%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU241+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 : n013.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 02:56:19 PM UTC 2026
% Result : Theorem 2.79s 1.25s
% Output : CNFRefutation 2.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 11
% Syntax : Number of formulae : 104 ( 16 unt; 5 def)
% Number of atoms : 428 ( 57 equ)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 504 ( 213 ~; 231 |; 42 &)
% ( 7 <=>; 9 =>; 0 <=; 2 <~>)
% 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 : 11 ( 9 usr; 6 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 183 ( 0 sgn 168 !; 15 ?; 70 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f6,axiom,
! [X0] :
( relation(X0)
=> ( antisymmetric(X0)
<=> is_antisymmetric_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_relat_2) ).
fof(f7,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( is_antisymmetric_in(X0,X1)
<=> ! [X2,X3] :
( ( in(ordered_pair(X3,X2),X0)
& in(ordered_pair(X2,X3),X0)
& in(X3,X1)
& in(X2,X1) )
=> X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_2) ).
fof(f8,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f25,conjecture,
! [X0] :
( relation(X0)
=> ( antisymmetric(X0)
<=> ! [X1,X2] :
( ( in(ordered_pair(X2,X1),X0)
& in(ordered_pair(X1,X2),X0) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_wellord1) ).
fof(f26,negated_conjecture,
~ ! [X0] :
( relation(X0)
=> ( antisymmetric(X0)
<=> ! [X1,X2] :
( ( in(ordered_pair(X2,X1),X0)
& in(ordered_pair(X1,X2),X0) )
=> X1 = X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f25]) ).
fof(f35,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X1,relation_field(X2))
& in(X0,relation_field(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_relat_1) ).
fof(f46,plain,
! [X0] :
( ~ relation(X0)
| ( antisymmetric(X0)
<=> is_antisymmetric_in(X0,relation_field(X0)) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f47,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( is_antisymmetric_in(X0,X1)
<=> ! [X2,X3] :
( ~ in(ordered_pair(X3,X2),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(X3,X1)
| ~ in(X2,X1)
| X2 = X3 ) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f48,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( is_antisymmetric_in(X0,X1)
<=> ! [X2,X3] :
( ~ in(ordered_pair(X3,X2),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(X3,X1)
| ~ in(X2,X1)
| X2 = X3 ) ) ),
inference(flattening,[],[f47]) ).
fof(f52,plain,
? [X0] :
( relation(X0)
& ( antisymmetric(X0)
<~> ! [X1,X2] :
( ~ in(ordered_pair(X2,X1),X0)
| ~ in(ordered_pair(X1,X2),X0)
| X1 = X2 ) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f53,plain,
? [X0] :
( relation(X0)
& ( antisymmetric(X0)
<~> ! [X1,X2] :
( ~ in(ordered_pair(X2,X1),X0)
| ~ in(ordered_pair(X1,X2),X0)
| X1 = X2 ) ) ),
inference(flattening,[],[f52]) ).
fof(f57,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2)
| ( in(X1,relation_field(X2))
& in(X0,relation_field(X2)) ) ),
inference(ennf_transformation,[],[f35]) ).
fof(f58,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2)
| ( in(X1,relation_field(X2))
& in(X0,relation_field(X2)) ) ),
inference(flattening,[],[f57]) ).
fof(f62,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ antisymmetric(X0)
| is_antisymmetric_in(X0,relation_field(X0)) )
& ( ~ is_antisymmetric_in(X0,relation_field(X0))
| antisymmetric(X0) ) ) ),
inference(nnf_transformation,[],[f46]) ).
fof(f63,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ~ is_antisymmetric_in(X0,X1)
| ! [X2,X3] :
( ~ in(ordered_pair(X3,X2),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(X3,X1)
| ~ in(X2,X1)
| X2 = X3 ) )
& ( ? [X2,X3] :
( in(ordered_pair(X3,X2),X0)
& in(ordered_pair(X2,X3),X0)
& in(X3,X1)
& in(X2,X1)
& X2 != X3 )
| is_antisymmetric_in(X0,X1) ) ) ),
inference(nnf_transformation,[],[f48]) ).
fof(f64,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ~ is_antisymmetric_in(X0,X1)
| ! [X4,X5] :
( ~ in(ordered_pair(X5,X4),X0)
| ~ in(ordered_pair(X4,X5),X0)
| ~ in(X5,X1)
| ~ in(X4,X1)
| X4 = X5 ) )
& ( ? [X2,X3] :
( in(ordered_pair(X3,X2),X0)
& in(ordered_pair(X2,X3),X0)
& in(X3,X1)
& in(X2,X1)
& X2 != X3 )
| is_antisymmetric_in(X0,X1) ) ) ),
inference(rectify,[],[f63]) ).
fof(f65,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ~ is_antisymmetric_in(X0,X1)
| ! [X4,X5] :
( ~ in(ordered_pair(X5,X4),X0)
| ~ in(ordered_pair(X4,X5),X0)
| ~ in(X5,X1)
| ~ in(X4,X1)
| X4 = X5 ) )
& ( ( in(ordered_pair(sK1(X0,X1),sK0(X0,X1)),X0)
& in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0)
& in(sK1(X0,X1),X1)
& in(sK0(X0,X1),X1)
& sK0(X0,X1) != sK1(X0,X1) )
| is_antisymmetric_in(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK0(X0,X1)),skolemize(X3,sK1(X0,X1))],[f64]) ).
fof(f67,plain,
? [X0] :
( relation(X0)
& ( antisymmetric(X0)
| ! [X1,X2] :
( ~ in(ordered_pair(X2,X1),X0)
| ~ in(ordered_pair(X1,X2),X0)
| X1 = X2 ) )
& ( ~ antisymmetric(X0)
| ? [X1,X2] :
( in(ordered_pair(X2,X1),X0)
& in(ordered_pair(X1,X2),X0)
& X1 != X2 ) ) ),
inference(nnf_transformation,[],[f53]) ).
fof(f68,plain,
? [X0] :
( relation(X0)
& ( antisymmetric(X0)
| ! [X1,X2] :
( ~ in(ordered_pair(X2,X1),X0)
| ~ in(ordered_pair(X1,X2),X0)
| X1 = X2 ) )
& ( ~ antisymmetric(X0)
| ? [X1,X2] :
( in(ordered_pair(X2,X1),X0)
& in(ordered_pair(X1,X2),X0)
& X1 != X2 ) ) ),
inference(flattening,[],[f67]) ).
fof(f69,plain,
? [X0] :
( relation(X0)
& ( antisymmetric(X0)
| ! [X3,X4] :
( ~ in(ordered_pair(X4,X3),X0)
| ~ in(ordered_pair(X3,X4),X0)
| X3 = X4 ) )
& ( ~ antisymmetric(X0)
| ? [X1,X2] :
( in(ordered_pair(X2,X1),X0)
& in(ordered_pair(X1,X2),X0)
& X1 != X2 ) ) ),
inference(rectify,[],[f68]) ).
fof(f70,plain,
( relation(sK3)
& ( antisymmetric(sK3)
| ! [X3,X4] :
( ~ in(ordered_pair(X4,X3),sK3)
| ~ in(ordered_pair(X3,X4),sK3)
| X3 = X4 ) )
& ( ~ antisymmetric(sK3)
| ( in(ordered_pair(sK5,sK4),sK3)
& in(ordered_pair(sK4,sK5),sK3)
& sK4 != sK5 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5)],[f69]) ).
fof(f80,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f82,plain,
! [X0] :
( ~ relation(X0)
| ~ antisymmetric(X0)
| is_antisymmetric_in(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f62]) ).
fof(f83,plain,
! [X0] :
( ~ relation(X0)
| ~ is_antisymmetric_in(X0,relation_field(X0))
| antisymmetric(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f84,plain,
! [X0,X1,X4,X5] :
( ~ relation(X0)
| ~ is_antisymmetric_in(X0,X1)
| ~ in(ordered_pair(X5,X4),X0)
| ~ in(ordered_pair(X4,X5),X0)
| ~ in(X5,X1)
| ~ in(X4,X1)
| X4 = X5 ),
inference(cnf_transformation,[],[f65]) ).
fof(f85,plain,
! [X0,X1] :
( ~ relation(X0)
| in(ordered_pair(sK1(X0,X1),sK0(X0,X1)),X0)
| is_antisymmetric_in(X0,X1) ),
inference(cnf_transformation,[],[f65]) ).
fof(f86,plain,
! [X0,X1] :
( ~ relation(X0)
| in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0)
| is_antisymmetric_in(X0,X1) ),
inference(cnf_transformation,[],[f65]) ).
fof(f89,plain,
! [X0,X1] :
( ~ relation(X0)
| sK0(X0,X1) != sK1(X0,X1)
| is_antisymmetric_in(X0,X1) ),
inference(cnf_transformation,[],[f65]) ).
fof(f90,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f8]) ).
fof(f98,plain,
relation(sK3),
inference(cnf_transformation,[],[f70]) ).
fof(f99,plain,
! [X3,X4] :
( antisymmetric(sK3)
| ~ in(ordered_pair(X4,X3),sK3)
| ~ in(ordered_pair(X3,X4),sK3)
| X3 = X4 ),
inference(cnf_transformation,[],[f70]) ).
fof(f100,plain,
( ~ antisymmetric(sK3)
| in(ordered_pair(sK5,sK4),sK3) ),
inference(cnf_transformation,[],[f70]) ).
fof(f101,plain,
( ~ antisymmetric(sK3)
| in(ordered_pair(sK4,sK5),sK3) ),
inference(cnf_transformation,[],[f70]) ).
fof(f102,plain,
( ~ antisymmetric(sK3)
| sK4 != sK5 ),
inference(cnf_transformation,[],[f70]) ).
fof(f115,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2)
| in(X1,relation_field(X2)) ),
inference(cnf_transformation,[],[f58]) ).
fof(f116,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2)
| in(X0,relation_field(X2)) ),
inference(cnf_transformation,[],[f58]) ).
fof(f120,plain,
! [X0,X1] :
( ~ relation(X0)
| in(unordered_pair(unordered_pair(sK0(X0,X1),sK1(X0,X1)),singleton(sK0(X0,X1))),X0)
| is_antisymmetric_in(X0,X1) ),
inference(definition_unfolding,[],[f86,f90]) ).
fof(f121,plain,
! [X0,X1] :
( ~ relation(X0)
| in(unordered_pair(unordered_pair(sK1(X0,X1),sK0(X0,X1)),singleton(sK1(X0,X1))),X0)
| is_antisymmetric_in(X0,X1) ),
inference(definition_unfolding,[],[f85,f90]) ).
fof(f122,plain,
! [X0,X1,X4,X5] :
( ~ relation(X0)
| ~ is_antisymmetric_in(X0,X1)
| ~ in(unordered_pair(unordered_pair(X5,X4),singleton(X5)),X0)
| ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),X0)
| ~ in(X5,X1)
| ~ in(X4,X1)
| X4 = X5 ),
inference(definition_unfolding,[],[f84,f90,f90]) ).
fof(f124,plain,
( ~ antisymmetric(sK3)
| in(unordered_pair(unordered_pair(sK4,sK5),singleton(sK4)),sK3) ),
inference(definition_unfolding,[],[f101,f90]) ).
fof(f125,plain,
( ~ antisymmetric(sK3)
| in(unordered_pair(unordered_pair(sK5,sK4),singleton(sK5)),sK3) ),
inference(definition_unfolding,[],[f100,f90]) ).
fof(f126,plain,
! [X3,X4] :
( antisymmetric(sK3)
| ~ in(unordered_pair(unordered_pair(X4,X3),singleton(X4)),sK3)
| ~ in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),sK3)
| X3 = X4 ),
inference(definition_unfolding,[],[f99,f90,f90]) ).
fof(f127,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2)
| in(X0,relation_field(X2)) ),
inference(definition_unfolding,[],[f116,f90]) ).
fof(f128,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2)
| in(X1,relation_field(X2)) ),
inference(definition_unfolding,[],[f115,f90]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f80]) ).
tcf(c_53,plain,
! [X0: $i] :
( antisymmetric(X0)
| ~ relation(X0)
| ~ is_antisymmetric_in(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_54,plain,
! [X0: $i] :
( is_antisymmetric_in(X0,relation_field(X0))
| ~ relation(X0)
| ~ antisymmetric(X0) ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( is_antisymmetric_in(X0,X1)
| ~ relation(X0)
| ( sK0(X0,X1) != sK1(X0,X1) ) ),
inference(cnf_transformation,[],[f89]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( is_antisymmetric_in(X0,X1)
| in(unordered_pair(unordered_pair(sK0(X0,X1),sK1(X0,X1)),singleton(sK0(X0,X1))),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f120]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( is_antisymmetric_in(X0,X1)
| in(unordered_pair(unordered_pair(sK1(X0,X1),sK0(X0,X1)),singleton(sK1(X0,X1))),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f121]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X1 )
| ~ relation(X2)
| ~ is_antisymmetric_in(X2,X3)
| ~ in(X1,X3)
| ~ in(X0,X3)
| ~ in(unordered_pair(unordered_pair(X1,X0),singleton(X1)),X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_68,negated_conjecture,
( ~ antisymmetric(sK3)
| ( sK4 != sK5 ) ),
inference(cnf_transformation,[],[f102]) ).
tcf(c_69,negated_conjecture,
( in(unordered_pair(unordered_pair(sK4,sK5),singleton(sK4)),sK3)
| ~ antisymmetric(sK3) ),
inference(cnf_transformation,[],[f124]) ).
tcf(c_70,negated_conjecture,
( in(unordered_pair(unordered_pair(sK5,sK4),singleton(sK5)),sK3)
| ~ antisymmetric(sK3) ),
inference(cnf_transformation,[],[f125]) ).
tcf(c_71,negated_conjecture,
! [X0: $i,X1: $i] :
( antisymmetric(sK3)
| ( X0 = X1 )
| ~ in(unordered_pair(unordered_pair(X1,X0),singleton(X1)),sK3)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK3) ),
inference(cnf_transformation,[],[f126]) ).
tcf(c_72,negated_conjecture,
relation(sK3),
inference(cnf_transformation,[],[f98]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_field(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
inference(cnf_transformation,[],[f127]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,relation_field(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
inference(cnf_transformation,[],[f128]) ).
tcf(c_335,plain,
( in(unordered_pair(singleton(sK5),unordered_pair(sK4,sK5)),sK3)
| ~ antisymmetric(sK3) ),
inference(demodulation,[status(thm)],[c_70,c_51]) ).
tcf(c_342,plain,
( in(unordered_pair(singleton(sK4),unordered_pair(sK4,sK5)),sK3)
| ~ antisymmetric(sK3) ),
inference(demodulation,[status(thm)],[c_69,c_51]) ).
tcf(c_371,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,relation_field(X2))
| ~ relation(X2)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2) ),
inference(demodulation,[status(thm)],[c_86,c_51]) ).
tcf(c_381,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_field(X2))
| ~ relation(X2)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2) ),
inference(demodulation,[status(thm)],[c_85,c_51]) ).
tcf(c_391,plain,
! [X0: $i,X1: $i] :
( is_antisymmetric_in(X0,X1)
| in(unordered_pair(singleton(sK1(X0,X1)),unordered_pair(sK0(X0,X1),sK1(X0,X1))),X0)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_59,c_51]) ).
tcf(c_401,plain,
! [X0: $i,X1: $i] :
( is_antisymmetric_in(X0,X1)
| in(unordered_pair(singleton(sK0(X0,X1)),unordered_pair(sK0(X0,X1),sK1(X0,X1))),X0)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_58,c_51]) ).
tcf(c_411,plain,
! [X0: $i,X1: $i] :
( antisymmetric(sK3)
| ( X0 = X1 )
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),sK3)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK3) ),
inference(demodulation,[status(thm)],[c_71,c_51]) ).
tcf(c_424,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X1 )
| ~ relation(X2)
| ~ is_antisymmetric_in(X2,X3)
| ~ in(X1,X3)
| ~ in(X0,X3)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),X2)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2) ),
inference(demodulation,[status(thm)],[c_60,c_51]) ).
tcf(c_853,plain,
! [X0: $i,X1: $i] :
( is_antisymmetric_in(X0,X1)
| in(unordered_pair(singleton(sK1(X0,X1)),unordered_pair(sK0(X0,X1),sK1(X0,X1))),X0)
| ( X0 != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_391,c_72]) ).
tcf(c_854,plain,
! [X0: $i] :
( is_antisymmetric_in(sK3,X0)
| in(unordered_pair(singleton(sK1(sK3,X0)),unordered_pair(sK0(sK3,X0),sK1(sK3,X0))),sK3) ),
inference(unflattening,[status(thm)],[c_853]) ).
tcf(c_885,plain,
! [X0: $i,X1: $i] :
( is_antisymmetric_in(X0,X1)
| ( X0 != sK3 )
| ( sK0(X0,X1) != sK1(X0,X1) ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_72]) ).
tcf(c_886,plain,
! [X0: $i] :
( is_antisymmetric_in(sK3,X0)
| ( sK0(sK3,X0) != sK1(sK3,X0) ) ),
inference(unflattening,[status(thm)],[c_885]) ).
tcf(c_2478,definition,
iPr_def_10 = singleton(sK4),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2479,definition,
iPr_def_11 = unordered_pair(sK4,sK5),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_2480,definition,
iPr_def_12 = unordered_pair(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_2481,definition,
iPr_def_13 = singleton(sK5),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_2482,definition,
iPr_def_14 = unordered_pair(iPr_def_13,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_2483,plain,
! [X0: $i,X1: $i] :
( antisymmetric(sK3)
| ( X0 = X1 )
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),sK3)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK3) ),
inference(demodulation,[status(thm)],[c_411]) ).
tcf(c_2484,plain,
( in(iPr_def_12,sK3)
| ~ antisymmetric(sK3) ),
inference(demodulation,[status(thm)],[c_342,c_2479,c_2478,c_2480]) ).
tcf(c_2485,plain,
( in(iPr_def_14,sK3)
| ~ antisymmetric(sK3) ),
inference(demodulation,[status(thm)],[c_335,c_2481,c_2482]) ).
tcf(c_2486,negated_conjecture,
relation(sK3),
inference(demodulation,[status(thm)],[c_72]) ).
tcf(c_3027,plain,
unordered_pair(iPr_def_11,iPr_def_13) = iPr_def_14,
inference(demodulation,[status(thm)],[c_2482,c_51]) ).
tcf(c_3054,plain,
! [X0: $i] :
( in(sK5,relation_field(X0))
| ~ relation(X0)
| ~ in(unordered_pair(singleton(sK4),iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_2479,c_371]) ).
tcf(c_3063,plain,
! [X0: $i] :
( in(sK5,relation_field(X0))
| ~ relation(X0)
| ~ in(iPr_def_12,X0) ),
inference(light_normalisation,[status(thm)],[c_3054,c_2478,c_2480]) ).
tcf(c_3073,plain,
( in(sK5,relation_field(sK3))
| ~ relation(sK3)
| ~ in(iPr_def_12,sK3) ),
inference(instantiation,[status(thm)],[c_3063]) ).
tcf(c_3144,plain,
! [X0: $i,X1: $i] :
( antisymmetric(sK3)
| ( X0 = X1 )
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),sK3)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK3) ),
inference(superposition,[status(thm)],[c_51,c_2483]) ).
tcf(c_3174,plain,
! [X0: $i,X1: $i] :
( antisymmetric(sK3)
| ( X0 = X1 )
| ~ in(unordered_pair(singleton(X1),unordered_pair(X0,X1)),sK3)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK3) ),
inference(superposition,[status(thm)],[c_51,c_3144]) ).
tcf(c_3239,plain,
! [X0: $i] :
( in(sK4,relation_field(X0))
| ~ relation(X0)
| ~ in(unordered_pair(singleton(sK4),iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_2479,c_381]) ).
tcf(c_3248,plain,
! [X0: $i] :
( in(sK4,relation_field(X0))
| ~ relation(X0)
| ~ in(iPr_def_12,X0) ),
inference(light_normalisation,[status(thm)],[c_3239,c_2478,c_2480]) ).
tcf(c_3261,plain,
( in(sK4,relation_field(sK3))
| ~ relation(sK3)
| ~ in(iPr_def_12,sK3) ),
inference(instantiation,[status(thm)],[c_3248]) ).
tcf(c_3527,plain,
! [X0: $i] :
( antisymmetric(sK3)
| is_antisymmetric_in(sK3,X0)
| ( sK0(sK3,X0) = sK1(sK3,X0) )
| ~ relation(sK3)
| ~ in(unordered_pair(singleton(sK0(sK3,X0)),unordered_pair(sK1(sK3,X0),sK0(sK3,X0))),sK3) ),
inference(superposition,[status(thm)],[c_391,c_3174]) ).
tcf(c_3534,plain,
! [X0: $i] :
( antisymmetric(sK3)
| is_antisymmetric_in(sK3,X0)
| ( sK0(sK3,X0) = sK1(sK3,X0) )
| ~ in(unordered_pair(singleton(sK0(sK3,X0)),unordered_pair(sK1(sK3,X0),sK0(sK3,X0))),sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3527,c_2486]) ).
tcf(c_3556,plain,
! [X0: $i] :
( antisymmetric(sK3)
| is_antisymmetric_in(sK3,X0)
| ( sK0(sK3,X0) = sK1(sK3,X0) )
| ~ relation(sK3)
| ~ in(unordered_pair(singleton(sK1(sK3,X0)),unordered_pair(sK0(sK3,X0),sK1(sK3,X0))),sK3) ),
inference(superposition,[status(thm)],[c_401,c_3144]) ).
tcf(c_3566,plain,
! [X0: $i] :
( antisymmetric(sK3)
| is_antisymmetric_in(sK3,X0)
| ( sK0(sK3,X0) = sK1(sK3,X0) )
| ~ in(unordered_pair(singleton(sK1(sK3,X0)),unordered_pair(sK0(sK3,X0),sK1(sK3,X0))),sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3556,c_2486]) ).
tcf(c_3607,plain,
! [X0: $i,X1: $i] :
( ( sK4 = sK5 )
| ~ relation(X0)
| ~ in(sK5,X1)
| ~ in(sK4,X1)
| ~ is_antisymmetric_in(X0,X1)
| ~ in(unordered_pair(singleton(sK4),iPr_def_11),X0)
| ~ in(unordered_pair(singleton(sK5),unordered_pair(sK5,sK4)),X0) ),
inference(superposition,[status(thm)],[c_2479,c_424]) ).
tcf(c_3624,plain,
! [X0: $i,X1: $i] :
( ( sK4 = sK5 )
| ~ relation(X0)
| ~ in(iPr_def_12,X0)
| ~ in(sK5,X1)
| ~ in(sK4,X1)
| ~ is_antisymmetric_in(X0,X1)
| ~ in(unordered_pair(iPr_def_13,unordered_pair(sK5,sK4)),X0) ),
inference(light_normalisation,[status(thm)],[c_3607,c_2478,c_2480,c_2481]) ).
tcf(c_3692,plain,
! [X0: $i] :
( antisymmetric(sK3)
| is_antisymmetric_in(sK3,X0) ),
inference(global_subsumption_just,[status(thm)],[c_3534,c_854,c_886,c_3566]) ).
tcf(c_3699,plain,
( antisymmetric(sK3)
| ~ relation(sK3) ),
inference(superposition,[status(thm)],[c_3692,c_53]) ).
tcf(c_3700,plain,
antisymmetric(sK3),
inference(forward_subsumption_resolution,[status(thm)],[c_3699,c_2486]) ).
tcf(c_4200,plain,
! [X0: $i,X1: $i] :
( ~ in(unordered_pair(iPr_def_13,unordered_pair(sK5,sK4)),X0)
| ~ is_antisymmetric_in(X0,X1)
| ~ in(sK4,X1)
| ~ in(sK5,X1)
| ~ in(iPr_def_12,X0)
| ~ relation(X0) ),
inference(global_subsumption_just,[status(thm)],[c_3624,c_68,c_3624,c_3700]) ).
tcf(c_4201,plain,
! [X0: $i,X1: $i] :
( ~ relation(X0)
| ~ in(iPr_def_12,X0)
| ~ in(sK5,X1)
| ~ in(sK4,X1)
| ~ is_antisymmetric_in(X0,X1)
| ~ in(unordered_pair(iPr_def_13,unordered_pair(sK5,sK4)),X0) ),
inference(renaming,[status(thm)],[c_4200]) ).
tcf(c_4203,plain,
! [X0: $i,X1: $i] :
( ~ relation(X0)
| ~ in(iPr_def_14,X0)
| ~ in(iPr_def_12,X0)
| ~ in(sK5,X1)
| ~ in(sK4,X1)
| ~ is_antisymmetric_in(X0,X1) ),
inference(demodulation,[status(thm)],[c_4201,c_51,c_2479,c_3027]) ).
tcf(c_4222,plain,
! [X0: $i] :
( ~ relation(X0)
| ~ antisymmetric(X0)
| ~ in(iPr_def_14,X0)
| ~ in(iPr_def_12,X0)
| ~ in(sK5,relation_field(X0))
| ~ in(sK4,relation_field(X0)) ),
inference(superposition,[status(thm)],[c_54,c_4203]) ).
tcf(c_4243,plain,
( ~ relation(sK3)
| ~ antisymmetric(sK3)
| ~ in(iPr_def_14,sK3)
| ~ in(iPr_def_12,sK3)
| ~ in(sK5,relation_field(sK3))
| ~ in(sK4,relation_field(sK3)) ),
inference(instantiation,[status(thm)],[c_4222]) ).
tcf(c_4244,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_4243,c_3700,c_3261,c_3073,c_2485,c_2484,c_72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU241+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n013.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 13:22:21 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 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
% 0.13/0.41 % Proving...
% 2.79/1.25 % SZS status Started for theBenchmark.p
% 2.79/1.25 % SZS status Theorem for theBenchmark.p
% 2.79/1.25
% 2.79/1.25 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.79/1.25
% 2.79/1.25 % ------ iProver source info
% 2.79/1.25
% 2.79/1.25 % git: date: 2026-07-19 20:42:38 +0200
% 2.79/1.25 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.79/1.25 % git: non_committed_changes: false
% 2.79/1.25
% 2.79/1.25 % ------ Parsing...
% 2.79/1.25 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.79/1.25
% 2.79/1.25 % ------ Preprocessing... sup_sim: 9 sf_s rm: 6 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 2.79/1.25
% 2.79/1.25 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.79/1.25
% 2.79/1.25 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.79/1.25 % ------ Proving...
% 2.79/1.25 % ------ Problem Properties
% 2.79/1.25
% 2.79/1.25 %
% 2.79/1.25 % clauses 40
% 2.79/1.25 % conjectures 2
% 2.79/1.25 % EPR 15
% 2.79/1.25 % Horn 34
% 2.79/1.25 % unary 18
% 2.79/1.25 % binary 10
% 2.79/1.25 % lits 79
% 2.79/1.25 % lits eq 16
% 2.79/1.25 % fd_pure 0
% 2.79/1.25 % fd_pseudo 0
% 2.79/1.25 % fd_cond 1
% 2.79/1.25 % fd_pseudo_cond 3
% 2.79/1.25 % AC symbols 0
% 2.79/1.25
% 2.79/1.25 % ------ Schedule dynamic 5 is on
% 2.79/1.25
% 2.79/1.25 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.79/1.25
% 2.79/1.25
% 2.79/1.25 % ------
% 2.79/1.25 % Current options:
% 2.79/1.25 % ------
% 2.79/1.25
% 2.79/1.25
% 2.79/1.25 %
% 2.79/1.25
% 2.79/1.25 % ------ Proving...
% 2.79/1.25 %
% 2.79/1.25
% 2.79/1.25 % SZS status Theorem for theBenchmark.p
% 2.79/1.25
% 2.79/1.25 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.79/1.25
% 2.79/1.25
%------------------------------------------------------------------------------