a @ ( c_PropLog_Opl_Ofalse @ ( v_q @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(10,plain,
t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( t_a @ ( c_PropLog_Opl_Ofalse @ ( v_q @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( C @ ( D @ ( A @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) )
| ~ ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Othms_OMP_0) ).
thf(13,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( C @ ( D @ ( A @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) )
| ~ ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(14,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( C @ ( D @ ( A @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) )
| ~ ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) ) ),
inference(cnf,[status(esa)],[13]) ).
thf(1,negated_conjecture,
t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( v_p @ c_in ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(9,plain,
t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( v_p @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_PropLog_Opl @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Othms_OH_0) ).
thf(17,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_PropLog_Opl @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(18,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_PropLog_Opl @ ( B @ ( A @ c_in ) ) ) ),
inference(cnf,[status(esa)],[17]) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( v_p @ c_in ) ) )
!= ( C @ tc_PropLog_Opl @ ( B @ ( A @ c_in ) ) ) )
| ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9,18]) ).
thf(40,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( v_p @ c_in ) ) )
!= ( C @ tc_PropLog_Opl @ ( B @ ( A @ c_in ) ) ) )
| ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[39]) ).
thf(41,plain,
t_a @ tc_PropLog_Opl @ ( t_a @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ c_PropLog_Othms ) @ ( v_p @ c_in ) ),
inference(pattern_uni,[status(thm)],[40:[bind(A,$thf( v_p )),bind(B,$thf( t_a @ ( v_H @ c_PropLog_Othms ) )),bind(C,$thf( t_a ))]]) ).
thf(94,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_PropLog_Opl @ ( t_a @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ c_PropLog_Othms ) @ ( v_p @ c_in ) ) )
!= ( C @ tc_PropLog_Opl @ ( B @ ( A @ c_in ) ) ) )
| ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41,18]) ).
thf(95,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_PropLog_Opl @ ( t_a @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ c_PropLog_Othms ) @ ( v_p @ c_in ) ) )
!= ( C @ tc_PropLog_Opl @ ( B @ ( A @ c_in ) ) ) )
| ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[94]) ).
thf(96,plain,
t_a @ tc_PropLog_Opl @ ( t_a @ ( t_a @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ c_PropLog_Othms ) @ c_PropLog_Othms ) @ ( v_p @ c_in ) ),
inference(pattern_uni,[status(thm)],[95:[bind(A,$thf( v_p )),bind(B,$thf( t_a @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ c_PropLog_Othms ) )),bind(C,$thf( t_a ))]]) ).
thf(130,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_PropLog_Opl @ ( t_a @ ( t_a @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ c_PropLog_Othms ) @ c_PropLog_Othms ) @ ( v_p @ c_in ) ) )
!= ( C @ tc_PropLog_Opl @ ( B @ ( A @ c_in ) ) ) )
| ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[96,18]) ).
thf(131,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_PropLog_Opl @ ( t_a @ ( t_a @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ c_PropLog_Othms ) @ c_PropLog_Othms ) @ ( v_p @ c_in ) ) )
!= ( C @ tc_PropLog_Opl @ ( B @ ( A @ c_in ) ) ) )
| ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[130]) ).
thf(132,plain,
t_a @ tc_PropLog_Opl @ ( t_a @ ( t_a @ ( t_a @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ c_PropLog_Othms ) @ c_PropLog_Othms ) @ c_PropLog_Othms ) @ ( v_p @ c_in ) ),
inference(pattern_uni,[status(thm)],[131:[bind(A,$thf( v_p )),bind(B,$thf( t_a @ ( t_a @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ c_PropLog_Othms ) @ c_PropLog_Othms ) )),bind(C,$thf( t_a ))]]) ).
thf(3,negated_conjecture,
~ ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( t_a @ ( c_PropLog_Opl_Ofalse @ ( t_a @ ( v_q @ ( v_p @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(11,plain,
~ ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( t_a @ ( c_PropLog_Opl_Ofalse @ ( t_a @ ( v_q @ ( v_p @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(12,plain,
~ ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( t_a @ ( c_PropLog_Opl_Ofalse @ ( t_a @ ( v_q @ ( v_p @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) ),
inference(polarity_switch,[status(thm)],[11]) ).
thf(42,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) )
!= ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( t_a @ ( c_PropLog_Opl_Ofalse @ ( t_a @ ( v_q @ ( v_p @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) ) )
| ~ $true
| ~ ( C @ tc_PropLog_Opl @ ( B @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[18,12]) ).
thf(43,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) )
!= ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( t_a @ ( c_PropLog_Opl_Ofalse @ ( t_a @ ( v_q @ ( v_p @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) ) )
| ~ ( C @ tc_PropLog_Opl @ ( B @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[42]) ).
thf(44,plain,
~ ( t_a @ tc_PropLog_Opl @ ( v_H @ ( t_a @ ( c_PropLog_Opl_Ofalse @ ( t_a @ ( v_q @ ( v_p @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[43:[bind(A,$thf( t_a @ ( c_PropLog_Opl_Ofalse @ ( t_a @ ( v_q @ ( v_p @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_PropLog_Opl_Oop_A_N_62 ) ) )),bind(B,$thf( v_H )),bind(C,$thf( t_a ))]]) ).
thf(7,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_PropLog_Opl @ ( C @ ( C @ tc_PropLog_Opl @ ( B @ ( D @ c_insert ) ) @ c_PropLog_Othms ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Oweaken__left__insert_0) ).
thf(19,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_PropLog_Opl @ ( C @ ( C @ tc_PropLog_Opl @ ( B @ ( D @ c_insert ) ) @ c_PropLog_Othms ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(20,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_PropLog_Opl @ ( C @ ( C @ tc_PropLog_Opl @ ( B @ ( D @ c_insert ) ) @ c_PropLog_Othms ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) ) ),
inference(cnf,[status(esa)],[19]) ).
thf(5,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_PropLog_Opl @ ( D @ ( C @ c_PropLog_Othms ) @ ( D @ ( A @ ( B @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) )
| ~ ( D @ tc_PropLog_Opl @ ( D @ ( D @ tc_PropLog_Opl @ ( C @ ( B @ c_insert ) ) @ c_PropLog_Othms ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Odeduction_0) ).
thf(15,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_PropLog_Opl @ ( D @ ( C @ c_PropLog_Othms ) @ ( D @ ( A @ ( B @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) )
| ~ ( D @ tc_PropLog_Opl @ ( D @ ( D @ tc_PropLog_Opl @ ( C @ ( B @ c_insert ) ) @ c_PropLog_Othms ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(16,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_PropLog_Opl @ ( D @ ( C @ c_PropLog_Othms ) @ ( D @ ( A @ ( B @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) )
| ~ ( D @ tc_PropLog_Opl @ ( D @ ( D @ tc_PropLog_Opl @ ( C @ ( B @ c_insert ) ) @ c_PropLog_Othms ) @ ( A @ c_in ) ) ) ),
inference(cnf,[status(esa)],[15]) ).
thf(246,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ tc_PropLog_Opl @ ( D @ ( C @ c_PropLog_Othms ) @ ( D @ ( A @ ( B @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) )
!= ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( t_a @ ( c_PropLog_Opl_Ofalse @ ( t_a @ ( v_q @ ( v_p @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) ) )
| ~ $true
| ~ ( D @ tc_PropLog_Opl @ ( D @ ( D @ tc_PropLog_Opl @ ( C @ ( B @ c_insert ) ) @ c_PropLog_Othms ) @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[16,12]) ).
thf(247,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ tc_PropLog_Opl @ ( D @ ( C @ c_PropLog_Othms ) @ ( D @ ( A @ ( B @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) )
!= ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( t_a @ ( c_PropLog_Opl_Ofalse @ ( t_a @ ( v_q @ ( v_p @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) ) )
| ~ ( D @ tc_PropLog_Opl @ ( D @ ( D @ tc_PropLog_Opl @ ( C @ ( B @ c_insert ) ) @ c_PropLog_Othms ) @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[246]) ).
thf(248,plain,
~ ( t_a @ tc_PropLog_Opl @ ( t_a @ ( t_a @ tc_PropLog_Opl @ ( v_H @ ( t_a @ ( v_q @ ( v_p @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_insert ) ) @ c_PropLog_Othms ) @ ( c_PropLog_Opl_Ofalse @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[247:[bind(A,$thf( c_PropLog_Opl_Ofalse )),bind(B,$thf( t_a @ ( v_q @ ( v_p @ c_PropLog_Opl_Oop_A_N_62 ) ) )),bind(C,$thf( v_H )),bind(D,$thf( t_a ))]]) ).
thf(510,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_PropLog_Opl @ ( C @ ( C @ tc_PropLog_Opl @ ( B @ ( D @ c_insert ) ) @ c_PropLog_Othms ) @ ( A @ c_in ) ) )
!= ( t_a @ tc_PropLog_Opl @ ( t_a @ ( t_a @ tc_PropLog_Opl @ ( v_H @ ( t_a @ ( v_q @ ( v_p @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_insert ) ) @ c_PropLog_Othms ) @ ( c_PropLog_Opl_Ofalse @ c_in ) ) ) )
| ~ $true
| ~ ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[20,248]) ).
thf(511,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_PropLog_Opl @ ( C @ ( C @ tc_PropLog_Opl @ ( B @ ( D @ c_insert ) ) @ c_PropLog_Othms ) @ ( A @ c_in ) ) )
!= ( t_a @ tc_PropLog_Opl @ ( t_a @ ( t_a @ tc_PropLog_Opl @ ( v_H @ ( t_a @ ( v_q @ ( v_p @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_insert ) ) @ c_PropLog_Othms ) @ ( c_PropLog_Opl_Ofalse @ c_in ) ) ) )
| ~ ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[510]) ).
thf(512,plain,
~ ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( c_PropLog_Opl_Ofalse @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[511:[bind(A,$thf( c_PropLog_Opl_Ofalse )),bind(B,$thf( v_H )),bind(C,$thf( t_a )),bind(D,$thf( t_a @ ( v_q @ ( v_p @ c_PropLog_Opl_Oop_A_N_62 ) ) ))]]) ).
thf(607,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) )
!= ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( c_PropLog_Opl_Ofalse @ c_in ) ) ) )
| ~ $true
| ~ ( C @ tc_PropLog_Opl @ ( B @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[18,512]) ).
thf(608,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) )
!= ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( c_PropLog_Opl_Ofalse @ c_in ) ) ) )
| ~ ( C @ tc_PropLog_Opl @ ( B @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[607]) ).
thf(609,plain,
~ ( t_a @ tc_PropLog_Opl @ ( v_H @ ( c_PropLog_Opl_Ofalse @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[608:[bind(A,$thf( c_PropLog_Opl_Ofalse )),bind(B,$thf( v_H )),bind(C,$thf( t_a ))]]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).
thf(21,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( t_a @ ( c_PropLog_Opl_Ofalse @ ( t_a @ ( v_q @ ( v_p @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21,12]) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( t_a @ ( c_PropLog_Opl_Ofalse @ ( t_a @ ( v_q @ ( v_p @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[32]) ).
thf(34,plain,
! [C: $i,B: $i,A: $i] :
( ( C
!= ( t_a @ tc_PropLog_Opl ) )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= ( t_a @ ( v_H @ c_PropLog_Othms ) ) )
| ( A
!= ( t_a @ ( c_PropLog_Opl_Ofalse @ ( t_a @ ( v_q @ ( v_p @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_PropLog_Opl_Oop_A_N_62 ) ) ) ) ),
inference(simp,[status(thm)],[33]) ).
thf(35,plain,
! [A: $i] :
( ( t_a @ tc_PropLog_Opl @ ( A @ ( t_a @ ( c_PropLog_Opl_Ofalse @ ( t_a @ ( v_q @ ( v_p @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_insert ) ) )
!= ( t_a @ ( v_H @ c_PropLog_Othms ) ) ),
inference(simp,[status(thm)],[34]) ).
thf(599,plain,
( ( ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( t_a @ ( c_PropLog_Opl_Ofalse @ ( v_q @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) )
!= ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( c_PropLog_Opl_Ofalse @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10,512]) ).
thf(600,plain,
( ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( t_a @ ( c_PropLog_Opl_Ofalse @ ( v_q @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) )
!= ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( c_PropLog_Opl_Ofalse @ c_in ) ) ) ),
inference(simp,[status(thm)],[599]) ).
thf(637,plain,
( ( ( t_a @ tc_PropLog_Opl )
!= ( t_a @ tc_PropLog_Opl ) )
| ( ( t_a @ ( v_H @ c_PropLog_Othms ) )
!= ( t_a @ ( v_H @ c_PropLog_Othms ) ) )
| ( ( t_a @ ( c_PropLog_Opl_Ofalse @ ( v_q @ c_PropLog_Opl_Oop_A_N_62 ) ) )
!= c_PropLog_Opl_Ofalse ) ),
inference(simp,[status(thm)],[600]) ).
thf(648,plain,
( ( t_a @ ( c_PropLog_Opl_Ofalse @ ( v_q @ c_PropLog_Opl_Oop_A_N_62 ) ) )
!= c_PropLog_Opl_Ofalse ),
inference(simp,[status(thm)],[637]) ).
thf(324,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) )
!= ( t_a @ tc_PropLog_Opl @ ( t_a @ ( t_a @ tc_PropLog_Opl @ ( v_H @ ( t_a @ ( v_q @ ( v_p @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_insert ) ) @ c_PropLog_Othms ) @ ( c_PropLog_Opl_Ofalse @ c_in ) ) ) )
| ~ $true
| ~ ( C @ tc_PropLog_Opl @ ( B @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[18,248]) ).
thf(325,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) )
!= ( t_a @ tc_PropLog_Opl @ ( t_a @ ( t_a @ tc_PropLog_Opl @ ( v_H @ ( t_a @ ( v_q @ ( v_p @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_insert ) ) @ c_PropLog_Othms ) @ ( c_PropLog_Opl_Ofalse @ c_in ) ) ) )
| ~ ( C @ tc_PropLog_Opl @ ( B @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[324]) ).
thf(326,plain,
~ ( t_a @ tc_PropLog_Opl @ ( t_a @ tc_PropLog_Opl @ ( v_H @ ( t_a @ ( v_q @ ( v_p @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_insert ) ) @ ( c_PropLog_Opl_Ofalse @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[325:[bind(A,$thf( c_PropLog_Opl_Ofalse )),bind(B,$thf( t_a @ tc_PropLog_Opl @ ( v_H @ ( t_a @ ( v_q @ ( v_p @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_insert ) ) )),bind(C,$thf( t_a ))]]) ).
thf(56,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( t_a @ ( c_PropLog_Opl_Ofalse @ ( v_q @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) )
!= ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( C @ ( D @ ( A @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) ) )
| ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( D @ c_in ) ) )
| ~ $true
| ~ ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[10,14]) ).
thf(57,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( t_a @ ( c_PropLog_Opl_Ofalse @ ( v_q @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) )
!= ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( C @ ( D @ ( A @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) ) )
| ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[56]) ).
thf(58,plain,
( ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( c_PropLog_Opl_Ofalse @ c_in ) ) )
| ~ ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( v_q @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[57:[bind(A,$thf( v_q )),bind(B,$thf( v_H )),bind(C,$thf( t_a )),bind(D,$thf( c_PropLog_Opl_Ofalse ))]]) ).
thf(595,plain,
( $false
| ~ ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( v_q @ c_in ) ) ) ),
inference(rewrite,[status(thm)],[58,512]) ).
thf(596,plain,
~ ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( v_q @ c_in ) ) ),
inference(simp,[status(thm)],[595]) ).
thf(760,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) )
!= ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( v_q @ c_in ) ) ) )
| ~ $true
| ~ ( C @ tc_PropLog_Opl @ ( B @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[18,596]) ).
thf(761,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) )
!= ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( v_q @ c_in ) ) ) )
| ~ ( C @ tc_PropLog_Opl @ ( B @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[760]) ).
thf(762,plain,
~ ( t_a @ tc_PropLog_Opl @ ( v_H @ ( v_q @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[761:[bind(A,$thf( v_q )),bind(B,$thf( v_H )),bind(C,$thf( t_a ))]]) ).
thf(109,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( t_a @ tc_PropLog_Opl @ ( v_H @ ( t_a @ ( c_PropLog_Opl_Ofalse @ ( t_a @ ( v_q @ ( v_p @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21,44]) ).
thf(110,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( t_a @ tc_PropLog_Opl @ ( v_H @ ( t_a @ ( c_PropLog_Opl_Ofalse @ ( t_a @ ( v_q @ ( v_p @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[109]) ).
thf(111,plain,
! [C: $i,B: $i,A: $i] :
( ( C
!= ( t_a @ tc_PropLog_Opl ) )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= v_H )
| ( A
!= ( t_a @ ( c_PropLog_Opl_Ofalse @ ( t_a @ ( v_q @ ( v_p @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_PropLog_Opl_Oop_A_N_62 ) ) ) ) ),
inference(simp,[status(thm)],[110]) ).
thf(120,plain,
! [A: $i] :
( ( t_a @ tc_PropLog_Opl @ ( A @ ( t_a @ ( c_PropLog_Opl_Ofalse @ ( t_a @ ( v_q @ ( v_p @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_insert ) ) )
!= v_H ),
inference(simp,[status(thm)],[111]) ).
thf(24,plain,
( ( ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( t_a @ ( c_PropLog_Opl_Ofalse @ ( t_a @ ( v_q @ ( v_p @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) )
!= ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( t_a @ ( c_PropLog_Opl_Ofalse @ ( v_q @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10,12]) ).
thf(25,plain,
( ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( t_a @ ( c_PropLog_Opl_Ofalse @ ( t_a @ ( v_q @ ( v_p @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) )
!= ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( t_a @ ( c_PropLog_Opl_Ofalse @ ( v_q @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[24]) ).
thf(27,plain,
( ( ( t_a @ tc_PropLog_Opl )
!= ( t_a @ tc_PropLog_Opl ) )
| ( ( t_a @ ( v_H @ c_PropLog_Othms ) )
!= ( t_a @ ( v_H @ c_PropLog_Othms ) ) )
| ( ( t_a @ ( c_PropLog_Opl_Ofalse @ ( t_a @ ( v_q @ ( v_p @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_PropLog_Opl_Oop_A_N_62 ) ) )
!= ( t_a @ ( c_PropLog_Opl_Ofalse @ ( v_q @ c_PropLog_Opl_Oop_A_N_62 ) ) ) ) ),
inference(simp,[status(thm)],[25]) ).
thf(29,plain,
( ( t_a @ ( c_PropLog_Opl_Ofalse @ ( t_a @ ( v_q @ ( v_p @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_PropLog_Opl_Oop_A_N_62 ) ) )
!= ( t_a @ ( c_PropLog_Opl_Ofalse @ ( v_q @ c_PropLog_Opl_Oop_A_N_62 ) ) ) ),
inference(simp,[status(thm)],[27]) ).
thf(184,plain,
( ( ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( v_q @ c_in ) ) )
!= ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( v_p @ c_in ) ) ) )
| ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( c_PropLog_Opl_Ofalse @ c_in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9,58]) ).
thf(185,plain,
( ( ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( v_q @ c_in ) ) )
!= ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( v_p @ c_in ) ) ) )
| ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( c_PropLog_Opl_Ofalse @ c_in ) ) ) ),
inference(simp,[status(thm)],[184]) ).
thf(206,plain,
( ( ( t_a @ tc_PropLog_Opl )
!= ( t_a @ tc_PropLog_Opl ) )
| ( ( t_a @ ( v_H @ c_PropLog_Othms ) )
!= ( t_a @ ( v_H @ c_PropLog_Othms ) ) )
| ( v_q != v_p )
| ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( c_PropLog_Opl_Ofalse @ c_in ) ) ) ),
inference(simp,[status(thm)],[185]) ).
thf(217,plain,
( ( v_q != v_p )
| ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( c_PropLog_Opl_Ofalse @ c_in ) ) ) ),
inference(simp,[status(thm)],[206]) ).
thf(597,plain,
( ( v_q != v_p )
| $false ),
inference(rewrite,[status(thm)],[217,512]) ).
thf(598,plain,
v_q != v_p,
inference(simp,[status(thm)],[597]) ).
thf(22,plain,
( ( ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( t_a @ ( c_PropLog_Opl_Ofalse @ ( t_a @ ( v_q @ ( v_p @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) )
!= ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( v_p @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9,12]) ).
thf(23,plain,
( ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( t_a @ ( c_PropLog_Opl_Ofalse @ ( t_a @ ( v_q @ ( v_p @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) )
!= ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( v_p @ c_in ) ) ) ),
inference(simp,[status(thm)],[22]) ).
thf(26,plain,
( ( ( t_a @ tc_PropLog_Opl )
!= ( t_a @ tc_PropLog_Opl ) )
| ( ( t_a @ ( v_H @ c_PropLog_Othms ) )
!= ( t_a @ ( v_H @ c_PropLog_Othms ) ) )
| ( ( t_a @ ( c_PropLog_Opl_Ofalse @ ( t_a @ ( v_q @ ( v_p @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_PropLog_Opl_Oop_A_N_62 ) ) )
!= v_p ) ),
inference(simp,[status(thm)],[23]) ).
thf(28,plain,
( ( t_a @ ( c_PropLog_Opl_Ofalse @ ( t_a @ ( v_q @ ( v_p @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_PropLog_Opl_Oop_A_N_62 ) ) )
!= v_p ),
inference(simp,[status(thm)],[26]) ).
thf(36,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( t_a @ ( c_PropLog_Opl_Ofalse @ ( v_q @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) )
!= ( C @ tc_PropLog_Opl @ ( B @ ( A @ c_in ) ) ) )
| ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10,18]) ).
thf(37,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( t_a @ ( c_PropLog_Opl_Ofalse @ ( v_q @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) )
!= ( C @ tc_PropLog_Opl @ ( B @ ( A @ c_in ) ) ) )
| ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[36]) ).
thf(38,plain,
t_a @ tc_PropLog_Opl @ ( t_a @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ c_PropLog_Othms ) @ ( t_a @ ( c_PropLog_Opl_Ofalse @ ( v_q @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ),
inference(pattern_uni,[status(thm)],[37:[bind(A,$thf( t_a @ ( c_PropLog_Opl_Ofalse @ ( v_q @ c_PropLog_Opl_Oop_A_N_62 ) ) )),bind(B,$thf( t_a @ ( v_H @ c_PropLog_Othms ) )),bind(C,$thf( t_a ))]]) ).
thf(513,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( v_p @ c_in ) ) )
!= ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) ) )
| ( C @ tc_PropLog_Opl @ ( C @ ( C @ tc_PropLog_Opl @ ( B @ ( D @ c_insert ) ) @ c_PropLog_Othms ) @ ( A @ c_in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9,20]) ).
thf(514,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( v_p @ c_in ) ) )
!= ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) ) )
| ( C @ tc_PropLog_Opl @ ( C @ ( C @ tc_PropLog_Opl @ ( B @ ( D @ c_insert ) ) @ c_PropLog_Othms ) @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[513]) ).
thf(515,plain,
! [A: $i] : ( t_a @ tc_PropLog_Opl @ ( t_a @ ( t_a @ tc_PropLog_Opl @ ( v_H @ ( A @ c_insert ) ) @ c_PropLog_Othms ) @ ( v_p @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[514:[bind(A,$thf( v_p )),bind(B,$thf( v_H )),bind(C,$thf( t_a ))]]) ).
thf(573,plain,
! [A: $i] : ( t_a @ tc_PropLog_Opl @ ( t_a @ ( t_a @ tc_PropLog_Opl @ ( v_H @ ( A @ c_insert ) ) @ c_PropLog_Othms ) @ ( v_p @ c_in ) ) ),
inference(simp,[status(thm)],[515]) ).
thf(601,plain,
( ( ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( c_PropLog_Opl_Ofalse @ c_in ) ) )
!= ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( v_p @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9,512]) ).
thf(602,plain,
( ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( c_PropLog_Opl_Ofalse @ c_in ) ) )
!= ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( v_p @ c_in ) ) ) ),
inference(simp,[status(thm)],[601]) ).
thf(629,plain,
( ( ( t_a @ tc_PropLog_Opl )
!= ( t_a @ tc_PropLog_Opl ) )
| ( ( t_a @ ( v_H @ c_PropLog_Othms ) )
!= ( t_a @ ( v_H @ c_PropLog_Othms ) ) )
| ( c_PropLog_Opl_Ofalse != v_p ) ),
inference(simp,[status(thm)],[602]) ).
thf(640,plain,
c_PropLog_Opl_Ofalse != v_p,
inference(simp,[status(thm)],[629]) ).
thf(30,plain,
( ( t_a != t_a )
| ( c_PropLog_Opl_Ofalse != c_PropLog_Opl_Ofalse )
| ( ( t_a @ ( v_q @ ( v_p @ c_PropLog_Opl_Oop_A_N_62 ) ) )
!= v_q ) ),
inference(simp,[status(thm)],[29]) ).
thf(31,plain,
( ( t_a @ ( v_q @ ( v_p @ c_PropLog_Opl_Oop_A_N_62 ) ) )
!= v_q ),
inference(simp,[status(thm)],[30]) ).
thf(149,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_PropLog_Opl @ ( t_a @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ c_PropLog_Othms ) @ ( t_a @ ( c_PropLog_Opl_Ofalse @ ( v_q @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) )
!= ( C @ tc_PropLog_Opl @ ( B @ ( A @ c_in ) ) ) )
| ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[38,18]) ).
thf(150,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_PropLog_Opl @ ( t_a @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ c_PropLog_Othms ) @ ( t_a @ ( c_PropLog_Opl_Ofalse @ ( v_q @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) )
!= ( C @ tc_PropLog_Opl @ ( B @ ( A @ c_in ) ) ) )
| ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[149]) ).
thf(151,plain,
t_a @ tc_PropLog_Opl @ ( t_a @ ( t_a @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ c_PropLog_Othms ) @ c_PropLog_Othms ) @ ( t_a @ ( c_PropLog_Opl_Ofalse @ ( v_q @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ),
inference(pattern_uni,[status(thm)],[150:[bind(A,$thf( t_a @ ( c_PropLog_Opl_Ofalse @ ( v_q @ c_PropLog_Opl_Oop_A_N_62 ) ) )),bind(B,$thf( t_a @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ c_PropLog_Othms ) )),bind(C,$thf( t_a ))]]) ).
thf(298,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_PropLog_Opl @ ( t_a @ ( t_a @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ c_PropLog_Othms ) @ c_PropLog_Othms ) @ ( t_a @ ( c_PropLog_Opl_Ofalse @ ( v_q @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) )
!= ( C @ tc_PropLog_Opl @ ( B @ ( A @ c_in ) ) ) )
| ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[151,18]) ).
thf(299,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_PropLog_Opl @ ( t_a @ ( t_a @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ c_PropLog_Othms ) @ c_PropLog_Othms ) @ ( t_a @ ( c_PropLog_Opl_Ofalse @ ( v_q @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) )
!= ( C @ tc_PropLog_Opl @ ( B @ ( A @ c_in ) ) ) )
| ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[298]) ).
thf(300,plain,
t_a @ tc_PropLog_Opl @ ( t_a @ ( t_a @ ( t_a @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ c_PropLog_Othms ) @ c_PropLog_Othms ) @ c_PropLog_Othms ) @ ( t_a @ ( c_PropLog_Opl_Ofalse @ ( v_q @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ),
inference(pattern_uni,[status(thm)],[299:[bind(A,$thf( t_a @ ( c_PropLog_Opl_Ofalse @ ( v_q @ c_PropLog_Opl_Oop_A_N_62 ) ) )),bind(B,$thf( t_a @ ( t_a @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ c_PropLog_Othms ) @ c_PropLog_Othms ) )),bind(C,$thf( t_a ))]]) ).
thf(166,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_PropLog_Opl @ ( t_a @ ( t_a @ ( t_a @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ c_PropLog_Othms ) @ c_PropLog_Othms ) @ c_PropLog_Othms ) @ ( v_p @ c_in ) ) )
!= ( C @ tc_PropLog_Opl @ ( B @ ( A @ c_in ) ) ) )
| ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[132,18]) ).
thf(167,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_PropLog_Opl @ ( t_a @ ( t_a @ ( t_a @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ c_PropLog_Othms ) @ c_PropLog_Othms ) @ c_PropLog_Othms ) @ ( v_p @ c_in ) ) )
!= ( C @ tc_PropLog_Opl @ ( B @ ( A @ c_in ) ) ) )
| ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[166]) ).
thf(168,plain,
t_a @ tc_PropLog_Opl @ ( t_a @ ( t_a @ ( t_a @ ( t_a @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ c_PropLog_Othms ) @ c_PropLog_Othms ) @ c_PropLog_Othms ) @ c_PropLog_Othms ) @ ( v_p @ c_in ) ),
inference(pattern_uni,[status(thm)],[167:[bind(A,$thf( v_p )),bind(B,$thf( t_a @ ( t_a @ ( t_a @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ c_PropLog_Othms ) @ c_PropLog_Othms ) @ c_PropLog_Othms ) )),bind(C,$thf( t_a ))]]) ).
thf(1064,plain,
$false,
inference(e,[status(thm)],[10,14,132,9,96,44,12,609,35,648,11,326,762,120,20,29,248,512,598,21,28,38,13,41,573,17,640,18,16,31,151,300,168,19,596,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL443-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.13/5.40 % Computer : n016.cluster.edu
% 0.13/5.40 % Model : x86_64 x86_64
% 0.13/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.40 % Memory : 8046.5625MB
% 0.13/5.40 % OS : Linux 6.8.0-71-generic
% 0.13/5.40 % CPULimit : 300
% 0.13/5.40 % WCLimit : 300
% 0.13/5.40 % DateTime : Fri Sep 25 22:39:06 UTC 2026
% 0.13/5.40 % CPUTime :
% 0.13/5.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.17/5.99 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.19/6.16 % [INFO] Parsing done (171ms).
% 1.19/6.18 % [INFO] Running in sequential loop mode.
% 1.80/6.57 % [INFO] eprover registered as external prover.
% 1.80/6.58 % [INFO] Scanning for conjecture ...
% 2.00/6.67 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 2.15/6.71 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 2.15/6.72 % [INFO] Problem is propositional (TPTP CNF).
% 2.15/6.72 % [INFO] Type checking passed.
% 2.15/6.73 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 10.83/8.84 % External prover 'e' found a proof!
% 10.83/8.84 % [INFO] Killing All external provers ...
% 10.83/8.84 % Time passed: 3294ms (effective reasoning time: 2661ms)
% 10.83/8.84 % Axioms used in derivation (5): cls_PropLog_Oweaken__left__insert_0, cls_PropLog_Othms_OMP_0, cls_PropLog_Odeduction_0, cls_PropLog_Othms_OH_0, cls_Set_OinsertCI_1
% 10.83/8.84 % No. of inferences in proof: 102
% 10.83/8.85 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 3294 ms resp. 2661 ms w/o parsing
% 9.90/8.95 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.90/8.95 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------