%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL443-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n002.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 02:06:40 PM UTC 2026
% Result : Unsatisfiable 0.68s 11.21s
% Output : CNFRefutation 0.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of formulae : 32 ( 11 unt; 0 def)
% Number of atoms : 59 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 56 ( 29 ~; 27 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 5 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 59 ( 0 sgn 59 !; 0 ?; 41 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1] :
( 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)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Othms_OMP_0) ).
fof(f2,axiom,
! [X2,X3,X0,X1] :
( 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)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Odeduction_0) ).
fof(f3,axiom,
! [X2,X0,X1] :
( c_in(X0,c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2))
| ~ c_in(X0,X1,tc_PropLog_Opl(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Othms_OH_0) ).
fof(f4,axiom,
! [X2,X3,X0,X1] :
( c_in(X0,c_PropLog_Othms(c_insert(X3,X1,tc_PropLog_Opl(X2)),X2),tc_PropLog_Opl(X2))
| ~ c_in(X0,c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Oweaken__left__insert_0) ).
fof(f5,axiom,
! [X2,X0,X1] : c_in(X0,c_insert(X0,X1,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).
fof(f6,negated_conjecture,
c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f7,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)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f8,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)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(X1,c_PropLog_Othms(X3,X2),tc_PropLog_Opl(X2))
| ~ c_in(X0,c_PropLog_Othms(X3,X2),tc_PropLog_Opl(X2))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(X0,X1,X2),c_PropLog_Othms(X3,X2),tc_PropLog_Opl(X2)) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( 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,[],[f2]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(X0,c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2))
| ~ c_in(X0,X1,tc_PropLog_Opl(X2)) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(X0,c_PropLog_Othms(c_insert(X3,X1,tc_PropLog_Opl(X2)),X2),tc_PropLog_Opl(X2))
| ~ c_in(X0,c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2)) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] : c_in(X0,c_insert(X0,X1,X2),X2),
inference(cnf_transformation,[],[f5]) ).
tcf(c_62,negated_conjecture,
c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(cnf_transformation,[],[f6]) ).
tcf(c_63,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)),
inference(cnf_transformation,[],[f7]) ).
tcf(c_64,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)),
inference(cnf_transformation,[],[f8]) ).
tcf(c_98,plain,
! [X0_iProver_c_in_1: iProver_c_in_1,X0_iProver_c_PropLog_Othms_1: iProver_c_PropLog_Othms_1,X0_iProver_c_in_3: iProver_c_in_3] : c_in(X0_iProver_c_in_1,c_insert(X0_iProver_c_in_1,X0_iProver_c_PropLog_Othms_1,X0_iProver_c_in_3),X0_iProver_c_in_3),
inference(subtyping,[status(esa)],[c_61]) ).
tcf(c_99,plain,
! [X0_iProver_c_in_1: iProver_c_in_1,X0_iProver_c_PropLog_Othms_1: iProver_c_PropLog_Othms_1,X0_iProver_tc_PropLog_Opl_1: iProver_tc_PropLog_Opl_1,X1_iProver_c_in_1: iProver_c_in_1] :
( c_in(X0_iProver_c_in_1,c_PropLog_Othms(c_insert(X1_iProver_c_in_1,X0_iProver_c_PropLog_Othms_1,tc_PropLog_Opl(X0_iProver_tc_PropLog_Opl_1)),X0_iProver_tc_PropLog_Opl_1),tc_PropLog_Opl(X0_iProver_tc_PropLog_Opl_1))
| ~ c_in(X0_iProver_c_in_1,c_PropLog_Othms(X0_iProver_c_PropLog_Othms_1,X0_iProver_tc_PropLog_Opl_1),tc_PropLog_Opl(X0_iProver_tc_PropLog_Opl_1)) ),
inference(subtyping,[status(esa)],[c_60]) ).
tcf(c_100,plain,
! [X0_iProver_c_in_1: iProver_c_in_1,X0_iProver_c_PropLog_Othms_1: iProver_c_PropLog_Othms_1,X0_iProver_tc_PropLog_Opl_1: iProver_tc_PropLog_Opl_1] :
( c_in(X0_iProver_c_in_1,c_PropLog_Othms(X0_iProver_c_PropLog_Othms_1,X0_iProver_tc_PropLog_Opl_1),tc_PropLog_Opl(X0_iProver_tc_PropLog_Opl_1))
| ~ c_in(X0_iProver_c_in_1,X0_iProver_c_PropLog_Othms_1,tc_PropLog_Opl(X0_iProver_tc_PropLog_Opl_1)) ),
inference(subtyping,[status(esa)],[c_59]) ).
tcf(c_101,plain,
! [X0_iProver_c_in_1: iProver_c_in_1,X0_iProver_c_PropLog_Othms_1: iProver_c_PropLog_Othms_1,X0_iProver_tc_PropLog_Opl_1: iProver_tc_PropLog_Opl_1,X1_iProver_c_in_1: iProver_c_in_1] :
( c_in(c_PropLog_Opl_Oop_A_N_62(X1_iProver_c_in_1,X0_iProver_c_in_1,X0_iProver_tc_PropLog_Opl_1),c_PropLog_Othms(X0_iProver_c_PropLog_Othms_1,X0_iProver_tc_PropLog_Opl_1),tc_PropLog_Opl(X0_iProver_tc_PropLog_Opl_1))
| ~ c_in(X0_iProver_c_in_1,c_PropLog_Othms(c_insert(X1_iProver_c_in_1,X0_iProver_c_PropLog_Othms_1,tc_PropLog_Opl(X0_iProver_tc_PropLog_Opl_1)),X0_iProver_tc_PropLog_Opl_1),tc_PropLog_Opl(X0_iProver_tc_PropLog_Opl_1)) ),
inference(subtyping,[status(esa)],[c_58]) ).
tcf(c_102,plain,
! [X0_iProver_c_in_1: iProver_c_in_1,X0_iProver_c_PropLog_Othms_1: iProver_c_PropLog_Othms_1,X0_iProver_tc_PropLog_Opl_1: iProver_tc_PropLog_Opl_1,X1_iProver_c_in_1: iProver_c_in_1] :
( c_in(X1_iProver_c_in_1,c_PropLog_Othms(X0_iProver_c_PropLog_Othms_1,X0_iProver_tc_PropLog_Opl_1),tc_PropLog_Opl(X0_iProver_tc_PropLog_Opl_1))
| ~ c_in(X0_iProver_c_in_1,c_PropLog_Othms(X0_iProver_c_PropLog_Othms_1,X0_iProver_tc_PropLog_Opl_1),tc_PropLog_Opl(X0_iProver_tc_PropLog_Opl_1))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(X0_iProver_c_in_1,X1_iProver_c_in_1,X0_iProver_tc_PropLog_Opl_1),c_PropLog_Othms(X0_iProver_c_PropLog_Othms_1,X0_iProver_tc_PropLog_Opl_1),tc_PropLog_Opl(X0_iProver_tc_PropLog_Opl_1)) ),
inference(subtyping,[status(esa)],[c_57]) ).
tcf(c_108,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_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)) ),
inference(instantiation,[status(thm)],[c_101]) ).
tcf(c_122,plain,
! [X0_iProver_c_in_1: iProver_c_in_1] :
( c_in(X0_iProver_c_in_1,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))
| ~ c_in(X0_iProver_c_in_1,c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),tc_PropLog_Opl(t_a)) ),
inference(instantiation,[status(thm)],[c_100]) ).
tcf(c_123,plain,
! [X0_iProver_c_in_1: iProver_c_in_1] :
( c_in(X0_iProver_c_in_1,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))
| ~ c_in(X0_iProver_c_in_1,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) ),
inference(instantiation,[status(thm)],[c_99]) ).
tcf(c_146,plain,
( c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),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))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),tc_PropLog_Opl(t_a)) ),
inference(instantiation,[status(thm)],[c_122]) ).
tcf(c_147,plain,
( c_in(v_p,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))
| ~ c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) ),
inference(instantiation,[status(thm)],[c_123]) ).
tcf(c_148,plain,
( c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),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))
| ~ 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(instantiation,[status(thm)],[c_123]) ).
tcf(c_186,plain,
! [X0_iProver_c_in_1: iProver_c_in_1,X1_iProver_c_in_1: iProver_c_in_1,X2_iProver_c_in_1: iProver_c_in_1] :
( c_in(X1_iProver_c_in_1,c_PropLog_Othms(c_insert(X2_iProver_c_in_1,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
| ~ c_in(X0_iProver_c_in_1,c_PropLog_Othms(c_insert(X2_iProver_c_in_1,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(X0_iProver_c_in_1,X1_iProver_c_in_1,t_a),c_PropLog_Othms(c_insert(X2_iProver_c_in_1,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) ),
inference(instantiation,[status(thm)],[c_102]) ).
tcf(c_203,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),tc_PropLog_Opl(t_a)),
inference(instantiation,[status(thm)],[c_98]) ).
tcf(c_317,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))
| ~ c_in(v_q,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))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),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)) ),
inference(instantiation,[status(thm)],[c_186]) ).
tcf(c_350,plain,
( c_in(v_q,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))
| ~ c_in(v_p,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))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),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)) ),
inference(instantiation,[status(thm)],[c_186]) ).
tcf(c_351,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_350,c_317,c_203,c_148,c_147,c_146,c_108,c_64,c_63,c_62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL443-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/10.38 % Computer : n002.cluster.edu
% 0.09/10.38 % Model : x86_64 x86_64
% 0.09/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.38 % Memory : 8046.5625MB
% 0.09/10.38 % OS : Linux 6.8.0-71-generic
% 0.09/10.38 % CPULimit : 300
% 0.09/10.38 % WCLimit : 300
% 0.09/10.38 % DateTime : Wed Sep 23 23:26:47 UTC 2026
% 0.09/10.39 % CPUTime :
% 0.09/10.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/10.42 Running first-order theorem proving
% 0.15/10.42 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/10.43
% 0.15/10.43 % ======== iProver multi-core TPTP/SMT =========
% 0.15/10.43
% 0.15/10.43 % Detected problem language: tptp
% 0.15/10.45 % Proving...
% 0.68/11.21 % SZS status Started for theBenchmark.p
% 0.68/11.21 % SZS status Unsatisfiable for theBenchmark.p
% 0.68/11.21
% 0.68/11.21 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.68/11.21
% 0.68/11.21 % ------ iProver source info
% 0.68/11.21
% 0.68/11.21 % git: date: 2026-07-19 20:42:38 +0200
% 0.68/11.21 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.68/11.21 % git: non_committed_changes: false
% 0.68/11.21
% 0.68/11.21 % ------ Parsing...% successful
% 0.68/11.21
% 0.68/11.21
% 0.68/11.21 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.68/11.21
% 0.68/11.21 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 0.68/11.21
% 0.68/11.21 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.68/11.21 % ------ Proving...
% 0.68/11.21 % ------ Problem Properties
% 0.68/11.21
% 0.68/11.21 %
% 0.68/11.21 % clauses 8
% 0.68/11.21 % conjectures 3
% 0.68/11.21 % EPR 0
% 0.68/11.21 % Horn 8
% 0.68/11.21 % unary 4
% 0.68/11.21 % binary 3
% 0.68/11.21 % lits 13
% 0.68/11.21 % lits eq 0
% 0.68/11.21 % fd_pure 0
% 0.68/11.21 % fd_pseudo 0
% 0.68/11.21 % fd_cond 0
% 0.68/11.21 % fd_pseudo_cond 0
% 0.68/11.21 % AC symbols 0
% 0.68/11.21
% 0.68/11.21 % ------ Input Options Time Limit: Unbounded
% 0.68/11.21
% 0.68/11.21
% 0.68/11.21 % ------
% 0.68/11.21 % Current options:
% 0.68/11.21 % ------
% 0.68/11.21
% 0.68/11.21
% 0.68/11.21 %
% 0.68/11.21
% 0.68/11.21 % ------ Proving...
% 0.68/11.21 %
% 0.68/11.21
% 0.68/11.21 % SZS status Unsatisfiable for theBenchmark.p
% 0.68/11.21
% 0.68/11.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.68/11.21
% 0.68/11.21
%------------------------------------------------------------------------------