%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET957+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n026.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 02:49:12 PM UTC 2026
% Result : Theorem 1.16s 1.29s
% Output : CNFRefutation 1.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 3
% Syntax : Number of formulae : 49 ( 8 unt; 0 def)
% Number of atoms : 143 ( 40 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 139 ( 45 ~; 57 |; 28 &)
% ( 5 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 15 ( 5 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; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 96 ( 0 sgn 74 !; 22 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X0,X1,X2,X3] :
~ ( ! [X4,X5] :
~ ( X3 = ordered_pair(X4,X5)
& in(X5,X2)
& in(X4,X1) )
& in(X3,X0)
& subset(X0,cartesian_product2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t103_zfmisc_1) ).
fof(f9,conjecture,
! [X0,X1,X2,X3,X4,X5] :
( ( ! [X6,X7] :
( in(ordered_pair(X6,X7),X0)
<=> in(ordered_pair(X6,X7),X3) )
& subset(X3,cartesian_product2(X4,X5))
& subset(X0,cartesian_product2(X1,X2)) )
=> X0 = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t110_zfmisc_1) ).
fof(f10,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5] :
( ( ! [X6,X7] :
( in(ordered_pair(X6,X7),X0)
<=> in(ordered_pair(X6,X7),X3) )
& subset(X3,cartesian_product2(X4,X5))
& subset(X0,cartesian_product2(X1,X2)) )
=> X0 = X3 ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
fof(f13,plain,
? [X0,X1,X2,X3,X4,X5] :
( ! [X6,X7] :
( in(ordered_pair(X6,X7),X0)
<=> in(ordered_pair(X6,X7),X3) )
& subset(X3,cartesian_product2(X4,X5))
& subset(X0,cartesian_product2(X1,X2))
& X0 != X3 ),
inference(ennf_transformation,[],[f10]) ).
fof(f14,plain,
? [X0,X1,X2,X3,X4,X5] :
( ! [X6,X7] :
( in(ordered_pair(X6,X7),X0)
<=> in(ordered_pair(X6,X7),X3) )
& subset(X3,cartesian_product2(X4,X5))
& subset(X0,cartesian_product2(X1,X2))
& X0 != X3 ),
inference(flattening,[],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( ? [X2] :
( in(X2,X0)
<~> in(X2,X1) )
| X0 = X1 ),
inference(ennf_transformation,[],[f11]) ).
fof(f17,plain,
! [X0,X1,X2,X3] :
( ? [X4,X5] :
( X3 = ordered_pair(X4,X5)
& in(X5,X2)
& in(X4,X1) )
| ~ in(X3,X0)
| ~ subset(X0,cartesian_product2(X1,X2)) ),
inference(ennf_transformation,[],[f8]) ).
fof(f18,plain,
? [X0,X1,X2,X3,X4,X5] :
( ! [X6,X7] :
( ( ~ in(ordered_pair(X6,X7),X0)
| in(ordered_pair(X6,X7),X3) )
& ( ~ in(ordered_pair(X6,X7),X3)
| in(ordered_pair(X6,X7),X0) ) )
& subset(X3,cartesian_product2(X4,X5))
& subset(X0,cartesian_product2(X1,X2))
& X0 != X3 ),
inference(nnf_transformation,[],[f14]) ).
fof(f19,plain,
( ! [X6,X7] :
( ( ~ in(ordered_pair(X6,X7),sK0)
| in(ordered_pair(X6,X7),sK3) )
& ( ~ in(ordered_pair(X6,X7),sK3)
| in(ordered_pair(X6,X7),sK0) ) )
& subset(sK3,cartesian_product2(sK4,sK5))
& subset(sK0,cartesian_product2(sK1,sK2))
& sK0 != sK3 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5)],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( ? [X2] :
( ( in(X2,X0)
| in(X2,X1) )
& ( ~ in(X2,X0)
| ~ in(X2,X1) ) )
| X0 = X1 ),
inference(nnf_transformation,[],[f15]) ).
fof(f21,plain,
! [X0,X1] :
( ( ( in(sK6(X0,X1),X0)
| in(sK6(X0,X1),X1) )
& ( ~ in(sK6(X0,X1),X0)
| ~ in(sK6(X0,X1),X1) ) )
| X0 = X1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X2,sK6(X0,X1))],[f20]) ).
fof(f22,plain,
! [X0,X1,X2,X3] :
( ( ordered_pair(sK7(X1,X2,X3),sK8(X1,X2,X3)) = X3
& in(sK8(X1,X2,X3),X2)
& in(sK7(X1,X2,X3),X1) )
| ~ in(X3,X0)
| ~ subset(X0,cartesian_product2(X1,X2)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X4,sK7(X1,X2,X3)),skolemize(X5,sK8(X1,X2,X3))],[f17]) ).
fof(f25,plain,
! [X6,X7] :
( ~ in(ordered_pair(X6,X7),sK0)
| in(ordered_pair(X6,X7),sK3) ),
inference(cnf_transformation,[],[f19]) ).
fof(f26,plain,
! [X6,X7] :
( ~ in(ordered_pair(X6,X7),sK3)
| in(ordered_pair(X6,X7),sK0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f27,plain,
subset(sK3,cartesian_product2(sK4,sK5)),
inference(cnf_transformation,[],[f19]) ).
fof(f28,plain,
subset(sK0,cartesian_product2(sK1,sK2)),
inference(cnf_transformation,[],[f19]) ).
fof(f29,plain,
sK0 != sK3,
inference(cnf_transformation,[],[f19]) ).
fof(f30,plain,
! [X0,X1] :
( in(sK6(X0,X1),X0)
| in(sK6(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f21]) ).
fof(f31,plain,
! [X0,X1] :
( ~ in(sK6(X0,X1),X0)
| ~ in(sK6(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f21]) ).
fof(f34,plain,
! [X2,X3,X0,X1] :
( ordered_pair(sK7(X1,X2,X3),sK8(X1,X2,X3)) = X3
| ~ in(X3,X0)
| ~ subset(X0,cartesian_product2(X1,X2)) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_49,negated_conjecture,
sK0 != sK3,
inference(cnf_transformation,[],[f29]) ).
tcf(c_50,negated_conjecture,
subset(sK0,cartesian_product2(sK1,sK2)),
inference(cnf_transformation,[],[f28]) ).
tcf(c_51,negated_conjecture,
subset(sK3,cartesian_product2(sK4,sK5)),
inference(cnf_transformation,[],[f27]) ).
tcf(c_52,negated_conjecture,
! [X0: $i,X1: $i] :
( in(ordered_pair(X0,X1),sK0)
| ~ in(ordered_pair(X0,X1),sK3) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_53,negated_conjecture,
! [X0: $i,X1: $i] :
( in(ordered_pair(X0,X1),sK3)
| ~ in(ordered_pair(X0,X1),sK0) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(sK6(X0,X1),X1)
| ~ in(sK6(X0,X1),X0) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( in(sK6(X0,X1),X1)
| in(sK6(X0,X1),X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ordered_pair(sK7(X1,X2,X3),sK8(X1,X2,X3)) = X3 )
| ~ in(X3,X0)
| ~ subset(X0,cartesian_product2(X1,X2)) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_788,plain,
! [X0: $i] :
( ( ordered_pair(sK7(sK1,sK2,X0),sK8(sK1,sK2,X0)) = X0 )
| ~ in(X0,sK0) ),
inference(superposition,[status(thm)],[c_50,c_60]) ).
tcf(c_789,plain,
! [X0: $i] :
( ( ordered_pair(sK7(sK4,sK5,X0),sK8(sK4,sK5,X0)) = X0 )
| ~ in(X0,sK3) ),
inference(superposition,[status(thm)],[c_51,c_60]) ).
tcf(c_810,plain,
! [X0: $i] :
( in(sK6(sK0,X0),X0)
| ( X0 = sK0 )
| ( ordered_pair(sK7(sK1,sK2,sK6(sK0,X0)),sK8(sK1,sK2,sK6(sK0,X0))) = sK6(sK0,X0) ) ),
inference(superposition,[status(thm)],[c_55,c_788]) ).
tcf(c_850,plain,
( ( sK0 = sK3 )
| ~ in(sK6(sK0,sK3),sK3)
| ~ in(sK6(sK0,sK3),sK0) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_873,plain,
( in(sK6(sK0,sK3),sK3)
| in(sK6(sK0,sK3),sK0)
| ( sK0 = sK3 ) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_894,plain,
( ( sK0 = sK3 )
| ( ordered_pair(sK7(sK4,sK5,sK6(sK0,sK3)),sK8(sK4,sK5,sK6(sK0,sK3))) = sK6(sK0,sK3) )
| ( ordered_pair(sK7(sK1,sK2,sK6(sK0,sK3)),sK8(sK1,sK2,sK6(sK0,sK3))) = sK6(sK0,sK3) ) ),
inference(superposition,[status(thm)],[c_810,c_789]) ).
tcf(c_898,plain,
( ( ordered_pair(sK7(sK4,sK5,sK6(sK0,sK3)),sK8(sK4,sK5,sK6(sK0,sK3))) = sK6(sK0,sK3) )
| ( ordered_pair(sK7(sK1,sK2,sK6(sK0,sK3)),sK8(sK1,sK2,sK6(sK0,sK3))) = sK6(sK0,sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_894,c_49]) ).
tcf(c_940,plain,
( in(ordered_pair(sK7(sK4,sK5,sK6(sK0,sK3)),sK8(sK4,sK5,sK6(sK0,sK3))),sK3)
| ( ordered_pair(sK7(sK1,sK2,sK6(sK0,sK3)),sK8(sK1,sK2,sK6(sK0,sK3))) = sK6(sK0,sK3) )
| ~ in(sK6(sK0,sK3),sK0) ),
inference(superposition,[status(thm)],[c_898,c_53]) ).
tcf(c_941,plain,
( in(ordered_pair(sK7(sK4,sK5,sK6(sK0,sK3)),sK8(sK4,sK5,sK6(sK0,sK3))),sK0)
| ( ordered_pair(sK7(sK1,sK2,sK6(sK0,sK3)),sK8(sK1,sK2,sK6(sK0,sK3))) = sK6(sK0,sK3) )
| ~ in(sK6(sK0,sK3),sK3) ),
inference(superposition,[status(thm)],[c_898,c_52]) ).
tcf(c_978,plain,
( in(sK6(sK0,sK3),sK0)
| ( ordered_pair(sK7(sK1,sK2,sK6(sK0,sK3)),sK8(sK1,sK2,sK6(sK0,sK3))) = sK6(sK0,sK3) )
| ~ in(sK6(sK0,sK3),sK3) ),
inference(superposition,[status(thm)],[c_898,c_941]) ).
tcf(c_979,plain,
( in(ordered_pair(sK7(sK4,sK5,sK6(sK0,sK3)),sK8(sK4,sK5,sK6(sK0,sK3))),sK3)
| ( ordered_pair(sK7(sK1,sK2,sK6(sK0,sK3)),sK8(sK1,sK2,sK6(sK0,sK3))) = sK6(sK0,sK3) )
| ~ in(sK6(sK0,sK3),sK3) ),
inference(superposition,[status(thm)],[c_941,c_53]) ).
tcf(c_1025,plain,
( in(ordered_pair(sK7(sK4,sK5,sK6(sK0,sK3)),sK8(sK4,sK5,sK6(sK0,sK3))),sK3)
| ( ordered_pair(sK7(sK1,sK2,sK6(sK0,sK3)),sK8(sK1,sK2,sK6(sK0,sK3))) = sK6(sK0,sK3) ) ),
inference(global_subsumption_just,[status(thm)],[c_979,c_49,c_873,c_940,c_979]) ).
tcf(c_1031,plain,
( in(sK6(sK0,sK3),sK3)
| ( ordered_pair(sK7(sK1,sK2,sK6(sK0,sK3)),sK8(sK1,sK2,sK6(sK0,sK3))) = sK6(sK0,sK3) ) ),
inference(superposition,[status(thm)],[c_898,c_1025]) ).
tcf(c_1032,plain,
( in(ordered_pair(sK7(sK4,sK5,sK6(sK0,sK3)),sK8(sK4,sK5,sK6(sK0,sK3))),sK0)
| ( ordered_pair(sK7(sK1,sK2,sK6(sK0,sK3)),sK8(sK1,sK2,sK6(sK0,sK3))) = sK6(sK0,sK3) ) ),
inference(superposition,[status(thm)],[c_1025,c_52]) ).
tcf(c_1086,plain,
ordered_pair(sK7(sK1,sK2,sK6(sK0,sK3)),sK8(sK1,sK2,sK6(sK0,sK3))) = sK6(sK0,sK3),
inference(global_subsumption_just,[status(thm)],[c_1032,c_49,c_850,c_978,c_1031]) ).
tcf(c_1090,plain,
( in(ordered_pair(sK7(sK1,sK2,sK6(sK0,sK3)),sK8(sK1,sK2,sK6(sK0,sK3))),sK3)
| ~ in(sK6(sK0,sK3),sK0) ),
inference(superposition,[status(thm)],[c_1086,c_53]) ).
tcf(c_1091,plain,
( in(ordered_pair(sK7(sK1,sK2,sK6(sK0,sK3)),sK8(sK1,sK2,sK6(sK0,sK3))),sK0)
| ~ in(sK6(sK0,sK3),sK3) ),
inference(superposition,[status(thm)],[c_1086,c_52]) ).
tcf(c_1092,plain,
( in(sK6(sK0,sK3),sK0)
| ~ in(sK6(sK0,sK3),sK3) ),
inference(light_normalisation,[status(thm)],[c_1091,c_1086]) ).
tcf(c_1095,plain,
( in(sK6(sK0,sK3),sK3)
| ~ in(sK6(sK0,sK3),sK0) ),
inference(light_normalisation,[status(thm)],[c_1090,c_1086]) ).
tcf(c_1160,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1092,c_1095,c_873,c_850,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET957+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.36 % Computer : n026.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Thu Sep 24 12:29:38 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 0.12/0.43
% 0.12/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.43
% 0.12/0.43 % Detected problem language: tptp
% 0.12/0.45 % Proving...
% 1.16/1.29 % SZS status Started for theBenchmark.p
% 1.16/1.29 % SZS status Theorem for theBenchmark.p
% 1.16/1.29
% 1.16/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.16/1.29
% 1.16/1.29 % ------ iProver source info
% 1.16/1.29
% 1.16/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 1.16/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.16/1.29 % git: non_committed_changes: false
% 1.16/1.29
% 1.16/1.29 % ------ Parsing...
% 1.16/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.16/1.29
% 1.16/1.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 1.16/1.29
% 1.16/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.16/1.29
% 1.16/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.16/1.29 % ------ Proving...
% 1.16/1.29 % ------ Problem Properties
% 1.16/1.29
% 1.16/1.29 %
% 1.16/1.29 % clauses 15
% 1.16/1.29 % conjectures 5
% 1.16/1.29 % EPR 5
% 1.16/1.29 % Horn 14
% 1.16/1.29 % unary 7
% 1.16/1.29 % binary 3
% 1.16/1.29 % lits 28
% 1.16/1.29 % lits eq 4
% 1.16/1.29 % fd_pure 0
% 1.16/1.29 % fd_pseudo 0
% 1.16/1.29 % fd_cond 0
% 1.16/1.29 % fd_pseudo_cond 2
% 1.16/1.29 % AC symbols 0
% 1.16/1.29
% 1.16/1.29 % ------ Schedule dynamic 5 is on
% 1.16/1.29
% 1.16/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.16/1.29
% 1.16/1.29
% 1.16/1.29 % ------
% 1.16/1.29 % Current options:
% 1.16/1.29 % ------
% 1.16/1.29
% 1.16/1.29
% 1.16/1.29 %
% 1.16/1.29
% 1.16/1.29 % ------ Proving...
% 1.16/1.29 %
% 1.16/1.29
% 1.16/1.29 % SZS status Theorem for theBenchmark.p
% 1.16/1.29
% 1.16/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.16/1.30
% 1.16/1.30
%------------------------------------------------------------------------------