%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET725+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 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 02:47:58 PM UTC 2026
% Result : Theorem 49.81s 11.43s
% Output : CNFRefutation 49.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 7
% Syntax : Number of formulae : 181 ( 28 unt; 0 def)
% Number of atoms : 641 ( 106 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 790 ( 330 ~; 339 |; 87 &)
% ( 9 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-5 aty)
% Number of variables : 438 ( 0 sgn 409 !; 29 ?; 188 :)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [X0,X1,X2] :
( maps(X0,X1,X2)
<=> ( ! [X3,X5,X6] :
( ( member(X6,X2)
& member(X5,X2)
& member(X3,X1) )
=> ( ( apply(X0,X3,X6)
& apply(X0,X3,X5) )
=> X5 = X6 ) )
& ! [X3] :
( member(X3,X1)
=> ? [X4] :
( apply(X0,X3,X4)
& member(X4,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax',maps) ).
fof(f14,axiom,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( member(X6,X4)
& member(X5,X2) )
=> ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
<=> ? [X7] :
( apply(X0,X7,X6)
& apply(X1,X5,X7)
& member(X7,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax',compose_function) ).
fof(f16,axiom,
! [X0,X1] :
( identity(X0,X1)
<=> ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax',identity) ).
fof(f17,axiom,
! [X0,X1,X2] :
( injective(X0,X1,X2)
<=> ! [X3,X4,X5] :
( ( member(X5,X2)
& member(X4,X1)
& member(X3,X1) )
=> ( ( apply(X0,X4,X5)
& apply(X0,X3,X5) )
=> X3 = X4 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax',injective) ).
fof(f18,axiom,
! [X0,X1,X2] :
( surjective(X0,X1,X2)
<=> ! [X3] :
( member(X3,X2)
=> ? [X4] :
( apply(X0,X4,X3)
& member(X4,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax',surjective) ).
fof(f19,axiom,
! [X0,X1,X2] :
( one_to_one(X0,X1,X2)
<=> ( surjective(X0,X1,X2)
& injective(X0,X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax',one_to_one) ).
fof(f29,conjecture,
! [X0,X1,X2,X3,X4] :
( ( identity(compose_function(X0,X2,X4,X3,X4),X4)
& identity(compose_function(X1,X0,X3,X4,X3),X3)
& maps(X2,X4,X3)
& maps(X1,X4,X3)
& maps(X0,X3,X4) )
=> one_to_one(X0,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thII16) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( ( identity(compose_function(X0,X2,X4,X3,X4),X4)
& identity(compose_function(X1,X0,X3,X4,X3),X3)
& maps(X2,X4,X3)
& maps(X1,X4,X3)
& maps(X0,X3,X4) )
=> one_to_one(X0,X3,X4) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f31,plain,
! [X0,X1,X2] :
( maps(X0,X1,X2)
<=> ( ! [X5,X6,X7] :
( ( member(X7,X2)
& member(X6,X2)
& member(X5,X1) )
=> ( ( apply(X0,X5,X7)
& apply(X0,X5,X6) )
=> X6 = X7 ) )
& ! [X3] :
( member(X3,X1)
=> ? [X4] :
( apply(X0,X3,X4)
& member(X4,X2) ) ) ) ),
inference(rectify,[],[f12]) ).
fof(f32,plain,
! [X0,X1,X2] :
( ( surjective(X0,X1,X2)
& injective(X0,X1,X2) )
=> one_to_one(X0,X1,X2) ),
inference(unused_predicate_definition_removal,[],[f19]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ! [X3,X4,X5] :
( ( member(X5,X2)
& member(X4,X1)
& member(X3,X1) )
=> ( ( apply(X0,X4,X5)
& apply(X0,X3,X5) )
=> X3 = X4 ) )
=> injective(X0,X1,X2) ),
inference(unused_predicate_definition_removal,[],[f17]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ! [X3] :
( member(X3,X2)
=> ? [X4] :
( apply(X0,X4,X3)
& member(X4,X1) ) )
=> surjective(X0,X1,X2) ),
inference(unused_predicate_definition_removal,[],[f18]) ).
fof(f35,plain,
! [X0,X1] :
( identity(X0,X1)
=> ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) ) ),
inference(unused_predicate_definition_removal,[],[f16]) ).
fof(f36,plain,
! [X0,X1,X2] :
( maps(X0,X1,X2)
=> ( ! [X5,X6,X7] :
( ( member(X7,X2)
& member(X6,X2)
& member(X5,X1) )
=> ( ( apply(X0,X5,X7)
& apply(X0,X5,X6) )
=> X6 = X7 ) )
& ! [X3] :
( member(X3,X1)
=> ? [X4] :
( apply(X0,X3,X4)
& member(X4,X2) ) ) ) ),
inference(unused_predicate_definition_removal,[],[f31]) ).
fof(f37,plain,
? [X0,X1,X2,X3,X4] :
( identity(compose_function(X0,X2,X4,X3,X4),X4)
& identity(compose_function(X1,X0,X3,X4,X3),X3)
& maps(X2,X4,X3)
& maps(X1,X4,X3)
& maps(X0,X3,X4)
& ~ one_to_one(X0,X3,X4) ),
inference(ennf_transformation,[],[f30]) ).
fof(f38,plain,
? [X0,X1,X2,X3,X4] :
( identity(compose_function(X0,X2,X4,X3,X4),X4)
& identity(compose_function(X1,X0,X3,X4,X3),X3)
& maps(X2,X4,X3)
& maps(X1,X4,X3)
& maps(X0,X3,X4)
& ~ one_to_one(X0,X3,X4) ),
inference(flattening,[],[f37]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ~ maps(X0,X1,X2)
| ( ! [X5,X6,X7] :
( ~ member(X7,X2)
| ~ member(X6,X2)
| ~ member(X5,X1)
| ~ apply(X0,X5,X7)
| ~ apply(X0,X5,X6)
| X6 = X7 )
& ! [X3] :
( ~ member(X3,X1)
| ? [X4] :
( apply(X0,X3,X4)
& member(X4,X2) ) ) ) ),
inference(ennf_transformation,[],[f36]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ~ maps(X0,X1,X2)
| ( ! [X5,X6,X7] :
( ~ member(X7,X2)
| ~ member(X6,X2)
| ~ member(X5,X1)
| ~ apply(X0,X5,X7)
| ~ apply(X0,X5,X6)
| X6 = X7 )
& ! [X3] :
( ~ member(X3,X1)
| ? [X4] :
( apply(X0,X3,X4)
& member(X4,X2) ) ) ) ),
inference(flattening,[],[f39]) ).
fof(f41,plain,
! [X0,X1] :
( ~ identity(X0,X1)
| ! [X2] :
( ~ member(X2,X1)
| apply(X0,X2,X2) ) ),
inference(ennf_transformation,[],[f35]) ).
fof(f42,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ member(X6,X4)
| ~ member(X5,X2)
| ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
<=> ? [X7] :
( apply(X0,X7,X6)
& apply(X1,X5,X7)
& member(X7,X3) ) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f43,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ member(X6,X4)
| ~ member(X5,X2)
| ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
<=> ? [X7] :
( apply(X0,X7,X6)
& apply(X1,X5,X7)
& member(X7,X3) ) ) ),
inference(flattening,[],[f42]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ~ surjective(X0,X1,X2)
| ~ injective(X0,X1,X2)
| one_to_one(X0,X1,X2) ),
inference(ennf_transformation,[],[f32]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ~ surjective(X0,X1,X2)
| ~ injective(X0,X1,X2)
| one_to_one(X0,X1,X2) ),
inference(flattening,[],[f44]) ).
fof(f46,plain,
! [X0,X1,X2] :
( ? [X3,X4,X5] :
( member(X5,X2)
& member(X4,X1)
& member(X3,X1)
& apply(X0,X4,X5)
& apply(X0,X3,X5)
& X3 != X4 )
| injective(X0,X1,X2) ),
inference(ennf_transformation,[],[f33]) ).
fof(f47,plain,
! [X0,X1,X2] :
( ? [X3,X4,X5] :
( member(X5,X2)
& member(X4,X1)
& member(X3,X1)
& apply(X0,X4,X5)
& apply(X0,X3,X5)
& X3 != X4 )
| injective(X0,X1,X2) ),
inference(flattening,[],[f46]) ).
fof(f48,plain,
! [X0,X1,X2] :
( ? [X3] :
( member(X3,X2)
& ! [X4] :
( ~ apply(X0,X4,X3)
| ~ member(X4,X1) ) )
| surjective(X0,X1,X2) ),
inference(ennf_transformation,[],[f34]) ).
fof(f49,plain,
( identity(compose_function(sK0,sK2,sK4,sK3,sK4),sK4)
& identity(compose_function(sK1,sK0,sK3,sK4,sK3),sK3)
& maps(sK2,sK4,sK3)
& maps(sK1,sK4,sK3)
& maps(sK0,sK3,sK4)
& ~ one_to_one(sK0,sK3,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f38]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ~ maps(X0,X1,X2)
| ( ! [X5,X6,X7] :
( ~ member(X7,X2)
| ~ member(X6,X2)
| ~ member(X5,X1)
| ~ apply(X0,X5,X7)
| ~ apply(X0,X5,X6)
| X6 = X7 )
& ! [X3] :
( ~ member(X3,X1)
| ( apply(X0,X3,sK5(X0,X2,X3))
& member(sK5(X0,X2,X3),X2) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X4,sK5(X0,X2,X3))],[f40]) ).
fof(f51,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ member(X6,X4)
| ~ member(X5,X2)
| ( ( ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| ? [X7] :
( apply(X0,X7,X6)
& apply(X1,X5,X7)
& member(X7,X3) ) )
& ( ! [X7] :
( ~ apply(X0,X7,X6)
| ~ apply(X1,X5,X7)
| ~ member(X7,X3) )
| apply(compose_function(X0,X1,X2,X3,X4),X5,X6) ) ) ),
inference(nnf_transformation,[],[f43]) ).
fof(f52,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ member(X6,X4)
| ~ member(X5,X2)
| ( ( ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| ? [X8] :
( apply(X0,X8,X6)
& apply(X1,X5,X8)
& member(X8,X3) ) )
& ( ! [X7] :
( ~ apply(X0,X7,X6)
| ~ apply(X1,X5,X7)
| ~ member(X7,X3) )
| apply(compose_function(X0,X1,X2,X3,X4),X5,X6) ) ) ),
inference(rectify,[],[f51]) ).
fof(f53,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ member(X6,X4)
| ~ member(X5,X2)
| ( ( ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| ( apply(X0,sK6(X0,X1,X3,X5,X6),X6)
& apply(X1,X5,sK6(X0,X1,X3,X5,X6))
& member(sK6(X0,X1,X3,X5,X6),X3) ) )
& ( ! [X7] :
( ~ apply(X0,X7,X6)
| ~ apply(X1,X5,X7)
| ~ member(X7,X3) )
| apply(compose_function(X0,X1,X2,X3,X4),X5,X6) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X8,sK6(X0,X1,X3,X5,X6))],[f52]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ( member(sK9(X0,X1,X2),X2)
& member(sK8(X0,X1,X2),X1)
& member(sK7(X0,X1,X2),X1)
& apply(X0,sK8(X0,X1,X2),sK9(X0,X1,X2))
& apply(X0,sK7(X0,X1,X2),sK9(X0,X1,X2))
& sK7(X0,X1,X2) != sK8(X0,X1,X2) )
| injective(X0,X1,X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9]),skolemize(X3,sK7(X0,X1,X2)),skolemize(X4,sK8(X0,X1,X2)),skolemize(X5,sK9(X0,X1,X2))],[f47]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ( member(sK10(X0,X1,X2),X2)
& ! [X4] :
( ~ apply(X0,X4,sK10(X0,X1,X2))
| ~ member(X4,X1) ) )
| surjective(X0,X1,X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X3,sK10(X0,X1,X2))],[f48]) ).
fof(f56,plain,
identity(compose_function(sK0,sK2,sK4,sK3,sK4),sK4),
inference(cnf_transformation,[],[f49]) ).
fof(f57,plain,
identity(compose_function(sK1,sK0,sK3,sK4,sK3),sK3),
inference(cnf_transformation,[],[f49]) ).
fof(f59,plain,
maps(sK1,sK4,sK3),
inference(cnf_transformation,[],[f49]) ).
fof(f60,plain,
maps(sK0,sK3,sK4),
inference(cnf_transformation,[],[f49]) ).
fof(f61,plain,
~ one_to_one(sK0,sK3,sK4),
inference(cnf_transformation,[],[f49]) ).
fof(f62,plain,
! [X2,X0,X1,X6,X7,X5] :
( ~ maps(X0,X1,X2)
| ~ member(X7,X2)
| ~ member(X6,X2)
| ~ member(X5,X1)
| ~ apply(X0,X5,X7)
| ~ apply(X0,X5,X6)
| X6 = X7 ),
inference(cnf_transformation,[],[f50]) ).
fof(f63,plain,
! [X2,X3,X0,X1] :
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| apply(X0,X3,sK5(X0,X2,X3)) ),
inference(cnf_transformation,[],[f50]) ).
fof(f64,plain,
! [X2,X3,X0,X1] :
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| member(sK5(X0,X2,X3),X2) ),
inference(cnf_transformation,[],[f50]) ).
fof(f65,plain,
! [X2,X0,X1] :
( ~ identity(X0,X1)
| ~ member(X2,X1)
| apply(X0,X2,X2) ),
inference(cnf_transformation,[],[f41]) ).
fof(f66,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ member(X6,X4)
| ~ member(X5,X2)
| ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| apply(X0,sK6(X0,X1,X3,X5,X6),X6) ),
inference(cnf_transformation,[],[f53]) ).
fof(f67,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ member(X6,X4)
| ~ member(X5,X2)
| ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| apply(X1,X5,sK6(X0,X1,X3,X5,X6)) ),
inference(cnf_transformation,[],[f53]) ).
fof(f68,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ member(X6,X4)
| ~ member(X5,X2)
| ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| member(sK6(X0,X1,X3,X5,X6),X3) ),
inference(cnf_transformation,[],[f53]) ).
fof(f70,plain,
! [X2,X0,X1] :
( ~ surjective(X0,X1,X2)
| ~ injective(X0,X1,X2)
| one_to_one(X0,X1,X2) ),
inference(cnf_transformation,[],[f45]) ).
fof(f71,plain,
! [X2,X0,X1] :
( member(sK9(X0,X1,X2),X2)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f54]) ).
fof(f72,plain,
! [X2,X0,X1] :
( member(sK8(X0,X1,X2),X1)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f54]) ).
fof(f73,plain,
! [X2,X0,X1] :
( member(sK7(X0,X1,X2),X1)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f54]) ).
fof(f74,plain,
! [X2,X0,X1] :
( apply(X0,sK8(X0,X1,X2),sK9(X0,X1,X2))
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f54]) ).
fof(f75,plain,
! [X2,X0,X1] :
( apply(X0,sK7(X0,X1,X2),sK9(X0,X1,X2))
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f54]) ).
fof(f76,plain,
! [X2,X0,X1] :
( sK7(X0,X1,X2) != sK8(X0,X1,X2)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f54]) ).
fof(f77,plain,
! [X2,X0,X1] :
( member(sK10(X0,X1,X2),X2)
| surjective(X0,X1,X2) ),
inference(cnf_transformation,[],[f55]) ).
fof(f78,plain,
! [X2,X0,X1,X4] :
( ~ apply(X0,X4,sK10(X0,X1,X2))
| ~ member(X4,X1)
| surjective(X0,X1,X2) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_49,negated_conjecture,
~ one_to_one(sK0,sK3,sK4),
inference(cnf_transformation,[],[f61]) ).
tcf(c_50,negated_conjecture,
maps(sK0,sK3,sK4),
inference(cnf_transformation,[],[f60]) ).
tcf(c_51,negated_conjecture,
maps(sK1,sK4,sK3),
inference(cnf_transformation,[],[f59]) ).
tcf(c_53,negated_conjecture,
identity(compose_function(sK1,sK0,sK3,sK4,sK3),sK3),
inference(cnf_transformation,[],[f57]) ).
tcf(c_54,negated_conjecture,
identity(compose_function(sK0,sK2,sK4,sK3,sK4),sK4),
inference(cnf_transformation,[],[f56]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK5(X0,X2,X3),X2)
| ~ member(X3,X1)
| ~ maps(X0,X1,X2) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,X3,sK5(X0,X2,X3))
| ~ member(X3,X1)
| ~ maps(X0,X1,X2) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( X4 = X5 )
| ~ member(X5,X2)
| ~ member(X4,X2)
| ~ member(X3,X1)
| ~ apply(X0,X3,X5)
| ~ apply(X0,X3,X4)
| ~ maps(X0,X1,X2) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( apply(X0,X2,X2)
| ~ member(X2,X1)
| ~ identity(X0,X1) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( member(sK6(X0,X1,X3,X5,X6),X3)
| ~ member(X6,X4)
| ~ member(X5,X2)
| ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( apply(X1,X5,sK6(X0,X1,X3,X5,X6))
| ~ member(X6,X4)
| ~ member(X5,X2)
| ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( apply(X0,sK6(X0,X1,X3,X5,X6),X6)
| ~ member(X6,X4)
| ~ member(X5,X2)
| ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( one_to_one(X0,X1,X2)
| ~ surjective(X0,X1,X2)
| ~ injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( injective(X0,X1,X2)
| ( sK7(X0,X1,X2) != sK8(X0,X1,X2) ) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( injective(X0,X1,X2)
| apply(X0,sK7(X0,X1,X2),sK9(X0,X1,X2)) ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i] :
( injective(X0,X1,X2)
| apply(X0,sK8(X0,X1,X2),sK9(X0,X1,X2)) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] :
( injective(X0,X1,X2)
| member(sK7(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] :
( injective(X0,X1,X2)
| member(sK8(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] :
( injective(X0,X1,X2)
| member(sK9(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( surjective(X0,X2,X3)
| ~ member(X1,X2)
| ~ apply(X0,X1,sK10(X0,X2,X3)) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i] :
( surjective(X0,X1,X2)
| member(sK10(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_324,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ surjective(X0,X1,X2)
| ~ injective(X0,X1,X2)
| ( X2 != sK4 )
| ( X1 != sK3 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_63]) ).
tcf(c_325,plain,
( ~ surjective(sK0,sK3,sK4)
| ~ injective(sK0,sK3,sK4) ),
inference(unflattening,[status(thm)],[c_324]) ).
tcf(c_334,plain,
! [X0: $i,X1: $i,X2: $i] :
( apply(X0,X2,X2)
| ~ member(X2,X1)
| ( X1 != sK3 )
| ( compose_function(sK1,sK0,sK3,sK4,sK3) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_58]) ).
tcf(c_335,plain,
! [X0: $i] :
( apply(compose_function(sK1,sK0,sK3,sK4,sK3),X0,X0)
| ~ member(X0,sK3) ),
inference(unflattening,[status(thm)],[c_334]) ).
tcf(c_343,plain,
! [X0: $i,X1: $i,X2: $i] :
( apply(X0,X2,X2)
| ~ member(X2,X1)
| ( X1 != sK4 )
| ( compose_function(sK0,sK2,sK4,sK3,sK4) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_58]) ).
tcf(c_344,plain,
! [X0: $i] :
( apply(compose_function(sK0,sK2,sK4,sK3,sK4),X0,X0)
| ~ member(X0,sK4) ),
inference(unflattening,[status(thm)],[c_343]) ).
tcf(c_356,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(sK10(X0,X1,X2),X2)
| ~ injective(sK0,sK3,sK4)
| ( X2 != sK4 )
| ( X1 != sK3 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_71,c_325]) ).
tcf(c_357,plain,
( member(sK10(sK0,sK3,sK4),sK4)
| ~ injective(sK0,sK3,sK4) ),
inference(unflattening,[status(thm)],[c_356]) ).
tcf(c_364,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ member(X3,X1)
| ~ injective(sK0,sK3,sK4)
| ~ apply(X0,X3,sK10(X0,X1,X2))
| ( X2 != sK4 )
| ( X1 != sK3 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_70,c_325]) ).
tcf(c_365,plain,
! [X0: $i] :
( ~ member(X0,sK3)
| ~ injective(sK0,sK3,sK4)
| ~ apply(sK0,X0,sK10(sK0,sK3,sK4)) ),
inference(unflattening,[status(thm)],[c_364]) ).
tcf(c_381,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( X4 = X5 )
| ~ member(X5,X2)
| ~ member(X4,X2)
| ~ member(X3,X1)
| ~ apply(X0,X3,X5)
| ~ apply(X0,X3,X4)
| ( X2 != sK4 )
| ( X1 != sK3 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_57]) ).
tcf(c_382,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ member(X2,sK4)
| ~ member(X1,sK4)
| ~ member(X0,sK3)
| ~ apply(sK0,X0,X2)
| ~ apply(sK0,X0,X1) ),
inference(unflattening,[status(thm)],[c_381]) ).
tcf(c_402,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,X3,sK5(X0,X2,X3))
| ~ member(X3,X1)
| ( X2 != sK4 )
| ( X1 != sK3 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_56]) ).
tcf(c_403,plain,
! [X0: $i] :
( apply(sK0,X0,sK5(sK0,sK4,X0))
| ~ member(X0,sK3) ),
inference(unflattening,[status(thm)],[c_402]) ).
tcf(c_411,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK5(X0,X2,X3),X2)
| ~ member(X3,X1)
| ( X2 != sK4 )
| ( X1 != sK3 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_55]) ).
tcf(c_412,plain,
! [X0: $i] :
( member(sK5(sK0,sK4,X0),sK4)
| ~ member(X0,sK3) ),
inference(unflattening,[status(thm)],[c_411]) ).
tcf(c_420,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( X4 = X5 )
| ~ member(X5,X0)
| ~ member(X4,X0)
| ~ member(X3,X1)
| ~ apply(X2,X3,X5)
| ~ apply(X2,X3,X4)
| ( X2 != sK1 )
| ( X1 != sK4 )
| ( X0 != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_57]) ).
tcf(c_421,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ member(X2,sK3)
| ~ member(X1,sK3)
| ~ member(X0,sK4)
| ~ apply(sK1,X0,X2)
| ~ apply(sK1,X0,X1) ),
inference(unflattening,[status(thm)],[c_420]) ).
tcf(c_528,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK9(X0,X1,X2),X2)
| ~ member(X3,sK3)
| ~ apply(sK0,X3,sK10(sK0,sK3,sK4))
| ( X2 != sK4 )
| ( X1 != sK3 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_69,c_365]) ).
tcf(c_529,plain,
! [X0: $i] :
( member(sK9(sK0,sK3,sK4),sK4)
| ~ member(X0,sK3)
| ~ apply(sK0,X0,sK10(sK0,sK3,sK4)) ),
inference(unflattening,[status(thm)],[c_528]) ).
tcf(c_540,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(sK10(sK0,sK3,sK4),sK4)
| member(sK9(X0,X1,X2),X2)
| ( X2 != sK4 )
| ( X1 != sK3 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_69,c_357]) ).
tcf(c_541,plain,
( member(sK10(sK0,sK3,sK4),sK4)
| member(sK9(sK0,sK3,sK4),sK4) ),
inference(unflattening,[status(thm)],[c_540]) ).
tcf(c_548,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK8(X0,X1,X2),X1)
| ~ member(X3,sK3)
| ~ apply(sK0,X3,sK10(sK0,sK3,sK4))
| ( X2 != sK4 )
| ( X1 != sK3 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_68,c_365]) ).
tcf(c_549,plain,
! [X0: $i] :
( member(sK8(sK0,sK3,sK4),sK3)
| ~ member(X0,sK3)
| ~ apply(sK0,X0,sK10(sK0,sK3,sK4)) ),
inference(unflattening,[status(thm)],[c_548]) ).
tcf(c_560,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(sK10(sK0,sK3,sK4),sK4)
| member(sK8(X0,X1,X2),X1)
| ( X2 != sK4 )
| ( X1 != sK3 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_68,c_357]) ).
tcf(c_561,plain,
( member(sK10(sK0,sK3,sK4),sK4)
| member(sK8(sK0,sK3,sK4),sK3) ),
inference(unflattening,[status(thm)],[c_560]) ).
tcf(c_568,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK7(X0,X1,X2),X1)
| ~ member(X3,sK3)
| ~ apply(sK0,X3,sK10(sK0,sK3,sK4))
| ( X2 != sK4 )
| ( X1 != sK3 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_67,c_365]) ).
tcf(c_569,plain,
! [X0: $i] :
( member(sK7(sK0,sK3,sK4),sK3)
| ~ member(X0,sK3)
| ~ apply(sK0,X0,sK10(sK0,sK3,sK4)) ),
inference(unflattening,[status(thm)],[c_568]) ).
tcf(c_580,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(sK10(sK0,sK3,sK4),sK4)
| member(sK7(X0,X1,X2),X1)
| ( X2 != sK4 )
| ( X1 != sK3 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_67,c_357]) ).
tcf(c_581,plain,
( member(sK10(sK0,sK3,sK4),sK4)
| member(sK7(sK0,sK3,sK4),sK3) ),
inference(unflattening,[status(thm)],[c_580]) ).
tcf(c_588,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,sK8(X0,X1,X2),sK9(X0,X1,X2))
| ~ member(X3,sK3)
| ~ apply(sK0,X3,sK10(sK0,sK3,sK4))
| ( X2 != sK4 )
| ( X1 != sK3 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_66,c_365]) ).
tcf(c_589,plain,
! [X0: $i] :
( apply(sK0,sK8(sK0,sK3,sK4),sK9(sK0,sK3,sK4))
| ~ member(X0,sK3)
| ~ apply(sK0,X0,sK10(sK0,sK3,sK4)) ),
inference(unflattening,[status(thm)],[c_588]) ).
tcf(c_600,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(sK10(sK0,sK3,sK4),sK4)
| apply(X0,sK8(X0,X1,X2),sK9(X0,X1,X2))
| ( X2 != sK4 )
| ( X1 != sK3 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_66,c_357]) ).
tcf(c_601,plain,
( member(sK10(sK0,sK3,sK4),sK4)
| apply(sK0,sK8(sK0,sK3,sK4),sK9(sK0,sK3,sK4)) ),
inference(unflattening,[status(thm)],[c_600]) ).
tcf(c_608,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,sK7(X0,X1,X2),sK9(X0,X1,X2))
| ~ member(X3,sK3)
| ~ apply(sK0,X3,sK10(sK0,sK3,sK4))
| ( X2 != sK4 )
| ( X1 != sK3 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_65,c_365]) ).
tcf(c_609,plain,
! [X0: $i] :
( apply(sK0,sK7(sK0,sK3,sK4),sK9(sK0,sK3,sK4))
| ~ member(X0,sK3)
| ~ apply(sK0,X0,sK10(sK0,sK3,sK4)) ),
inference(unflattening,[status(thm)],[c_608]) ).
tcf(c_620,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(sK10(sK0,sK3,sK4),sK4)
| apply(X0,sK7(X0,X1,X2),sK9(X0,X1,X2))
| ( X2 != sK4 )
| ( X1 != sK3 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_65,c_357]) ).
tcf(c_621,plain,
( member(sK10(sK0,sK3,sK4),sK4)
| apply(sK0,sK7(sK0,sK3,sK4),sK9(sK0,sK3,sK4)) ),
inference(unflattening,[status(thm)],[c_620]) ).
tcf(c_628,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ member(X3,sK3)
| ~ apply(sK0,X3,sK10(sK0,sK3,sK4))
| ( X2 != sK4 )
| ( X1 != sK3 )
| ( X0 != sK0 )
| ( sK7(X0,X1,X2) != sK8(X0,X1,X2) ) ),
inference(resolution_lifted,[status(thm)],[c_64,c_365]) ).
tcf(c_629,plain,
! [X0: $i] :
( ~ member(X0,sK3)
| ~ apply(sK0,X0,sK10(sK0,sK3,sK4))
| ( sK7(sK0,sK3,sK4) != sK8(sK0,sK3,sK4) ) ),
inference(unflattening,[status(thm)],[c_628]) ).
tcf(c_640,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(sK10(sK0,sK3,sK4),sK4)
| ( X2 != sK4 )
| ( X1 != sK3 )
| ( X0 != sK0 )
| ( sK7(X0,X1,X2) != sK8(X0,X1,X2) ) ),
inference(resolution_lifted,[status(thm)],[c_64,c_357]) ).
tcf(c_641,plain,
( member(sK10(sK0,sK3,sK4),sK4)
| ( sK7(sK0,sK3,sK4) != sK8(sK0,sK3,sK4) ) ),
inference(unflattening,[status(thm)],[c_640]) ).
tcf(c_1269,plain,
! [X0: $i] :
( member(sK6(sK1,sK0,sK4,X0,X0),sK4)
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_335,c_60]) ).
tcf(c_1270,plain,
! [X0: $i] :
( member(sK6(sK0,sK2,sK3,X0,X0),sK3)
| ~ member(X0,sK4) ),
inference(superposition,[status(thm)],[c_344,c_60]) ).
tcf(c_1285,plain,
! [X0: $i] :
( apply(sK0,X0,sK6(sK1,sK0,sK4,X0,X0))
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_335,c_61]) ).
tcf(c_1302,plain,
! [X0: $i] :
( apply(sK0,sK6(sK0,sK2,sK3,X0,X0),X0)
| ~ member(X0,sK4) ),
inference(superposition,[status(thm)],[c_344,c_62]) ).
tcf(c_1341,plain,
! [X0: $i,X1: $i] :
( ( sK5(sK0,sK4,X0) = X1 )
| ~ member(X1,sK4)
| ~ member(X0,sK3)
| ~ apply(sK0,X0,X1)
| ~ member(sK5(sK0,sK4,X0),sK4) ),
inference(superposition,[status(thm)],[c_403,c_382]) ).
tcf(c_1391,plain,
! [X0: $i,X1: $i] :
( ( sK6(sK1,sK0,sK4,X0,X0) = X1 )
| ~ member(X1,sK4)
| ~ member(X0,sK3)
| ~ apply(sK0,X0,X1)
| ~ member(sK6(sK1,sK0,sK4,X0,X0),sK4) ),
inference(superposition,[status(thm)],[c_1285,c_382]) ).
tcf(c_1488,plain,
( member(sK9(sK0,sK3,sK4),sK4)
| ~ member(sK10(sK0,sK3,sK4),sK4)
| ~ member(sK6(sK0,sK2,sK3,sK10(sK0,sK3,sK4),sK10(sK0,sK3,sK4)),sK3) ),
inference(superposition,[status(thm)],[c_1302,c_529]) ).
tcf(c_1552,plain,
( member(sK8(sK0,sK3,sK4),sK3)
| ~ member(sK10(sK0,sK3,sK4),sK4)
| ~ member(sK6(sK0,sK2,sK3,sK10(sK0,sK3,sK4),sK10(sK0,sK3,sK4)),sK3) ),
inference(superposition,[status(thm)],[c_1302,c_549]) ).
tcf(c_1562,plain,
( member(sK7(sK0,sK3,sK4),sK3)
| ~ member(sK10(sK0,sK3,sK4),sK4)
| ~ member(sK6(sK0,sK2,sK3,sK10(sK0,sK3,sK4),sK10(sK0,sK3,sK4)),sK3) ),
inference(superposition,[status(thm)],[c_1302,c_569]) ).
tcf(c_1572,plain,
( apply(sK0,sK8(sK0,sK3,sK4),sK9(sK0,sK3,sK4))
| ~ member(sK10(sK0,sK3,sK4),sK4)
| ~ member(sK6(sK0,sK2,sK3,sK10(sK0,sK3,sK4),sK10(sK0,sK3,sK4)),sK3) ),
inference(superposition,[status(thm)],[c_1302,c_589]) ).
tcf(c_1582,plain,
( apply(sK0,sK7(sK0,sK3,sK4),sK9(sK0,sK3,sK4))
| ~ member(sK10(sK0,sK3,sK4),sK4)
| ~ member(sK6(sK0,sK2,sK3,sK10(sK0,sK3,sK4),sK10(sK0,sK3,sK4)),sK3) ),
inference(superposition,[status(thm)],[c_1302,c_609]) ).
tcf(c_1628,plain,
( apply(compose_function(sK0,sK2,sK4,sK3,sK4),sK10(sK0,sK3,sK4),sK10(sK0,sK3,sK4))
| ~ member(sK10(sK0,sK3,sK4),sK4) ),
inference(instantiation,[status(thm)],[c_344]) ).
tcf(c_1629,plain,
! [X0: $i,X1: $i] :
( ( sK6(sK1,sK0,sK4,X0,X0) = X1 )
| ~ member(X1,sK4)
| ~ member(X0,sK3)
| ~ apply(sK0,X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_1391,c_1269,c_1391]) ).
tcf(c_1640,plain,
! [X0: $i] :
( ( sK6(sK1,sK0,sK4,X0,X0) = sK5(sK0,sK4,X0) )
| ~ member(X0,sK3)
| ~ member(sK5(sK0,sK4,X0),sK4) ),
inference(superposition,[status(thm)],[c_403,c_1629]) ).
tcf(c_1667,plain,
! [X0: $i] :
( ( sK6(sK1,sK0,sK4,X0,X0) = sK5(sK0,sK4,X0) )
| ~ member(X0,sK3) ),
inference(global_subsumption_just,[status(thm)],[c_1640,c_412,c_1640]) ).
tcf(c_1688,plain,
! [X0: $i] :
( ( sK7(sK0,sK3,sK4) = sK8(sK0,sK3,sK4) )
| ~ member(X0,sK4)
| ~ member(sK8(sK0,sK3,sK4),sK3)
| ~ member(sK7(sK0,sK3,sK4),sK3)
| ~ apply(sK1,X0,sK8(sK0,sK3,sK4))
| ~ apply(sK1,X0,sK7(sK0,sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_421]) ).
tcf(c_2982,plain,
( ( sK7(sK0,sK3,sK4) = sK8(sK0,sK3,sK4) )
| ~ member(sK9(sK0,sK3,sK4),sK4)
| ~ member(sK8(sK0,sK3,sK4),sK3)
| ~ member(sK7(sK0,sK3,sK4),sK3)
| ~ apply(sK1,sK9(sK0,sK3,sK4),sK8(sK0,sK3,sK4))
| ~ apply(sK1,sK9(sK0,sK3,sK4),sK7(sK0,sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_1688]) ).
tcf(c_4193,plain,
( member(sK9(sK0,sK3,sK4),sK4)
| ~ member(sK6(sK0,sK2,sK3,sK10(sK0,sK3,sK4),sK10(sK0,sK3,sK4)),sK3) ),
inference(global_subsumption_just,[status(thm)],[c_1488,c_541,c_1488]) ).
tcf(c_4199,plain,
( member(sK9(sK0,sK3,sK4),sK4)
| ~ member(sK10(sK0,sK3,sK4),sK4) ),
inference(superposition,[status(thm)],[c_1270,c_4193]) ).
tcf(c_4202,plain,
member(sK9(sK0,sK3,sK4),sK4),
inference(global_subsumption_just,[status(thm)],[c_4199,c_541,c_4199]) ).
tcf(c_12652,plain,
( member(sK8(sK0,sK3,sK4),sK3)
| ~ member(sK6(sK0,sK2,sK3,sK10(sK0,sK3,sK4),sK10(sK0,sK3,sK4)),sK3) ),
inference(global_subsumption_just,[status(thm)],[c_1552,c_561,c_1552]) ).
tcf(c_12658,plain,
( member(sK8(sK0,sK3,sK4),sK3)
| ~ member(sK10(sK0,sK3,sK4),sK4) ),
inference(superposition,[status(thm)],[c_1270,c_12652]) ).
tcf(c_12661,plain,
member(sK8(sK0,sK3,sK4),sK3),
inference(global_subsumption_just,[status(thm)],[c_12658,c_561,c_12658]) ).
tcf(c_17532,plain,
( member(sK7(sK0,sK3,sK4),sK3)
| ~ member(sK6(sK0,sK2,sK3,sK10(sK0,sK3,sK4),sK10(sK0,sK3,sK4)),sK3) ),
inference(global_subsumption_just,[status(thm)],[c_1562,c_581,c_1562]) ).
tcf(c_17538,plain,
( member(sK7(sK0,sK3,sK4),sK3)
| ~ member(sK10(sK0,sK3,sK4),sK4) ),
inference(superposition,[status(thm)],[c_1270,c_17532]) ).
tcf(c_17685,plain,
! [X0: $i] :
( member(sK6(sK0,sK2,sK3,X0,X0),sK3)
| ~ member(X0,sK4) ),
inference(superposition,[status(thm)],[c_344,c_60]) ).
tcf(c_17698,plain,
! [X0: $i] :
( apply(sK0,X0,sK6(sK1,sK0,sK4,X0,X0))
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_335,c_61]) ).
tcf(c_17713,plain,
! [X0: $i] :
( apply(sK0,sK6(sK0,sK2,sK3,X0,X0),X0)
| ~ member(X0,sK4) ),
inference(superposition,[status(thm)],[c_344,c_62]) ).
tcf(c_17777,plain,
member(sK8(sK0,sK3,sK4),sK3),
inference(global_subsumption_just,[status(thm)],[c_549,c_12661]) ).
tcf(c_17791,plain,
! [X0: $i,X1: $i] :
( ( sK5(sK0,sK4,X0) = X1 )
| ~ member(X1,sK4)
| ~ member(X0,sK3)
| ~ apply(sK0,X0,X1)
| ~ member(sK5(sK0,sK4,X0),sK4) ),
inference(superposition,[status(thm)],[c_403,c_382]) ).
tcf(c_17892,plain,
! [X0: $i,X1: $i] :
( ( sK5(sK0,sK4,X0) = X1 )
| ~ member(X1,sK4)
| ~ member(X0,sK3)
| ~ apply(sK0,X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_17791,c_412,c_1341]) ).
tcf(c_17903,plain,
! [X0: $i] :
( ( sK6(sK1,sK0,sK4,X0,X0) = sK5(sK0,sK4,X0) )
| ~ member(X0,sK3)
| ~ member(sK6(sK1,sK0,sK4,X0,X0),sK4) ),
inference(superposition,[status(thm)],[c_17698,c_17892]) ).
tcf(c_17907,plain,
member(sK7(sK0,sK3,sK4),sK3),
inference(global_subsumption_just,[status(thm)],[c_581,c_581,c_17538]) ).
tcf(c_17947,plain,
! [X0: $i] :
( ( sK6(sK1,sK0,sK4,X0,X0) = sK5(sK0,sK4,X0) )
| ~ member(X0,sK3) ),
inference(global_subsumption_just,[status(thm)],[c_17903,c_1667]) ).
tcf(c_17955,plain,
sK6(sK1,sK0,sK4,sK8(sK0,sK3,sK4),sK8(sK0,sK3,sK4)) = sK5(sK0,sK4,sK8(sK0,sK3,sK4)),
inference(superposition,[status(thm)],[c_17777,c_17947]) ).
tcf(c_17956,plain,
sK6(sK1,sK0,sK4,sK7(sK0,sK3,sK4),sK7(sK0,sK3,sK4)) = sK5(sK0,sK4,sK7(sK0,sK3,sK4)),
inference(superposition,[status(thm)],[c_17907,c_17947]) ).
tcf(c_18146,plain,
( apply(sK0,sK8(sK0,sK3,sK4),sK9(sK0,sK3,sK4))
| ~ member(sK10(sK0,sK3,sK4),sK4)
| ~ member(sK6(sK0,sK2,sK3,sK10(sK0,sK3,sK4),sK10(sK0,sK3,sK4)),sK3) ),
inference(superposition,[status(thm)],[c_17713,c_589]) ).
tcf(c_18313,plain,
( apply(sK0,sK7(sK0,sK3,sK4),sK9(sK0,sK3,sK4))
| ~ member(sK10(sK0,sK3,sK4),sK4)
| ~ member(sK6(sK0,sK2,sK3,sK10(sK0,sK3,sK4),sK10(sK0,sK3,sK4)),sK3) ),
inference(superposition,[status(thm)],[c_17713,c_609]) ).
tcf(c_19005,plain,
( apply(sK0,sK8(sK0,sK3,sK4),sK9(sK0,sK3,sK4))
| ~ member(sK6(sK0,sK2,sK3,sK10(sK0,sK3,sK4),sK10(sK0,sK3,sK4)),sK3) ),
inference(global_subsumption_just,[status(thm)],[c_18146,c_601,c_1572]) ).
tcf(c_19011,plain,
( apply(sK0,sK8(sK0,sK3,sK4),sK9(sK0,sK3,sK4))
| ~ member(sK10(sK0,sK3,sK4),sK4) ),
inference(superposition,[status(thm)],[c_17685,c_19005]) ).
tcf(c_19014,plain,
( apply(sK0,sK7(sK0,sK3,sK4),sK9(sK0,sK3,sK4))
| ~ member(sK6(sK0,sK2,sK3,sK10(sK0,sK3,sK4),sK10(sK0,sK3,sK4)),sK3) ),
inference(global_subsumption_just,[status(thm)],[c_18313,c_621,c_1582]) ).
tcf(c_19020,plain,
( apply(sK0,sK7(sK0,sK3,sK4),sK9(sK0,sK3,sK4))
| ~ member(sK10(sK0,sK3,sK4),sK4) ),
inference(superposition,[status(thm)],[c_17685,c_19014]) ).
tcf(c_78005,plain,
! [X0: $i] :
( apply(sK1,sK6(sK1,sK0,sK4,X0,X0),X0)
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_335,c_62]) ).
tcf(c_78058,plain,
member(sK9(sK0,sK3,sK4),sK4),
inference(global_subsumption_just,[status(thm)],[c_541,c_4202]) ).
tcf(c_78060,plain,
member(sK8(sK0,sK3,sK4),sK3),
inference(global_subsumption_just,[status(thm)],[c_561,c_561,c_12658]) ).
tcf(c_78062,plain,
member(sK7(sK0,sK3,sK4),sK3),
inference(global_subsumption_just,[status(thm)],[c_581,c_581,c_17538]) ).
tcf(c_78080,plain,
! [X0: $i,X1: $i] :
( ( sK5(sK0,sK4,X0) = X1 )
| ~ member(X1,sK4)
| ~ member(X0,sK3)
| ~ apply(sK0,X0,X1)
| ~ member(sK5(sK0,sK4,X0),sK4) ),
inference(superposition,[status(thm)],[c_403,c_382]) ).
tcf(c_78207,plain,
apply(sK0,sK8(sK0,sK3,sK4),sK9(sK0,sK3,sK4)),
inference(global_subsumption_just,[status(thm)],[c_601,c_601,c_19011]) ).
tcf(c_78222,plain,
apply(sK0,sK7(sK0,sK3,sK4),sK9(sK0,sK3,sK4)),
inference(global_subsumption_just,[status(thm)],[c_621,c_621,c_19020]) ).
tcf(c_78258,plain,
! [X0: $i,X1: $i] :
( ( sK5(sK0,sK4,X0) = X1 )
| ~ member(X1,sK4)
| ~ member(X0,sK3)
| ~ apply(sK0,X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_78080,c_412,c_1341]) ).
tcf(c_78269,plain,
( ( sK5(sK0,sK4,sK8(sK0,sK3,sK4)) = sK9(sK0,sK3,sK4) )
| ~ member(sK9(sK0,sK3,sK4),sK4)
| ~ member(sK8(sK0,sK3,sK4),sK3) ),
inference(superposition,[status(thm)],[c_78207,c_78258]) ).
tcf(c_78270,plain,
( ( sK5(sK0,sK4,sK7(sK0,sK3,sK4)) = sK9(sK0,sK3,sK4) )
| ~ member(sK9(sK0,sK3,sK4),sK4)
| ~ member(sK7(sK0,sK3,sK4),sK3) ),
inference(superposition,[status(thm)],[c_78222,c_78258]) ).
tcf(c_78279,plain,
sK5(sK0,sK4,sK7(sK0,sK3,sK4)) = sK9(sK0,sK3,sK4),
inference(forward_subsumption_resolution,[status(thm)],[c_78270,c_78058,c_78062]) ).
tcf(c_78280,plain,
sK5(sK0,sK4,sK8(sK0,sK3,sK4)) = sK9(sK0,sK3,sK4),
inference(forward_subsumption_resolution,[status(thm)],[c_78269,c_78058,c_78060]) ).
tcf(c_78401,plain,
sK6(sK1,sK0,sK4,sK8(sK0,sK3,sK4),sK8(sK0,sK3,sK4)) = sK9(sK0,sK3,sK4),
inference(light_normalisation,[status(thm)],[c_17955,c_78280]) ).
tcf(c_78402,plain,
( apply(sK1,sK9(sK0,sK3,sK4),sK8(sK0,sK3,sK4))
| ~ member(sK8(sK0,sK3,sK4),sK3) ),
inference(superposition,[status(thm)],[c_78401,c_78005]) ).
tcf(c_78405,plain,
apply(sK1,sK9(sK0,sK3,sK4),sK8(sK0,sK3,sK4)),
inference(forward_subsumption_resolution,[status(thm)],[c_78402,c_78060]) ).
tcf(c_78635,plain,
sK6(sK1,sK0,sK4,sK7(sK0,sK3,sK4),sK7(sK0,sK3,sK4)) = sK9(sK0,sK3,sK4),
inference(light_normalisation,[status(thm)],[c_17956,c_78279]) ).
tcf(c_78637,plain,
( apply(sK1,sK9(sK0,sK3,sK4),sK7(sK0,sK3,sK4))
| ~ member(sK7(sK0,sK3,sK4),sK3) ),
inference(superposition,[status(thm)],[c_78635,c_78005]) ).
tcf(c_78640,plain,
apply(sK1,sK9(sK0,sK3,sK4),sK7(sK0,sK3,sK4)),
inference(forward_subsumption_resolution,[status(thm)],[c_78637,c_78062]) ).
tcf(c_78765,plain,
( apply(sK0,sK6(sK0,sK2,sK3,sK10(sK0,sK3,sK4),sK10(sK0,sK3,sK4)),sK10(sK0,sK3,sK4))
| ~ member(sK10(sK0,sK3,sK4),sK4)
| ~ apply(compose_function(sK0,sK2,sK4,sK3,sK4),sK10(sK0,sK3,sK4),sK10(sK0,sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_78767,plain,
( member(sK6(sK0,sK2,sK3,sK10(sK0,sK3,sK4),sK10(sK0,sK3,sK4)),sK3)
| ~ member(sK10(sK0,sK3,sK4),sK4)
| ~ apply(compose_function(sK0,sK2,sK4,sK3,sK4),sK10(sK0,sK3,sK4),sK10(sK0,sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_79655,plain,
( ~ member(sK6(sK0,sK2,sK3,sK10(sK0,sK3,sK4),sK10(sK0,sK3,sK4)),sK3)
| ~ apply(sK0,sK6(sK0,sK2,sK3,sK10(sK0,sK3,sK4),sK10(sK0,sK3,sK4)),sK10(sK0,sK3,sK4))
| ( sK7(sK0,sK3,sK4) != sK8(sK0,sK3,sK4) ) ),
inference(instantiation,[status(thm)],[c_629]) ).
tcf(c_79656,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_79655,c_78765,c_78767,c_78640,c_78405,c_17907,c_12661,c_4202,c_2982,c_1628,c_641]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET725+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n018.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 11:48:34 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.40 Running first-order theorem proving
% 0.08/0.40 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
% 0.08/0.41
% 0.08/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.41
% 0.08/0.41 % Detected problem language: tptp
% 0.08/0.42 % Proving...
% 49.81/11.43 % SZS status Started for theBenchmark.p
% 49.81/11.43 % SZS status Theorem for theBenchmark.p
% 49.81/11.43
% 49.81/11.43 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 49.81/11.43
% 49.81/11.43 % ------ iProver source info
% 49.81/11.43
% 49.81/11.43 % git: date: 2026-07-19 20:42:38 +0200
% 49.81/11.43 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 49.81/11.43 % git: non_committed_changes: false
% 49.81/11.43
% 49.81/11.43 % ------ Parsing...
% 49.81/11.43 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 49.81/11.43
% 49.81/11.43 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e %
% 49.81/11.43
% 49.81/11.43 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 49.81/11.43
% 49.81/11.43 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 49.81/11.43 % ------ Proving...
% 49.81/11.43 % ------ Problem Properties
% 49.81/11.43
% 49.81/11.43 %
% 49.81/11.43 % clauses 27
% 49.81/11.43 % conjectures 0
% 49.81/11.43 % EPR 3
% 49.81/11.43 % Horn 22
% 49.81/11.43 % unary 0
% 49.81/11.43 % binary 14
% 49.81/11.43 % lits 82
% 49.81/11.43 % lits eq 5
% 49.81/11.43 % fd_pure 0
% 49.81/11.43 % fd_pseudo 0
% 49.81/11.43 % fd_cond 0
% 49.81/11.43 % fd_pseudo_cond 3
% 49.81/11.43 % AC symbols 0
% 49.81/11.43
% 49.81/11.43 % ------ Schedule dynamic 5 is on
% 49.81/11.43
% 49.81/11.43 % ------ no conjectures: strip conj schedule
% 49.81/11.43
% 49.81/11.43 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 49.81/11.43
% 49.81/11.43
% 49.81/11.43 % ------
% 49.81/11.43 % Current options:
% 49.81/11.43 % ------
% 49.81/11.43
% 49.81/11.43
% 49.81/11.43 %
% 49.81/11.43
% 49.81/11.43 % ------ Proving...
% 49.81/11.43 % Proof_search_loop: time out after: 2009 full_loop iterations
% 49.81/11.43
% 49.81/11.43 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" stripped conjectures Time Limit: 15.
% 49.81/11.43
% 49.81/11.43
% 49.81/11.43 % ------
% 49.81/11.43 % Current options:
% 49.81/11.43 % ------
% 49.81/11.43
% 49.81/11.43
% 49.81/11.43 %
% 49.81/11.43
% 49.81/11.43 % ------ Proving...
% 49.81/11.43 %
% 49.81/11.43
% 49.81/11.43 % SZS status Theorem for theBenchmark.p
% 49.81/11.43
% 49.81/11.43 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 49.81/11.43
% 49.81/11.43
%------------------------------------------------------------------------------