%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU167+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n018.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 02:55:43 PM UTC 2026
% Result : Theorem 0.60s 11.30s
% Output : CNFRefutation 4.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 26 ( 7 unt; 0 def)
% Number of atoms : 59 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 58 ( 25 ~; 18 |; 11 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 57 ( 0 sgn 49 !; 8 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
fof(f53,axiom,
! [X0,X1,X2] :
( subset(X0,X1)
=> ( subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
& subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t118_zfmisc_1) ).
fof(f54,conjecture,
! [X0,X1,X2,X3] :
( ( subset(X2,X3)
& subset(X0,X1) )
=> subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_zfmisc_1) ).
fof(f55,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( subset(X2,X3)
& subset(X0,X1) )
=> subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
inference(negated_conjecture,[status(cth)],[f54]) ).
fof(f60,axiom,
! [X0,X1,X2] :
( ( subset(X1,X2)
& subset(X0,X1) )
=> subset(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(f121,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| ( subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
& subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2)) ) ),
inference(ennf_transformation,[],[f53]) ).
fof(f122,plain,
? [X0,X1,X2,X3] :
( subset(X2,X3)
& subset(X0,X1)
& ~ subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
inference(ennf_transformation,[],[f55]) ).
fof(f123,plain,
? [X0,X1,X2,X3] :
( subset(X2,X3)
& subset(X0,X1)
& ~ subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
inference(flattening,[],[f122]) ).
fof(f127,plain,
! [X0,X1,X2] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ),
inference(ennf_transformation,[],[f60]) ).
fof(f128,plain,
! [X0,X1,X2] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ),
inference(flattening,[],[f127]) ).
fof(f198,plain,
( subset(sK20,sK21)
& subset(sK18,sK19)
& ~ subset(cartesian_product2(sK18,sK20),cartesian_product2(sK19,sK21)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18,sK19,sK20,sK21]),skolemize(X0,sK18),skolemize(X1,sK19),skolemize(X2,sK20),skolemize(X3,sK21)],[f123]) ).
fof(f305,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1)) ),
inference(cnf_transformation,[],[f121]) ).
fof(f306,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2)) ),
inference(cnf_transformation,[],[f121]) ).
fof(f307,plain,
subset(sK20,sK21),
inference(cnf_transformation,[],[f198]) ).
fof(f308,plain,
subset(sK18,sK19),
inference(cnf_transformation,[],[f198]) ).
fof(f309,plain,
~ subset(cartesian_product2(sK18,sK20),cartesian_product2(sK19,sK21)),
inference(cnf_transformation,[],[f198]) ).
fof(f314,plain,
! [X2,X0,X1] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ),
inference(cnf_transformation,[],[f128]) ).
tcf(c_142,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f306]) ).
tcf(c_143,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f305]) ).
tcf(c_144,negated_conjecture,
~ subset(cartesian_product2(sK18,sK20),cartesian_product2(sK19,sK21)),
inference(cnf_transformation,[],[f309]) ).
tcf(c_145,negated_conjecture,
subset(sK18,sK19),
inference(cnf_transformation,[],[f308]) ).
tcf(c_146,negated_conjecture,
subset(sK20,sK21),
inference(cnf_transformation,[],[f307]) ).
tcf(c_151,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X2,X1)
| ~ subset(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f314]) ).
tcf(c_264,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X0,cartesian_product2(X1,X3))
| ~ subset(X2,X3)
| ~ subset(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_143,c_151]) ).
tcf(c_384,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_142,c_264]) ).
tcf(c_707,plain,
( ~ subset(sK20,sK21)
| ~ subset(sK18,sK19) ),
inference(superposition,[status(thm)],[c_384,c_144]) ).
tcf(c_714,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_707,c_145,c_146]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU167+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/10.38 % Computer : n018.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 : Thu Sep 24 13:03:30 UTC 2026
% 0.09/10.39 % CPUTime :
% 0.09/10.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/10.42 Running first-order theorem proving
% 0.13/10.42 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
% 0.13/10.43
% 0.13/10.43 % ======== iProver multi-core TPTP/SMT =========
% 0.13/10.43
% 0.13/10.43 % Detected problem language: tptp
% 0.13/10.44 % Proving...
% 0.60/11.30 % SZS status Started for theBenchmark.p
% 0.60/11.30 % SZS status Theorem for theBenchmark.p
% 0.60/11.30
% 0.60/11.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.60/11.30
% 0.60/11.30 % ------ iProver source info
% 0.60/11.30
% 0.60/11.30 % git: date: 2026-07-19 20:42:38 +0200
% 0.60/11.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.60/11.30 % git: non_committed_changes: false
% 0.60/11.30
% 0.60/11.30 % ------ Parsing...
% 0.60/11.30 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 0.60/11.30 % ------ Proving...
% 0.60/11.30 % ------ Problem Properties
% 0.60/11.30
% 0.60/11.30 %
% 0.60/11.30 % clauses 152
% 0.60/11.30 % conjectures 3
% 0.60/11.30 % EPR 25
% 0.60/11.30 % Horn 122
% 0.60/11.30 % unary 37
% 0.60/11.30 % binary 68
% 0.60/11.30 % lits 321
% 0.60/11.30 % lits eq 88
% 0.60/11.30 % fd_pure 0
% 0.60/11.30 % fd_pseudo 0
% 0.60/11.30 % fd_cond 3
% 0.60/11.30 % fd_pseudo_cond 36
% 0.60/11.30 % AC symbols 0
% 0.60/11.30
% 0.60/11.30 % ------ Input Options Time Limit: Unbounded
% 0.60/11.30
% 0.60/11.30
% 0.60/11.30 % ------
% 0.60/11.30 % Current options:
% 0.60/11.30 % ------
% 0.60/11.30
% 0.60/11.30
% 0.60/11.30 %
% 0.60/11.30
% 0.60/11.30 % ------ Proving...
% 0.60/11.30 %
% 0.60/11.30
% 0.60/11.30 % SZS status Theorem for theBenchmark.p
% 0.60/11.30
% 0.60/11.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.34/11.30
% 4.34/11.30
%------------------------------------------------------------------------------