%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET825-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n003.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 02:48:40 PM UTC 2026
% Result : Unsatisfiable 17.23s 4.26s
% Output : CNFRefutation 17.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 27 ( 10 unt; 0 def)
% Number of atoms : 55 ( 16 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 45 ( 17 ~; 28 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 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 : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-4 aty)
% Number of variables : 14 ( 0 sgn 14 !; 0 ?; 7 :)
% Comments :
%------------------------------------------------------------------------------
fof(f173,axiom,
! [X0,X1] : c_in(c_Pair(X0,X0,X1,X1),c_Relation_OId,tc_prod(X1,X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-2.ax',cls_Relation_OIdI_0) ).
fof(f178,axiom,
! [X2,X0,X1] :
( X0 = X1
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_OId,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-2.ax',cls_Relation_Opair__in__Id__conv__iff1_0) ).
fof(f1434,negated_conjecture,
v_Q(v_n),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1435,negated_conjecture,
~ v_Q(v_m),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f1436,negated_conjecture,
! [X0] :
( ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),X0,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_x(X0),v_xa(X0),tc_nat,tc_nat),X0,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),X0,tc_prod(tc_nat,tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f1437,negated_conjecture,
! [X0] :
( ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),X0,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_Suc(v_x(X0)),c_Suc(v_xa(X0)),tc_nat,tc_nat),X0,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),X0,tc_prod(tc_nat,tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
tcf(c_1535,plain,
! [X0: $i,X1: $i] : c_in(c_Pair(X0,X0,X1,X1),c_Relation_OId,tc_prod(X1,X1)),
inference(cnf_transformation,[],[f173]) ).
tcf(c_1540,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_OId,tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f178]) ).
tcf(c_2001,negated_conjecture,
v_Q(v_n),
inference(cnf_transformation,[],[f1434]) ).
tcf(c_2002,negated_conjecture,
~ v_Q(v_m),
inference(cnf_transformation,[],[f1435]) ).
tcf(c_2003,negated_conjecture,
! [X0: $i] :
( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),X0,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_x(X0),v_xa(X0),tc_nat,tc_nat),X0,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),X0,tc_prod(tc_nat,tc_nat)) ),
inference(cnf_transformation,[],[f1436]) ).
tcf(c_2004,negated_conjecture,
! [X0: $i] :
( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),X0,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),X0,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_Suc(v_x(X0)),c_Suc(v_xa(X0)),tc_nat,tc_nat),X0,tc_prod(tc_nat,tc_nat)) ),
inference(cnf_transformation,[],[f1437]) ).
tcf(c_3189,plain,
c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)),
inference(instantiation,[status(thm)],[c_1535]) ).
tcf(c_10682,plain,
( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| ( v_x(c_Relation_OId) = v_xa(c_Relation_OId) )
| ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),
inference(superposition,[status(thm)],[c_2003,c_1540]) ).
tcf(c_10800,plain,
( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| ( v_x(c_Relation_OId) = v_xa(c_Relation_OId) ) ),
inference(global_subsumption_just,[status(thm)],[c_10682,c_3189,c_10682]) ).
tcf(c_10802,plain,
( ( v_n = v_m )
| ( v_x(c_Relation_OId) = v_xa(c_Relation_OId) ) ),
inference(superposition,[status(thm)],[c_10800,c_1540]) ).
tcf(c_11638,plain,
( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| ( v_n = v_m )
| ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_Suc(v_x(c_Relation_OId)),c_Suc(v_x(c_Relation_OId)),tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),
inference(superposition,[status(thm)],[c_10802,c_2004]) ).
tcf(c_11643,plain,
( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| ( v_n = v_m )
| ~ c_in(c_Pair(c_Suc(v_x(c_Relation_OId)),c_Suc(v_x(c_Relation_OId)),tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),
inference(global_subsumption_just,[status(thm)],[c_11638,c_3189,c_11638]) ).
tcf(c_11645,plain,
( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| ( v_n = v_m ) ),
inference(superposition,[status(thm)],[c_1535,c_11643]) ).
tcf(c_19513,plain,
( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| ( v_x(c_Relation_OId) = v_xa(c_Relation_OId) )
| ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),
inference(superposition,[status(thm)],[c_2003,c_1540]) ).
tcf(c_19673,plain,
( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| ( v_x(c_Relation_OId) = v_xa(c_Relation_OId) ) ),
inference(global_subsumption_just,[status(thm)],[c_19513,c_10800]) ).
tcf(c_19675,plain,
( ( v_n = v_m )
| ( v_x(c_Relation_OId) = v_xa(c_Relation_OId) ) ),
inference(superposition,[status(thm)],[c_19673,c_1540]) ).
tcf(c_19860,plain,
( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_x(c_Relation_OId),v_x(c_Relation_OId),tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| ( v_n = v_m )
| ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),
inference(superposition,[status(thm)],[c_19675,c_2003]) ).
tcf(c_20097,plain,
( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| ( v_n = v_m ) ),
inference(global_subsumption_just,[status(thm)],[c_19860,c_11645]) ).
tcf(c_20099,plain,
v_n = v_m,
inference(superposition,[status(thm)],[c_20097,c_1540]) ).
tcf(c_20446,plain,
~ v_Q(v_n),
inference(superposition,[status(thm)],[c_20099,c_2002]) ).
tcf(c_20447,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_20446,c_2001]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET825-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n003.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 12:06:21 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 17.23/4.26 % SZS status Started for theBenchmark.p
% 17.23/4.26 % SZS status Unsatisfiable for theBenchmark.p
% 17.23/4.26
% 17.23/4.26 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 17.23/4.26
% 17.23/4.26 % ------ iProver source info
% 17.23/4.26
% 17.23/4.26 % git: date: 2026-07-19 20:42:38 +0200
% 17.23/4.26 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 17.23/4.26 % git: non_committed_changes: false
% 17.23/4.26
% 17.23/4.26 % ------ Parsing...% successful
% 17.23/4.26
% 17.23/4.26
% 17.23/4.26 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 17.23/4.26
% 17.23/4.26 % ------ Preprocessing... sup_sim: 0 sf_s rm: 18 0s sf_e sup_sim: 0 sf_s rm: 4 0s sf_e %
% 17.23/4.26
% 17.23/4.26 % ------ Preprocessing...%
% 17.23/4.26
% 17.23/4.26 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 17.23/4.26 % ------ Proving...
% 17.23/4.26 % ------ Problem Properties
% 17.23/4.26
% 17.23/4.26 %
% 17.23/4.26 % clauses 554
% 17.23/4.26 % conjectures 32
% 17.23/4.26 % EPR 286
% 17.23/4.26 % Horn 526
% 17.23/4.26 % unary 126
% 17.23/4.26 % binary 371
% 17.23/4.26 % lits 1039
% 17.23/4.26 % lits eq 157
% 17.23/4.26 % fd_pure 0
% 17.23/4.26 % fd_pseudo 0
% 17.23/4.26 % fd_cond 21
% 17.23/4.26 % fd_pseudo_cond 37
% 17.23/4.26 % AC symbols 0
% 17.23/4.26
% 17.23/4.26 % ------ Input Options Time Limit: Unbounded
% 17.23/4.26
% 17.23/4.26
% 17.23/4.26 % ------
% 17.23/4.26 % Current options:
% 17.23/4.26 % ------
% 17.23/4.26
% 17.23/4.26
% 17.23/4.26 %
% 17.23/4.26
% 17.23/4.26 % ------ Proving...
% 17.23/4.26 %
% 17.23/4.26
% 17.23/4.26 % SZS status Unsatisfiable for theBenchmark.p
% 17.23/4.26
% 17.23/4.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 17.23/4.26
% 17.23/4.26
%------------------------------------------------------------------------------