%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET956+1 : 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 : n011.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 4.23s 1.20s
% Output : CNFRefutation 4.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 35 ( 8 unt; 0 def)
% Number of atoms : 99 ( 12 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 106 ( 42 ~; 35 |; 22 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 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 : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 85 ( 0 sgn 73 !; 12 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f9,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(f10,conjecture,
! [X0,X1,X2,X3] :
( ( ! [X4,X5] :
( in(ordered_pair(X4,X5),X0)
=> in(ordered_pair(X4,X5),X3) )
& subset(X0,cartesian_product2(X1,X2)) )
=> subset(X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t109_zfmisc_1) ).
fof(f11,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( ! [X4,X5] :
( in(ordered_pair(X4,X5),X0)
=> in(ordered_pair(X4,X5),X3) )
& subset(X0,cartesian_product2(X1,X2)) )
=> subset(X0,X3) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f13,plain,
? [X0,X1,X2,X3] :
( ! [X4,X5] :
( ~ in(ordered_pair(X4,X5),X0)
| in(ordered_pair(X4,X5),X3) )
& subset(X0,cartesian_product2(X1,X2))
& ~ subset(X0,X3) ),
inference(ennf_transformation,[],[f11]) ).
fof(f14,plain,
? [X0,X1,X2,X3] :
( ! [X4,X5] :
( ~ in(ordered_pair(X4,X5),X0)
| in(ordered_pair(X4,X5),X3) )
& subset(X0,cartesian_product2(X1,X2))
& ~ subset(X0,X3) ),
inference(flattening,[],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f3]) ).
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,[],[f9]) ).
fof(f18,plain,
( ! [X4,X5] :
( ~ in(ordered_pair(X4,X5),sK0)
| in(ordered_pair(X4,X5),sK3) )
& subset(sK0,cartesian_product2(sK1,sK2))
& ~ subset(sK0,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f14]) ).
fof(f19,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f20,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(rectify,[],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK4(X0,X1),X0)
& ~ in(sK4(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X2,sK4(X0,X1))],[f20]) ).
fof(f22,plain,
! [X0,X1,X2,X3] :
( ( ordered_pair(sK5(X1,X2,X3),sK6(X1,X2,X3)) = X3
& in(sK6(X1,X2,X3),X2)
& in(sK5(X1,X2,X3),X1) )
| ~ in(X3,X0)
| ~ subset(X0,cartesian_product2(X1,X2)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X4,sK5(X1,X2,X3)),skolemize(X5,sK6(X1,X2,X3))],[f17]) ).
fof(f25,plain,
! [X4,X5] :
( ~ in(ordered_pair(X4,X5),sK0)
| in(ordered_pair(X4,X5),sK3) ),
inference(cnf_transformation,[],[f18]) ).
fof(f26,plain,
subset(sK0,cartesian_product2(sK1,sK2)),
inference(cnf_transformation,[],[f18]) ).
fof(f27,plain,
~ subset(sK0,sK3),
inference(cnf_transformation,[],[f18]) ).
fof(f29,plain,
! [X0,X1] :
( in(sK4(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f30,plain,
! [X0,X1] :
( ~ in(sK4(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f34,plain,
! [X2,X3,X0,X1] :
( ordered_pair(sK5(X1,X2,X3),sK6(X1,X2,X3)) = X3
| ~ in(X3,X0)
| ~ subset(X0,cartesian_product2(X1,X2)) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_49,negated_conjecture,
~ subset(sK0,sK3),
inference(cnf_transformation,[],[f27]) ).
tcf(c_50,negated_conjecture,
subset(sK0,cartesian_product2(sK1,sK2)),
inference(cnf_transformation,[],[f26]) ).
tcf(c_51,negated_conjecture,
! [X0: $i,X1: $i] :
( in(ordered_pair(X0,X1),sK3)
| ~ in(ordered_pair(X0,X1),sK0) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK4(X0,X1),X1) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK4(X0,X1),X0) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ordered_pair(sK5(X1,X2,X3),sK6(X1,X2,X3)) = X3 )
| ~ in(X3,X0)
| ~ subset(X0,cartesian_product2(X1,X2)) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_209,plain,
! [X0: $i,X1: $i] :
( in(sK4(X0,X1),X0)
| ( X1 != sK3 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_53]) ).
tcf(c_210,plain,
in(sK4(sK0,sK3),sK0),
inference(unflattening,[status(thm)],[c_209]) ).
tcf(c_214,plain,
! [X0: $i,X1: $i] :
( ~ in(sK4(X0,X1),X1)
| ( X1 != sK3 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_52]) ).
tcf(c_215,plain,
~ in(sK4(sK0,sK3),sK3),
inference(unflattening,[status(thm)],[c_214]) ).
tcf(c_736,plain,
! [X0: $i] :
( ( ordered_pair(sK5(sK1,sK2,X0),sK6(sK1,sK2,X0)) = X0 )
| ~ in(X0,sK0) ),
inference(superposition,[status(thm)],[c_50,c_60]) ).
tcf(c_750,plain,
! [X0: $i] :
( subset(sK0,X0)
| ( ordered_pair(sK5(sK1,sK2,sK4(sK0,X0)),sK6(sK1,sK2,sK4(sK0,X0))) = sK4(sK0,X0) ) ),
inference(superposition,[status(thm)],[c_53,c_736]) ).
tcf(c_782,plain,
ordered_pair(sK5(sK1,sK2,sK4(sK0,sK3)),sK6(sK1,sK2,sK4(sK0,sK3))) = sK4(sK0,sK3),
inference(superposition,[status(thm)],[c_750,c_49]) ).
tcf(c_804,plain,
( in(ordered_pair(sK5(sK1,sK2,sK4(sK0,sK3)),sK6(sK1,sK2,sK4(sK0,sK3))),sK3)
| ~ in(sK4(sK0,sK3),sK0) ),
inference(superposition,[status(thm)],[c_782,c_51]) ).
tcf(c_805,plain,
( in(sK4(sK0,sK3),sK3)
| ~ in(sK4(sK0,sK3),sK0) ),
inference(light_normalisation,[status(thm)],[c_804,c_782]) ).
tcf(c_808,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_805,c_215,c_210]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET956+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n011.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 12:26:57 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/0.40 Running first-order theorem proving
% 0.15/0.40 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
% 0.15/0.41
% 0.15/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.41
% 0.15/0.41 % Detected problem language: tptp
% 0.15/0.43 % Proving...
% 4.23/1.20 % SZS status Started for theBenchmark.p
% 4.23/1.20 % SZS status Theorem for theBenchmark.p
% 4.23/1.20
% 4.23/1.20 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.23/1.20
% 4.23/1.20 % ------ iProver source info
% 4.23/1.20
% 4.23/1.20 % git: date: 2026-07-19 20:42:38 +0200
% 4.23/1.20 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.23/1.20 % git: non_committed_changes: false
% 4.23/1.20
% 4.23/1.20 % ------ Parsing...
% 4.23/1.20 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.23/1.20
% 4.23/1.20 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 4.23/1.20
% 4.23/1.20 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.23/1.20
% 4.23/1.20 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.23/1.20 % ------ Proving...
% 4.23/1.20 % ------ Problem Properties
% 4.23/1.20
% 4.23/1.20 %
% 4.23/1.20 % clauses 15
% 4.23/1.20 % conjectures 3
% 4.23/1.20 % EPR 6
% 4.23/1.20 % Horn 14
% 4.23/1.20 % unary 7
% 4.23/1.20 % binary 4
% 4.23/1.20 % lits 27
% 4.23/1.20 % lits eq 2
% 4.23/1.20 % fd_pure 0
% 4.23/1.20 % fd_pseudo 0
% 4.23/1.20 % fd_cond 0
% 4.23/1.20 % fd_pseudo_cond 0
% 4.23/1.20 % AC symbols 0
% 4.23/1.20
% 4.23/1.20 % ------ Schedule dynamic 5 is on
% 4.23/1.20
% 4.23/1.20 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.23/1.20
% 4.23/1.20
% 4.23/1.20 % ------
% 4.23/1.20 % Current options:
% 4.23/1.20 % ------
% 4.23/1.20
% 4.23/1.20
% 4.23/1.20 %
% 4.23/1.20
% 4.23/1.20 % ------ Proving...
% 4.23/1.20 %
% 4.23/1.20
% 4.23/1.20 % SZS status Theorem for theBenchmark.p
% 4.23/1.20
% 4.23/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.23/1.21
% 4.23/1.21
%------------------------------------------------------------------------------