%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU194+1 : 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 : n001.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 02:55:50 PM UTC 2026
% Result : Theorem 3.47s 1.20s
% Output : CNFRefutation 3.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 42 ( 9 unt; 0 def)
% Number of atoms : 165 ( 28 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 200 ( 77 ~; 87 |; 29 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 85 ( 0 sgn 80 !; 5 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f4,axiom,
! [X0,X1,X2] :
( X2 = set_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f27,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_dom(relation_dom_restriction(X2,X1)))
<=> ( in(X0,relation_dom(X2))
& in(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_relat_1) ).
fof(f29,conjecture,
! [X0,X1] :
( relation(X1)
=> relation_dom(relation_dom_restriction(X1,X0)) = set_intersection2(relation_dom(X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t90_relat_1) ).
fof(f30,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> relation_dom(relation_dom_restriction(X1,X0)) = set_intersection2(relation_dom(X1),X0) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f46,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( in(X0,relation_dom(relation_dom_restriction(X2,X1)))
<=> ( in(X0,relation_dom(X2))
& in(X0,X1) ) ) ),
inference(ennf_transformation,[],[f27]) ).
fof(f48,plain,
? [X0,X1] :
( relation(X1)
& relation_dom(relation_dom_restriction(X1,X0)) != set_intersection2(relation_dom(X1),X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(flattening,[],[f49]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( in(X4,X1)
& in(X4,X0) ) )
& ( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(rectify,[],[f50]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( in(X4,X1)
& in(X4,X0) ) )
& ( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ) ) )
& ( ( ( in(sK0(X0,X1,X2),X2)
| ( in(sK0(X0,X1,X2),X1)
& in(sK0(X0,X1,X2),X0) ) )
& ( ~ in(sK0(X0,X1,X2),X2)
| ~ in(sK0(X0,X1,X2),X1)
| ~ in(sK0(X0,X1,X2),X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f51]) ).
fof(f60,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ~ in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ( in(X0,relation_dom(X2))
& in(X0,X1) ) )
& ( ~ in(X0,relation_dom(X2))
| ~ in(X0,X1)
| in(X0,relation_dom(relation_dom_restriction(X2,X1))) ) ) ),
inference(nnf_transformation,[],[f46]) ).
fof(f61,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ~ in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ( in(X0,relation_dom(X2))
& in(X0,X1) ) )
& ( ~ in(X0,relation_dom(X2))
| ~ in(X0,X1)
| in(X0,relation_dom(relation_dom_restriction(X2,X1))) ) ) ),
inference(flattening,[],[f60]) ).
fof(f62,plain,
( relation(sK8)
& relation_dom(relation_dom_restriction(sK8,sK7)) != set_intersection2(relation_dom(sK8),sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X0,sK7),skolemize(X1,sK8)],[f48]) ).
fof(f65,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f69,plain,
! [X2,X0,X1] :
( in(sK0(X0,X1,X2),X2)
| in(sK0(X0,X1,X2),X1)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f52]) ).
fof(f70,plain,
! [X2,X0,X1] :
( in(sK0(X0,X1,X2),X2)
| in(sK0(X0,X1,X2),X0)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f52]) ).
fof(f71,plain,
! [X2,X0,X1] :
( ~ in(sK0(X0,X1,X2),X2)
| ~ in(sK0(X0,X1,X2),X1)
| ~ in(sK0(X0,X1,X2),X0)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f52]) ).
fof(f95,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| in(X0,relation_dom(X2)) ),
inference(cnf_transformation,[],[f61]) ).
fof(f96,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| in(X0,X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f97,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_dom(X2))
| ~ in(X0,X1)
| in(X0,relation_dom(relation_dom_restriction(X2,X1))) ),
inference(cnf_transformation,[],[f61]) ).
fof(f99,plain,
relation(sK8),
inference(cnf_transformation,[],[f62]) ).
fof(f100,plain,
relation_dom(relation_dom_restriction(sK8,sK7)) != set_intersection2(relation_dom(sK8),sK7),
inference(cnf_transformation,[],[f62]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f65]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X0,X1) = X2 )
| ~ in(sK0(X0,X1,X2),X2)
| ~ in(sK0(X0,X1,X2),X1)
| ~ in(sK0(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X0,X1,X2),X2)
| in(sK0(X0,X1,X2),X0)
| ( set_intersection2(X0,X1) = X2 ) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X0,X1,X2),X2)
| in(sK0(X0,X1,X2),X1)
| ( set_intersection2(X0,X1) = X2 ) ),
inference(cnf_transformation,[],[f69]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_dom(relation_dom_restriction(X1,X2)))
| ~ relation(X1)
| ~ in(X0,X2)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f97]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ relation(X1)
| ~ in(X0,relation_dom(relation_dom_restriction(X1,X2))) ),
inference(cnf_transformation,[],[f96]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_dom(X1))
| ~ relation(X1)
| ~ in(X0,relation_dom(relation_dom_restriction(X1,X2))) ),
inference(cnf_transformation,[],[f95]) ).
tcf(c_85,negated_conjecture,
set_intersection2(relation_dom(sK8),sK7) != relation_dom(relation_dom_restriction(sK8,sK7)),
inference(cnf_transformation,[],[f100]) ).
tcf(c_86,negated_conjecture,
relation(sK8),
inference(cnf_transformation,[],[f99]) ).
tcf(c_253,plain,
set_intersection2(sK7,relation_dom(sK8)) != relation_dom(relation_dom_restriction(sK8,sK7)),
inference(demodulation,[status(thm)],[c_85,c_51]) ).
tcf(c_814,plain,
( ( set_intersection2(sK7,relation_dom(sK8)) = relation_dom(relation_dom_restriction(sK8,sK7)) )
| ~ in(sK0(sK7,relation_dom(sK8),relation_dom(relation_dom_restriction(sK8,sK7))),sK7)
| ~ in(sK0(sK7,relation_dom(sK8),relation_dom(relation_dom_restriction(sK8,sK7))),relation_dom(sK8))
| ~ in(sK0(sK7,relation_dom(sK8),relation_dom(relation_dom_restriction(sK8,sK7))),relation_dom(relation_dom_restriction(sK8,sK7))) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_815,plain,
( in(sK0(sK7,relation_dom(sK8),relation_dom(relation_dom_restriction(sK8,sK7))),sK7)
| in(sK0(sK7,relation_dom(sK8),relation_dom(relation_dom_restriction(sK8,sK7))),relation_dom(relation_dom_restriction(sK8,sK7)))
| ( set_intersection2(sK7,relation_dom(sK8)) = relation_dom(relation_dom_restriction(sK8,sK7)) ) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_816,plain,
( in(sK0(sK7,relation_dom(sK8),relation_dom(relation_dom_restriction(sK8,sK7))),relation_dom(sK8))
| in(sK0(sK7,relation_dom(sK8),relation_dom(relation_dom_restriction(sK8,sK7))),relation_dom(relation_dom_restriction(sK8,sK7)))
| ( set_intersection2(sK7,relation_dom(sK8)) = relation_dom(relation_dom_restriction(sK8,sK7)) ) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_836,plain,
! [X0: $i] :
( in(sK0(sK7,relation_dom(sK8),relation_dom(relation_dom_restriction(sK8,sK7))),sK7)
| ~ relation(X0)
| ~ in(sK0(sK7,relation_dom(sK8),relation_dom(relation_dom_restriction(sK8,sK7))),relation_dom(relation_dom_restriction(X0,sK7))) ),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_998,plain,
( in(sK0(sK7,relation_dom(sK8),relation_dom(relation_dom_restriction(sK8,sK7))),relation_dom(relation_dom_restriction(sK8,sK7)))
| ~ relation(sK8)
| ~ in(sK0(sK7,relation_dom(sK8),relation_dom(relation_dom_restriction(sK8,sK7))),sK7)
| ~ in(sK0(sK7,relation_dom(sK8),relation_dom(relation_dom_restriction(sK8,sK7))),relation_dom(sK8)) ),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_1056,plain,
( in(sK0(sK7,relation_dom(sK8),relation_dom(relation_dom_restriction(sK8,sK7))),sK7)
| ~ relation(sK8)
| ~ in(sK0(sK7,relation_dom(sK8),relation_dom(relation_dom_restriction(sK8,sK7))),relation_dom(relation_dom_restriction(sK8,sK7))) ),
inference(instantiation,[status(thm)],[c_836]) ).
tcf(c_1193,plain,
! [X0: $i] :
( in(sK0(sK7,relation_dom(sK8),relation_dom(relation_dom_restriction(sK8,sK7))),relation_dom(sK8))
| ~ relation(sK8)
| ~ in(sK0(sK7,relation_dom(sK8),relation_dom(relation_dom_restriction(sK8,sK7))),relation_dom(relation_dom_restriction(sK8,X0))) ),
inference(instantiation,[status(thm)],[c_83]) ).
tcf(c_2935,plain,
( in(sK0(sK7,relation_dom(sK8),relation_dom(relation_dom_restriction(sK8,sK7))),relation_dom(sK8))
| ~ relation(sK8)
| ~ in(sK0(sK7,relation_dom(sK8),relation_dom(relation_dom_restriction(sK8,sK7))),relation_dom(relation_dom_restriction(sK8,sK7))) ),
inference(instantiation,[status(thm)],[c_1193]) ).
tcf(c_2936,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2935,c_1056,c_998,c_814,c_815,c_816,c_253,c_86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU194+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n001.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Thu Sep 24 13:13:37 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.13/0.40
% 0.13/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40
% 0.13/0.40 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 3.47/1.20 % SZS status Started for theBenchmark.p
% 3.47/1.20 % SZS status Theorem for theBenchmark.p
% 3.47/1.20
% 3.47/1.20 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.47/1.20
% 3.47/1.20 % ------ iProver source info
% 3.47/1.20
% 3.47/1.20 % git: date: 2026-07-19 20:42:38 +0200
% 3.47/1.20 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.47/1.20 % git: non_committed_changes: false
% 3.47/1.20
% 3.47/1.20 % ------ Parsing...
% 3.47/1.20 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.47/1.20
% 3.47/1.20 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 3.47/1.20
% 3.47/1.20 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.47/1.20
% 3.47/1.20 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.47/1.20 % ------ Proving...
% 3.47/1.20 % ------ Problem Properties
% 3.47/1.20
% 3.47/1.20 %
% 3.47/1.20 % clauses 35
% 3.47/1.20 % conjectures 1
% 3.47/1.20 % EPR 14
% 3.47/1.20 % Horn 31
% 3.47/1.20 % unary 13
% 3.47/1.20 % binary 10
% 3.47/1.20 % lits 71
% 3.47/1.20 % lits eq 11
% 3.47/1.20 % fd_pure 0
% 3.47/1.20 % fd_pseudo 0
% 3.47/1.20 % fd_cond 1
% 3.47/1.20 % fd_pseudo_cond 6
% 3.47/1.20 % AC symbols 0
% 3.47/1.20
% 3.47/1.20 % ------ Input Options Time Limit: Unbounded
% 3.47/1.20
% 3.47/1.20
% 3.47/1.20 % ------
% 3.47/1.20 % Current options:
% 3.47/1.20 % ------
% 3.47/1.20
% 3.47/1.20
% 3.47/1.20 %
% 3.47/1.20
% 3.47/1.20 % ------ Proving...
% 3.47/1.20 %
% 3.47/1.20
% 3.47/1.20 % SZS status Theorem for theBenchmark.p
% 3.47/1.20
% 3.47/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.47/1.20
% 3.47/1.20
%------------------------------------------------------------------------------