%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET724+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 : n004.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 33.82s 7.30s
% Output : CNFRefutation 34.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 7
% Syntax : Number of formulae : 204 ( 39 unt; 0 def)
% Number of atoms : 791 ( 184 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 1027 ( 440 ~; 475 |; 85 &)
% ( 9 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 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 : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-5 aty)
% Number of variables : 525 ( 0 sgn 494 !; 31 ?; 276 :)
% 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(f15,axiom,
! [X0,X1,X2,X3] :
( equal_maps(X0,X1,X2,X3)
<=> ! [X4,X5,X6] :
( ( member(X6,X3)
& member(X5,X3)
& member(X4,X2) )
=> ( ( apply(X1,X4,X6)
& apply(X0,X4,X5) )
=> X5 = X6 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax',equal_maps) ).
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(f29,conjecture,
! [X0,X1,X2,X3,X4,X5] :
( ( equal_maps(compose_function(X1,X0,X3,X4,X5),compose_function(X2,X0,X3,X4,X5),X3,X5)
& surjective(X0,X3,X4)
& maps(X2,X4,X5)
& maps(X1,X4,X5)
& maps(X0,X3,X4) )
=> equal_maps(X1,X2,X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thII15) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5] :
( ( equal_maps(compose_function(X1,X0,X3,X4,X5),compose_function(X2,X0,X3,X4,X5),X3,X5)
& surjective(X0,X3,X4)
& maps(X2,X4,X5)
& maps(X1,X4,X5)
& maps(X0,X3,X4) )
=> equal_maps(X1,X2,X4,X5) ),
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)
=> ! [X3] :
( member(X3,X2)
=> ? [X4] :
( apply(X0,X4,X3)
& member(X4,X1) ) ) ),
inference(unused_predicate_definition_removal,[],[f18]) ).
fof(f33,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(f34,plain,
? [X0,X1,X2,X3,X4,X5] :
( equal_maps(compose_function(X1,X0,X3,X4,X5),compose_function(X2,X0,X3,X4,X5),X3,X5)
& surjective(X0,X3,X4)
& maps(X2,X4,X5)
& maps(X1,X4,X5)
& maps(X0,X3,X4)
& ~ equal_maps(X1,X2,X4,X5) ),
inference(ennf_transformation,[],[f30]) ).
fof(f35,plain,
? [X0,X1,X2,X3,X4,X5] :
( equal_maps(compose_function(X1,X0,X3,X4,X5),compose_function(X2,X0,X3,X4,X5),X3,X5)
& surjective(X0,X3,X4)
& maps(X2,X4,X5)
& maps(X1,X4,X5)
& maps(X0,X3,X4)
& ~ equal_maps(X1,X2,X4,X5) ),
inference(flattening,[],[f34]) ).
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(ennf_transformation,[],[f33]) ).
fof(f37,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,[],[f36]) ).
fof(f38,plain,
! [X0,X1,X2,X3] :
( equal_maps(X0,X1,X2,X3)
<=> ! [X4,X5,X6] :
( ~ member(X6,X3)
| ~ member(X5,X3)
| ~ member(X4,X2)
| ~ apply(X1,X4,X6)
| ~ apply(X0,X4,X5)
| X5 = X6 ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f39,plain,
! [X0,X1,X2,X3] :
( equal_maps(X0,X1,X2,X3)
<=> ! [X4,X5,X6] :
( ~ member(X6,X3)
| ~ member(X5,X3)
| ~ member(X4,X2)
| ~ apply(X1,X4,X6)
| ~ apply(X0,X4,X5)
| X5 = X6 ) ),
inference(flattening,[],[f38]) ).
fof(f40,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(f41,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,[],[f40]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ~ surjective(X0,X1,X2)
| ! [X3] :
( ~ member(X3,X2)
| ? [X4] :
( apply(X0,X4,X3)
& member(X4,X1) ) ) ),
inference(ennf_transformation,[],[f32]) ).
fof(f43,plain,
( equal_maps(compose_function(sK1,sK0,sK3,sK4,sK5),compose_function(sK2,sK0,sK3,sK4,sK5),sK3,sK5)
& surjective(sK0,sK3,sK4)
& maps(sK2,sK4,sK5)
& maps(sK1,sK4,sK5)
& maps(sK0,sK3,sK4)
& ~ equal_maps(sK1,sK2,sK4,sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5)],[f35]) ).
fof(f44,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,sK6(X0,X2,X3))
& member(sK6(X0,X2,X3),X2) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X4,sK6(X0,X2,X3))],[f37]) ).
fof(f45,plain,
! [X0,X1,X2,X3] :
( ( ~ equal_maps(X0,X1,X2,X3)
| ! [X4,X5,X6] :
( ~ member(X6,X3)
| ~ member(X5,X3)
| ~ member(X4,X2)
| ~ apply(X1,X4,X6)
| ~ apply(X0,X4,X5)
| X5 = X6 ) )
& ( ? [X4,X5,X6] :
( member(X6,X3)
& member(X5,X3)
& member(X4,X2)
& apply(X1,X4,X6)
& apply(X0,X4,X5)
& X5 != X6 )
| equal_maps(X0,X1,X2,X3) ) ),
inference(nnf_transformation,[],[f39]) ).
fof(f46,plain,
! [X0,X1,X2,X3] :
( ( ~ equal_maps(X0,X1,X2,X3)
| ! [X7,X8,X9] :
( ~ member(X9,X3)
| ~ member(X8,X3)
| ~ member(X7,X2)
| ~ apply(X1,X7,X9)
| ~ apply(X0,X7,X8)
| X8 = X9 ) )
& ( ? [X4,X5,X6] :
( member(X6,X3)
& member(X5,X3)
& member(X4,X2)
& apply(X1,X4,X6)
& apply(X0,X4,X5)
& X5 != X6 )
| equal_maps(X0,X1,X2,X3) ) ),
inference(rectify,[],[f45]) ).
fof(f47,plain,
! [X0,X1,X2,X3] :
( ( ~ equal_maps(X0,X1,X2,X3)
| ! [X7,X8,X9] :
( ~ member(X9,X3)
| ~ member(X8,X3)
| ~ member(X7,X2)
| ~ apply(X1,X7,X9)
| ~ apply(X0,X7,X8)
| X8 = X9 ) )
& ( ( member(sK9(X0,X1,X2,X3),X3)
& member(sK8(X0,X1,X2,X3),X3)
& member(sK7(X0,X1,X2,X3),X2)
& apply(X1,sK7(X0,X1,X2,X3),sK9(X0,X1,X2,X3))
& apply(X0,sK7(X0,X1,X2,X3),sK8(X0,X1,X2,X3))
& sK8(X0,X1,X2,X3) != sK9(X0,X1,X2,X3) )
| equal_maps(X0,X1,X2,X3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9]),skolemize(X4,sK7(X0,X1,X2,X3)),skolemize(X5,sK8(X0,X1,X2,X3)),skolemize(X6,sK9(X0,X1,X2,X3))],[f46]) ).
fof(f48,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,[],[f41]) ).
fof(f49,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,[],[f48]) ).
fof(f50,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,sK10(X0,X1,X3,X5,X6),X6)
& apply(X1,X5,sK10(X0,X1,X3,X5,X6))
& member(sK10(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,[sK10]),skolemize(X8,sK10(X0,X1,X3,X5,X6))],[f49]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ~ surjective(X0,X1,X2)
| ! [X3] :
( ~ member(X3,X2)
| ( apply(X0,sK11(X0,X1,X3),X3)
& member(sK11(X0,X1,X3),X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X4,sK11(X0,X1,X3))],[f42]) ).
fof(f52,plain,
equal_maps(compose_function(sK1,sK0,sK3,sK4,sK5),compose_function(sK2,sK0,sK3,sK4,sK5),sK3,sK5),
inference(cnf_transformation,[],[f43]) ).
fof(f53,plain,
surjective(sK0,sK3,sK4),
inference(cnf_transformation,[],[f43]) ).
fof(f54,plain,
maps(sK2,sK4,sK5),
inference(cnf_transformation,[],[f43]) ).
fof(f55,plain,
maps(sK1,sK4,sK5),
inference(cnf_transformation,[],[f43]) ).
fof(f56,plain,
maps(sK0,sK3,sK4),
inference(cnf_transformation,[],[f43]) ).
fof(f57,plain,
~ equal_maps(sK1,sK2,sK4,sK5),
inference(cnf_transformation,[],[f43]) ).
fof(f58,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,[],[f44]) ).
fof(f59,plain,
! [X2,X3,X0,X1] :
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| apply(X0,X3,sK6(X0,X2,X3)) ),
inference(cnf_transformation,[],[f44]) ).
fof(f60,plain,
! [X2,X3,X0,X1] :
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| member(sK6(X0,X2,X3),X2) ),
inference(cnf_transformation,[],[f44]) ).
fof(f61,plain,
! [X2,X3,X0,X1,X8,X9,X7] :
( ~ equal_maps(X0,X1,X2,X3)
| ~ member(X9,X3)
| ~ member(X8,X3)
| ~ member(X7,X2)
| ~ apply(X1,X7,X9)
| ~ apply(X0,X7,X8)
| X8 = X9 ),
inference(cnf_transformation,[],[f47]) ).
fof(f62,plain,
! [X2,X3,X0,X1] :
( member(sK9(X0,X1,X2,X3),X3)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f47]) ).
fof(f63,plain,
! [X2,X3,X0,X1] :
( member(sK8(X0,X1,X2,X3),X3)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f47]) ).
fof(f64,plain,
! [X2,X3,X0,X1] :
( member(sK7(X0,X1,X2,X3),X2)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f47]) ).
fof(f65,plain,
! [X2,X3,X0,X1] :
( apply(X1,sK7(X0,X1,X2,X3),sK9(X0,X1,X2,X3))
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f47]) ).
fof(f66,plain,
! [X2,X3,X0,X1] :
( apply(X0,sK7(X0,X1,X2,X3),sK8(X0,X1,X2,X3))
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f47]) ).
fof(f67,plain,
! [X2,X3,X0,X1] :
( sK8(X0,X1,X2,X3) != sK9(X0,X1,X2,X3)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f47]) ).
fof(f71,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ member(X6,X4)
| ~ member(X5,X2)
| ~ apply(X0,X7,X6)
| ~ apply(X1,X5,X7)
| ~ member(X7,X3)
| apply(compose_function(X0,X1,X2,X3,X4),X5,X6) ),
inference(cnf_transformation,[],[f50]) ).
fof(f72,plain,
! [X2,X3,X0,X1] :
( ~ surjective(X0,X1,X2)
| ~ member(X3,X2)
| apply(X0,sK11(X0,X1,X3),X3) ),
inference(cnf_transformation,[],[f51]) ).
fof(f73,plain,
! [X2,X3,X0,X1] :
( ~ surjective(X0,X1,X2)
| ~ member(X3,X2)
| member(sK11(X0,X1,X3),X1) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_49,negated_conjecture,
~ equal_maps(sK1,sK2,sK4,sK5),
inference(cnf_transformation,[],[f57]) ).
tcf(c_50,negated_conjecture,
maps(sK0,sK3,sK4),
inference(cnf_transformation,[],[f56]) ).
tcf(c_51,negated_conjecture,
maps(sK1,sK4,sK5),
inference(cnf_transformation,[],[f55]) ).
tcf(c_52,negated_conjecture,
maps(sK2,sK4,sK5),
inference(cnf_transformation,[],[f54]) ).
tcf(c_53,negated_conjecture,
surjective(sK0,sK3,sK4),
inference(cnf_transformation,[],[f53]) ).
tcf(c_54,negated_conjecture,
equal_maps(compose_function(sK1,sK0,sK3,sK4,sK5),compose_function(sK2,sK0,sK3,sK4,sK5),sK3,sK5),
inference(cnf_transformation,[],[f52]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK6(X0,X2,X3),X2)
| ~ member(X3,X1)
| ~ maps(X0,X1,X2) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,X3,sK6(X0,X2,X3))
| ~ member(X3,X1)
| ~ maps(X0,X1,X2) ),
inference(cnf_transformation,[],[f59]) ).
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,[],[f58]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equal_maps(X0,X1,X2,X3)
| ( sK8(X0,X1,X2,X3) != sK9(X0,X1,X2,X3) ) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equal_maps(X0,X1,X2,X3)
| apply(X0,sK7(X0,X1,X2,X3),sK8(X0,X1,X2,X3)) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equal_maps(X1,X0,X2,X3)
| apply(X0,sK7(X1,X0,X2,X3),sK9(X1,X0,X2,X3)) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equal_maps(X0,X1,X2,X3)
| member(sK7(X0,X1,X2,X3),X2) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equal_maps(X0,X1,X2,X3)
| member(sK8(X0,X1,X2,X3),X3) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equal_maps(X0,X1,X2,X3)
| member(sK9(X0,X1,X2,X3),X3) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( X5 = X6 )
| ~ member(X6,X3)
| ~ member(X5,X3)
| ~ member(X4,X2)
| ~ apply(X1,X4,X6)
| ~ apply(X0,X4,X5)
| ~ equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( apply(compose_function(X0,X3,X7,X6,X5),X4,X2)
| ~ member(X4,X7)
| ~ member(X2,X5)
| ~ member(X1,X6)
| ~ apply(X3,X4,X1)
| ~ apply(X0,X1,X2) ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK11(X0,X1,X3),X1)
| ~ member(X3,X2)
| ~ surjective(X0,X1,X2) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,sK11(X0,X1,X3),X3)
| ~ member(X3,X2)
| ~ surjective(X0,X1,X2) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_330,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X1,sK11(X1,X2,X3),X3)
| ~ member(X3,X0)
| ( X2 != sK3 )
| ( X1 != sK0 )
| ( X0 != sK4 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_70]) ).
tcf(c_331,plain,
! [X0: $i] :
( apply(sK0,sK11(sK0,sK3,X0),X0)
| ~ member(X0,sK4) ),
inference(unflattening,[status(thm)],[c_330]) ).
tcf(c_339,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK11(X1,X2,X3),X2)
| ~ member(X3,X0)
| ( X2 != sK3 )
| ( X1 != sK0 )
| ( X0 != sK4 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_69]) ).
tcf(c_340,plain,
! [X0: $i] :
( member(sK11(sK0,sK3,X0),sK3)
| ~ member(X0,sK4) ),
inference(unflattening,[status(thm)],[c_339]) ).
tcf(c_352,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( X4 = X5 )
| ~ member(X5,X0)
| ~ member(X4,X0)
| ~ member(X3,X2)
| ~ apply(X1,X3,X5)
| ~ apply(X1,X3,X4)
| ( X2 != sK3 )
| ( X1 != sK0 )
| ( X0 != sK4 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_57]) ).
tcf(c_353,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_352]) ).
tcf(c_373,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X1,X3,sK6(X1,X0,X3))
| ~ member(X3,X2)
| ( X2 != sK3 )
| ( X1 != sK0 )
| ( X0 != sK4 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_56]) ).
tcf(c_374,plain,
! [X0: $i] :
( apply(sK0,X0,sK6(sK0,sK4,X0))
| ~ member(X0,sK3) ),
inference(unflattening,[status(thm)],[c_373]) ).
tcf(c_382,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK6(X1,X0,X3),X0)
| ~ member(X3,X2)
| ( X2 != sK3 )
| ( X1 != sK0 )
| ( X0 != sK4 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_55]) ).
tcf(c_383,plain,
! [X0: $i] :
( member(sK6(sK0,sK4,X0),sK4)
| ~ member(X0,sK3) ),
inference(unflattening,[status(thm)],[c_382]) ).
tcf(c_391,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 != sK5 )
| ( X1 != sK4 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_57]) ).
tcf(c_392,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ member(X2,sK5)
| ~ member(X1,sK5)
| ~ member(X0,sK4)
| ~ apply(sK1,X0,X2)
| ~ apply(sK1,X0,X1) ),
inference(unflattening,[status(thm)],[c_391]) ).
tcf(c_412,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,X3,sK6(X0,X2,X3))
| ~ member(X3,X1)
| ( X2 != sK5 )
| ( X1 != sK4 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_56]) ).
tcf(c_413,plain,
! [X0: $i] :
( apply(sK1,X0,sK6(sK1,sK5,X0))
| ~ member(X0,sK4) ),
inference(unflattening,[status(thm)],[c_412]) ).
tcf(c_421,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK6(X0,X2,X3),X2)
| ~ member(X3,X1)
| ( X2 != sK5 )
| ( X1 != sK4 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_55]) ).
tcf(c_422,plain,
! [X0: $i] :
( member(sK6(sK1,sK5,X0),sK5)
| ~ member(X0,sK4) ),
inference(unflattening,[status(thm)],[c_421]) ).
tcf(c_430,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 != sK5 )
| ( X1 != sK4 )
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_57]) ).
tcf(c_431,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ member(X2,sK5)
| ~ member(X1,sK5)
| ~ member(X0,sK4)
| ~ apply(sK2,X0,X2)
| ~ apply(sK2,X0,X1) ),
inference(unflattening,[status(thm)],[c_430]) ).
tcf(c_451,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,X3,sK6(X0,X2,X3))
| ~ member(X3,X1)
| ( X2 != sK5 )
| ( X1 != sK4 )
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_56]) ).
tcf(c_452,plain,
! [X0: $i] :
( apply(sK2,X0,sK6(sK2,sK5,X0))
| ~ member(X0,sK4) ),
inference(unflattening,[status(thm)],[c_451]) ).
tcf(c_460,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK6(X0,X2,X3),X2)
| ~ member(X3,X1)
| ( X2 != sK5 )
| ( X1 != sK4 )
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_55]) ).
tcf(c_461,plain,
! [X0: $i] :
( member(sK6(sK2,sK5,X0),sK5)
| ~ member(X0,sK4) ),
inference(unflattening,[status(thm)],[c_460]) ).
tcf(c_632,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK9(X0,X1,X2,X3),X3)
| ( X3 != sK5 )
| ( X2 != sK4 )
| ( X1 != sK2 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_63]) ).
tcf(c_633,plain,
member(sK9(sK1,sK2,sK4,sK5),sK5),
inference(unflattening,[status(thm)],[c_632]) ).
tcf(c_637,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK8(X0,X1,X2,X3),X3)
| ( X3 != sK5 )
| ( X2 != sK4 )
| ( X1 != sK2 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_62]) ).
tcf(c_638,plain,
member(sK8(sK1,sK2,sK4,sK5),sK5),
inference(unflattening,[status(thm)],[c_637]) ).
tcf(c_642,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK7(X0,X1,X2,X3),X2)
| ( X3 != sK5 )
| ( X2 != sK4 )
| ( X1 != sK2 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_61]) ).
tcf(c_643,plain,
member(sK7(sK1,sK2,sK4,sK5),sK4),
inference(unflattening,[status(thm)],[c_642]) ).
tcf(c_647,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,sK7(X0,X1,X2,X3),sK8(X0,X1,X2,X3))
| ( X3 != sK5 )
| ( X2 != sK4 )
| ( X1 != sK2 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_59]) ).
tcf(c_648,plain,
apply(sK1,sK7(sK1,sK2,sK4,sK5),sK8(sK1,sK2,sK4,sK5)),
inference(unflattening,[status(thm)],[c_647]) ).
tcf(c_652,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 != sK5 )
| ( X2 != sK4 )
| ( X1 != sK2 )
| ( X0 != sK1 )
| ( sK8(X0,X1,X2,X3) != sK9(X0,X1,X2,X3) ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_58]) ).
tcf(c_653,plain,
sK8(sK1,sK2,sK4,sK5) != sK9(sK1,sK2,sK4,sK5),
inference(unflattening,[status(thm)],[c_652]) ).
tcf(c_657,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X1,sK7(X0,X1,X2,X3),sK9(X0,X1,X2,X3))
| ( X3 != sK5 )
| ( X2 != sK4 )
| ( X1 != sK2 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_60]) ).
tcf(c_658,plain,
apply(sK2,sK7(sK1,sK2,sK4,sK5),sK9(sK1,sK2,sK4,sK5)),
inference(unflattening,[status(thm)],[c_657]) ).
tcf(c_765,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_767,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1286,plain,
! [X0: $i,X1: $i] :
( ( sK6(sK0,sK4,X0) = X1 )
| ~ member(X1,sK4)
| ~ member(X0,sK3)
| ~ apply(sK0,X0,X1)
| ~ member(sK6(sK0,sK4,X0),sK4) ),
inference(superposition,[status(thm)],[c_374,c_353]) ).
tcf(c_1326,plain,
! [X0: $i,X1: $i] :
( ( sK6(sK1,sK5,X0) = X1 )
| ~ member(X1,sK5)
| ~ member(X0,sK4)
| ~ apply(sK1,X0,X1)
| ~ member(sK6(sK1,sK5,X0),sK5) ),
inference(superposition,[status(thm)],[c_413,c_392]) ).
tcf(c_1361,plain,
! [X0: $i,X1: $i] :
( ( sK6(sK2,sK5,X0) = X1 )
| ~ member(X1,sK5)
| ~ member(X0,sK4)
| ~ apply(sK2,X0,X1)
| ~ member(sK6(sK2,sK5,X0),sK5) ),
inference(superposition,[status(thm)],[c_452,c_431]) ).
tcf(c_1399,plain,
! [X0: $i,X1: $i] :
( ( sK6(sK0,sK4,X0) = X1 )
| ~ member(X1,sK4)
| ~ member(X0,sK3)
| ~ apply(sK0,X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_1286,c_383,c_1286]) ).
tcf(c_1412,plain,
! [X0: $i] :
( ( sK6(sK0,sK4,sK11(sK0,sK3,X0)) = X0 )
| ~ member(X0,sK4)
| ~ member(sK11(sK0,sK3,X0),sK3) ),
inference(superposition,[status(thm)],[c_331,c_1399]) ).
tcf(c_1428,plain,
! [X0: $i] :
( ( sK6(sK0,sK4,sK11(sK0,sK3,X0)) = X0 )
| ~ member(X0,sK4) ),
inference(global_subsumption_just,[status(thm)],[c_1412,c_340,c_1412]) ).
tcf(c_1435,plain,
! [X0: $i,X1: $i,X2: $i] :
( equal_maps(X0,X1,sK4,X2)
| ( sK6(sK0,sK4,sK11(sK0,sK3,sK7(X0,X1,sK4,X2))) = sK7(X0,X1,sK4,X2) ) ),
inference(superposition,[status(thm)],[c_61,c_1428]) ).
tcf(c_1496,plain,
sK6(sK0,sK4,sK11(sK0,sK3,sK7(sK1,sK2,sK4,sK5))) = sK7(sK1,sK2,sK4,sK5),
inference(superposition,[status(thm)],[c_1435,c_49]) ).
tcf(c_1634,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ member(X2,sK5)
| ~ member(X1,sK5)
| ~ member(X0,sK3)
| ~ apply(compose_function(sK2,sK0,sK3,sK4,sK5),X0,X2)
| ~ apply(compose_function(sK1,sK0,sK3,sK4,sK5),X0,X1) ),
inference(superposition,[status(thm)],[c_54,c_64]) ).
tcf(c_1635,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( X2 = X4 )
| ( sK6(sK0,sK4,sK11(sK0,sK3,sK7(X0,X3,sK4,X5))) = sK7(X0,X3,sK4,X5) )
| ~ member(X1,sK4)
| ~ member(X4,X5)
| ~ member(X2,X5)
| ~ apply(X3,X1,X4)
| ~ apply(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_1435,c_64]) ).
tcf(c_1650,plain,
( member(sK7(sK1,sK2,sK4,sK5),sK4)
| ~ member(sK11(sK0,sK3,sK7(sK1,sK2,sK4,sK5)),sK3) ),
inference(superposition,[status(thm)],[c_1496,c_383]) ).
tcf(c_1655,plain,
member(sK7(sK1,sK2,sK4,sK5),sK4),
inference(global_subsumption_just,[status(thm)],[c_1650,c_643]) ).
tcf(c_1730,plain,
! [X0: $i,X1: $i] :
( ( sK6(sK1,sK5,X0) = X1 )
| ~ member(X1,sK5)
| ~ member(X0,sK4)
| ~ apply(sK1,X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_1326,c_422,c_1326]) ).
tcf(c_1741,plain,
! [X0: $i,X1: $i,X2: $i] :
( equal_maps(sK1,X0,X1,X2)
| ( sK6(sK1,sK5,sK7(sK1,X0,X1,X2)) = sK8(sK1,X0,X1,X2) )
| ~ member(sK7(sK1,X0,X1,X2),sK4)
| ~ member(sK8(sK1,X0,X1,X2),sK5) ),
inference(superposition,[status(thm)],[c_59,c_1730]) ).
tcf(c_1742,plain,
! [X0: $i,X1: $i,X2: $i] :
( equal_maps(X0,sK1,X1,X2)
| ( sK6(sK1,sK5,sK7(X0,sK1,X1,X2)) = sK9(X0,sK1,X1,X2) )
| ~ member(sK7(X0,sK1,X1,X2),sK4)
| ~ member(sK9(X0,sK1,X1,X2),sK5) ),
inference(superposition,[status(thm)],[c_60,c_1730]) ).
tcf(c_1754,plain,
! [X0: $i,X1: $i] :
( ( sK6(sK2,sK5,X0) = X1 )
| ~ member(X1,sK5)
| ~ member(X0,sK4)
| ~ apply(sK2,X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_1361,c_461,c_1361]) ).
tcf(c_1765,plain,
! [X0: $i,X1: $i,X2: $i] :
( equal_maps(sK2,X0,X1,X2)
| ( sK6(sK2,sK5,sK7(sK2,X0,X1,X2)) = sK8(sK2,X0,X1,X2) )
| ~ member(sK7(sK2,X0,X1,X2),sK4)
| ~ member(sK8(sK2,X0,X1,X2),sK5) ),
inference(superposition,[status(thm)],[c_59,c_1754]) ).
tcf(c_1766,plain,
! [X0: $i,X1: $i,X2: $i] :
( equal_maps(X0,sK2,X1,X2)
| ( sK6(sK2,sK5,sK7(X0,sK2,X1,X2)) = sK9(X0,sK2,X1,X2) )
| ~ member(sK7(X0,sK2,X1,X2),sK4)
| ~ member(sK9(X0,sK2,X1,X2),sK5) ),
inference(superposition,[status(thm)],[c_60,c_1754]) ).
tcf(c_1927,plain,
! [X0: $i] :
( ( sK8(sK1,sK2,sK4,sK5) = sK9(sK1,sK2,sK4,sK5) )
| ( sK9(sK1,sK2,sK4,sK5) != X0 )
| ( sK8(sK1,sK2,sK4,sK5) != X0 ) ),
inference(instantiation,[status(thm)],[c_767]) ).
tcf(c_2747,plain,
( ( sK8(sK1,sK2,sK4,sK5) = sK9(sK1,sK2,sK4,sK5) )
| ( sK9(sK1,sK2,sK4,sK5) != sK8(sK1,sK2,sK4,sK5) )
| ( sK8(sK1,sK2,sK4,sK5) != sK8(sK1,sK2,sK4,sK5) ) ),
inference(instantiation,[status(thm)],[c_1927]) ).
tcf(c_2748,plain,
sK8(sK1,sK2,sK4,sK5) = sK8(sK1,sK2,sK4,sK5),
inference(instantiation,[status(thm)],[c_765]) ).
tcf(c_4390,plain,
( equal_maps(sK1,sK2,sK4,sK5)
| ( sK6(sK1,sK5,sK7(sK1,sK2,sK4,sK5)) = sK8(sK1,sK2,sK4,sK5) )
| ~ member(sK8(sK1,sK2,sK4,sK5),sK5) ),
inference(superposition,[status(thm)],[c_1655,c_1741]) ).
tcf(c_4391,plain,
( ( sK6(sK1,sK5,sK7(sK1,sK2,sK4,sK5)) = sK8(sK1,sK2,sK4,sK5) )
| ~ member(sK8(sK1,sK2,sK4,sK5),sK5) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4390,c_49]) ).
tcf(c_4414,plain,
sK6(sK1,sK5,sK7(sK1,sK2,sK4,sK5)) = sK8(sK1,sK2,sK4,sK5),
inference(global_subsumption_just,[status(thm)],[c_4391,c_638,c_4391]) ).
tcf(c_4417,plain,
( apply(sK1,sK7(sK1,sK2,sK4,sK5),sK8(sK1,sK2,sK4,sK5))
| ~ member(sK7(sK1,sK2,sK4,sK5),sK4) ),
inference(superposition,[status(thm)],[c_4414,c_413]) ).
tcf(c_4418,plain,
( member(sK8(sK1,sK2,sK4,sK5),sK5)
| ~ member(sK7(sK1,sK2,sK4,sK5),sK4) ),
inference(superposition,[status(thm)],[c_4414,c_422]) ).
tcf(c_4426,plain,
member(sK8(sK1,sK2,sK4,sK5),sK5),
inference(forward_subsumption_resolution,[status(thm)],[c_4418,c_1655]) ).
tcf(c_4427,plain,
apply(sK1,sK7(sK1,sK2,sK4,sK5),sK8(sK1,sK2,sK4,sK5)),
inference(forward_subsumption_resolution,[status(thm)],[c_4417,c_1655]) ).
tcf(c_4526,plain,
! [X0: $i] :
( ( sK8(sK1,sK2,sK4,sK5) = X0 )
| ~ member(X0,sK5)
| ~ member(sK7(sK1,sK2,sK4,sK5),sK4)
| ~ member(sK8(sK1,sK2,sK4,sK5),sK5)
| ~ apply(sK1,sK7(sK1,sK2,sK4,sK5),X0) ),
inference(superposition,[status(thm)],[c_4427,c_392]) ).
tcf(c_4527,plain,
! [X0: $i] :
( ( sK8(sK1,sK2,sK4,sK5) = X0 )
| ~ member(X0,sK5)
| ~ apply(sK1,sK7(sK1,sK2,sK4,sK5),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4526,c_1655,c_4426]) ).
tcf(c_4925,plain,
! [X0: $i,X1: $i] :
( equal_maps(X0,sK1,sK4,X1)
| ( sK6(sK1,sK5,sK7(X0,sK1,sK4,X1)) = sK9(X0,sK1,sK4,X1) )
| ~ member(sK9(X0,sK1,sK4,X1),sK5) ),
inference(superposition,[status(thm)],[c_61,c_1742]) ).
tcf(c_4936,plain,
! [X0: $i] :
( equal_maps(X0,sK1,sK4,sK5)
| ( sK6(sK1,sK5,sK7(X0,sK1,sK4,sK5)) = sK9(X0,sK1,sK4,sK5) ) ),
inference(superposition,[status(thm)],[c_63,c_4925]) ).
tcf(c_4944,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = X3 )
| ( sK6(sK1,sK5,sK7(X0,sK1,sK4,sK5)) = sK9(X0,sK1,sK4,sK5) )
| ~ member(X3,sK5)
| ~ member(X2,sK5)
| ~ member(X1,sK4)
| ~ apply(sK1,X1,X3)
| ~ apply(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_4936,c_64]) ).
tcf(c_7038,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK9(sK1,sK2,sK4,sK5) = sK8(sK1,sK2,sK4,sK5) )
| ~ member(X1,X4)
| ~ equal_maps(X0,X2,X4,X3)
| ~ member(sK9(sK1,sK2,sK4,sK5),X3)
| ~ member(sK8(sK1,sK2,sK4,sK5),X3)
| ~ apply(X2,X1,sK8(sK1,sK2,sK4,sK5))
| ~ apply(X0,X1,sK9(sK1,sK2,sK4,sK5)) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_7567,plain,
! [X0: $i,X1: $i] :
( equal_maps(sK2,X0,sK4,X1)
| ( sK6(sK2,sK5,sK7(sK2,X0,sK4,X1)) = sK8(sK2,X0,sK4,X1) )
| ~ member(sK8(sK2,X0,sK4,X1),sK5) ),
inference(superposition,[status(thm)],[c_61,c_1765]) ).
tcf(c_7578,plain,
! [X0: $i] :
( equal_maps(sK2,X0,sK4,sK5)
| ( sK6(sK2,sK5,sK7(sK2,X0,sK4,sK5)) = sK8(sK2,X0,sK4,sK5) ) ),
inference(superposition,[status(thm)],[c_62,c_7567]) ).
tcf(c_7586,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = X3 )
| ( sK6(sK2,sK5,sK7(sK2,X0,sK4,sK5)) = sK8(sK2,X0,sK4,sK5) )
| ~ member(X3,sK5)
| ~ member(X2,sK5)
| ~ member(X1,sK4)
| ~ apply(sK2,X1,X3)
| ~ apply(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_7578,c_64]) ).
tcf(c_7603,plain,
( equal_maps(sK1,sK2,sK4,sK5)
| ( sK6(sK2,sK5,sK7(sK1,sK2,sK4,sK5)) = sK9(sK1,sK2,sK4,sK5) )
| ~ member(sK9(sK1,sK2,sK4,sK5),sK5) ),
inference(superposition,[status(thm)],[c_1655,c_1766]) ).
tcf(c_7604,plain,
( ( sK6(sK2,sK5,sK7(sK1,sK2,sK4,sK5)) = sK9(sK1,sK2,sK4,sK5) )
| ~ member(sK9(sK1,sK2,sK4,sK5),sK5) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7603,c_49]) ).
tcf(c_7623,plain,
sK6(sK2,sK5,sK7(sK1,sK2,sK4,sK5)) = sK9(sK1,sK2,sK4,sK5),
inference(global_subsumption_just,[status(thm)],[c_7604,c_633,c_7604]) ).
tcf(c_7626,plain,
( apply(sK2,sK7(sK1,sK2,sK4,sK5),sK9(sK1,sK2,sK4,sK5))
| ~ member(sK7(sK1,sK2,sK4,sK5),sK4) ),
inference(superposition,[status(thm)],[c_7623,c_452]) ).
tcf(c_7627,plain,
( member(sK9(sK1,sK2,sK4,sK5),sK5)
| ~ member(sK7(sK1,sK2,sK4,sK5),sK4) ),
inference(superposition,[status(thm)],[c_7623,c_461]) ).
tcf(c_7637,plain,
member(sK9(sK1,sK2,sK4,sK5),sK5),
inference(forward_subsumption_resolution,[status(thm)],[c_7627,c_1655]) ).
tcf(c_7638,plain,
apply(sK2,sK7(sK1,sK2,sK4,sK5),sK9(sK1,sK2,sK4,sK5)),
inference(forward_subsumption_resolution,[status(thm)],[c_7626,c_1655]) ).
tcf(c_18589,plain,
! [X0: $i,X1: $i] :
( ( sK6(sK2,sK5,X0) = X1 )
| ~ member(X1,sK5)
| ~ member(X0,sK4)
| ~ apply(sK2,X0,X1)
| ~ member(sK6(sK2,sK5,X0),sK5) ),
inference(superposition,[status(thm)],[c_452,c_431]) ).
tcf(c_18648,plain,
! [X0: $i,X1: $i] :
( ( sK6(sK2,sK5,X0) = X1 )
| ~ member(X1,sK5)
| ~ member(X0,sK4)
| ~ apply(sK2,X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_18589,c_461,c_1361]) ).
tcf(c_18658,plain,
! [X0: $i,X1: $i,X2: $i] :
( equal_maps(sK2,X0,X1,X2)
| ( sK6(sK2,sK5,sK7(sK2,X0,X1,X2)) = sK8(sK2,X0,X1,X2) )
| ~ member(sK7(sK2,X0,X1,X2),sK4)
| ~ member(sK8(sK2,X0,X1,X2),sK5) ),
inference(superposition,[status(thm)],[c_59,c_18648]) ).
tcf(c_18727,plain,
! [X0: $i,X1: $i] :
( equal_maps(sK2,X0,sK4,X1)
| ( sK6(sK2,sK5,sK7(sK2,X0,sK4,X1)) = sK8(sK2,X0,sK4,X1) )
| ~ member(sK8(sK2,X0,sK4,X1),sK5) ),
inference(superposition,[status(thm)],[c_61,c_18658]) ).
tcf(c_20833,plain,
! [X0: $i] :
( equal_maps(sK2,X0,sK4,sK5)
| ( sK6(sK2,sK5,sK7(sK2,X0,sK4,sK5)) = sK8(sK2,X0,sK4,sK5) ) ),
inference(superposition,[status(thm)],[c_62,c_18727]) ).
tcf(c_23476,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK9(sK1,sK2,sK4,sK5) = sK8(sK1,sK2,sK4,sK5) )
| ~ member(X1,X3)
| ~ equal_maps(X0,X2,X3,sK5)
| ~ member(sK9(sK1,sK2,sK4,sK5),sK5)
| ~ member(sK8(sK1,sK2,sK4,sK5),sK5)
| ~ apply(X2,X1,sK8(sK1,sK2,sK4,sK5))
| ~ apply(X0,X1,sK9(sK1,sK2,sK4,sK5)) ),
inference(instantiation,[status(thm)],[c_7038]) ).
tcf(c_23758,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = X3 )
| ( sK6(sK2,sK5,sK7(sK2,X0,sK4,sK5)) = sK8(sK2,X0,sK4,sK5) )
| ~ member(X3,sK5)
| ~ member(X2,sK5)
| ~ member(X1,sK4)
| ~ apply(sK2,X1,X3)
| ~ apply(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_20833,c_64]) ).
tcf(c_24749,plain,
! [X0: $i,X1: $i] :
( ( sK6(sK1,sK5,X0) = X1 )
| ( sK6(sK2,sK5,sK7(sK2,sK1,sK4,sK5)) = sK8(sK2,sK1,sK4,sK5) )
| ~ member(X1,sK5)
| ~ member(X0,sK4)
| ~ apply(sK2,X0,X1)
| ~ member(sK6(sK1,sK5,X0),sK5) ),
inference(superposition,[status(thm)],[c_413,c_23758]) ).
tcf(c_26627,plain,
! [X0: $i,X1: $i] :
( ( sK9(sK1,sK2,sK4,sK5) = sK8(sK1,sK2,sK4,sK5) )
| ~ equal_maps(sK2,X0,X1,sK5)
| ~ member(sK9(sK1,sK2,sK4,sK5),sK5)
| ~ member(sK8(sK1,sK2,sK4,sK5),sK5)
| ~ member(sK7(sK1,sK2,sK4,sK5),X1)
| ~ apply(sK2,sK7(sK1,sK2,sK4,sK5),sK9(sK1,sK2,sK4,sK5))
| ~ apply(X0,sK7(sK1,sK2,sK4,sK5),sK8(sK1,sK2,sK4,sK5)) ),
inference(instantiation,[status(thm)],[c_23476]) ).
tcf(c_36029,plain,
! [X0: $i] :
( ( sK9(sK1,sK2,sK4,sK5) = sK8(sK1,sK2,sK4,sK5) )
| ~ equal_maps(sK2,sK1,X0,sK5)
| ~ member(sK9(sK1,sK2,sK4,sK5),sK5)
| ~ member(sK8(sK1,sK2,sK4,sK5),sK5)
| ~ member(sK7(sK1,sK2,sK4,sK5),X0)
| ~ apply(sK2,sK7(sK1,sK2,sK4,sK5),sK9(sK1,sK2,sK4,sK5))
| ~ apply(sK1,sK7(sK1,sK2,sK4,sK5),sK8(sK1,sK2,sK4,sK5)) ),
inference(instantiation,[status(thm)],[c_26627]) ).
tcf(c_36030,plain,
( ( sK9(sK1,sK2,sK4,sK5) = sK8(sK1,sK2,sK4,sK5) )
| ~ equal_maps(sK2,sK1,sK4,sK5)
| ~ member(sK7(sK1,sK2,sK4,sK5),sK4)
| ~ member(sK9(sK1,sK2,sK4,sK5),sK5)
| ~ member(sK8(sK1,sK2,sK4,sK5),sK5)
| ~ apply(sK2,sK7(sK1,sK2,sK4,sK5),sK9(sK1,sK2,sK4,sK5))
| ~ apply(sK1,sK7(sK1,sK2,sK4,sK5),sK8(sK1,sK2,sK4,sK5)) ),
inference(instantiation,[status(thm)],[c_36029]) ).
tcf(c_36197,plain,
! [X0: $i] :
( ( sK9(sK1,sK2,sK4,sK5) = X0 )
| ( sK6(sK1,sK5,sK7(sK2,sK1,sK4,sK5)) = sK9(sK2,sK1,sK4,sK5) )
| ~ member(X0,sK5)
| ~ member(sK7(sK1,sK2,sK4,sK5),sK4)
| ~ member(sK9(sK1,sK2,sK4,sK5),sK5)
| ~ apply(sK1,sK7(sK1,sK2,sK4,sK5),X0) ),
inference(superposition,[status(thm)],[c_7638,c_4944]) ).
tcf(c_36268,plain,
! [X0: $i] :
( ( sK9(sK1,sK2,sK4,sK5) = X0 )
| ( sK6(sK1,sK5,sK7(sK2,sK1,sK4,sK5)) = sK9(sK2,sK1,sK4,sK5) )
| ~ member(X0,sK5)
| ~ apply(sK1,sK7(sK1,sK2,sK4,sK5),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_36197,c_1655,c_7637]) ).
tcf(c_37097,plain,
! [X0: $i,X1: $i] :
( ( sK6(sK1,sK5,X0) = X1 )
| ( sK6(sK2,sK5,sK7(sK2,sK1,sK4,sK5)) = sK8(sK2,sK1,sK4,sK5) )
| ~ member(X1,sK5)
| ~ member(X0,sK4)
| ~ apply(sK2,X0,X1)
| ~ member(sK6(sK1,sK5,X0),sK5) ),
inference(superposition,[status(thm)],[c_413,c_7586]) ).
tcf(c_38805,plain,
! [X0: $i] :
( ~ apply(sK1,sK7(sK1,sK2,sK4,sK5),X0)
| ~ member(X0,sK5)
| ( sK6(sK1,sK5,sK7(sK2,sK1,sK4,sK5)) = sK9(sK2,sK1,sK4,sK5) ) ),
inference(global_subsumption_just,[status(thm)],[c_36268,c_653,c_1927,c_4527,c_36268]) ).
tcf(c_38806,plain,
! [X0: $i] :
( ( sK6(sK1,sK5,sK7(sK2,sK1,sK4,sK5)) = sK9(sK2,sK1,sK4,sK5) )
| ~ member(X0,sK5)
| ~ apply(sK1,sK7(sK1,sK2,sK4,sK5),X0) ),
inference(renaming,[status(thm)],[c_38805]) ).
tcf(c_38816,plain,
( ( sK6(sK1,sK5,sK7(sK2,sK1,sK4,sK5)) = sK9(sK2,sK1,sK4,sK5) )
| ~ member(sK8(sK1,sK2,sK4,sK5),sK5) ),
inference(superposition,[status(thm)],[c_4427,c_38806]) ).
tcf(c_38817,plain,
sK6(sK1,sK5,sK7(sK2,sK1,sK4,sK5)) = sK9(sK2,sK1,sK4,sK5),
inference(forward_subsumption_resolution,[status(thm)],[c_38816,c_4426]) ).
tcf(c_38824,plain,
! [X0: $i,X1: $i] :
( ( sK6(sK1,sK5,X0) = X1 )
| ( sK6(sK2,sK5,sK7(sK2,sK1,sK4,sK5)) = sK8(sK2,sK1,sK4,sK5) )
| ~ member(X1,sK5)
| ~ member(X0,sK4)
| ~ apply(sK2,X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_37097,c_422,c_24749]) ).
tcf(c_38839,plain,
! [X0: $i] :
( ( sK6(sK1,sK5,X0) = sK6(sK2,sK5,X0) )
| ( sK6(sK2,sK5,sK7(sK2,sK1,sK4,sK5)) = sK8(sK2,sK1,sK4,sK5) )
| ~ member(X0,sK4)
| ~ member(sK6(sK2,sK5,X0),sK5) ),
inference(superposition,[status(thm)],[c_452,c_38824]) ).
tcf(c_38840,plain,
( ( sK6(sK2,sK5,sK7(sK2,sK1,sK4,sK5)) = sK8(sK2,sK1,sK4,sK5) )
| ( sK6(sK1,sK5,sK7(sK1,sK2,sK4,sK5)) = sK9(sK1,sK2,sK4,sK5) )
| ~ member(sK7(sK1,sK2,sK4,sK5),sK4)
| ~ member(sK9(sK1,sK2,sK4,sK5),sK5) ),
inference(superposition,[status(thm)],[c_7638,c_38824]) ).
tcf(c_38868,plain,
( ( sK8(sK1,sK2,sK4,sK5) = sK9(sK1,sK2,sK4,sK5) )
| ( sK6(sK2,sK5,sK7(sK2,sK1,sK4,sK5)) = sK8(sK2,sK1,sK4,sK5) )
| ~ member(sK7(sK1,sK2,sK4,sK5),sK4)
| ~ member(sK9(sK1,sK2,sK4,sK5),sK5) ),
inference(light_normalisation,[status(thm)],[c_38840,c_4414]) ).
tcf(c_38869,plain,
( ( sK8(sK1,sK2,sK4,sK5) = sK9(sK1,sK2,sK4,sK5) )
| ( sK6(sK2,sK5,sK7(sK2,sK1,sK4,sK5)) = sK8(sK2,sK1,sK4,sK5) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_38868,c_1655,c_7637]) ).
tcf(c_39241,plain,
sK6(sK2,sK5,sK7(sK2,sK1,sK4,sK5)) = sK8(sK2,sK1,sK4,sK5),
inference(global_subsumption_just,[status(thm)],[c_38839,c_653,c_38869]) ).
tcf(c_39247,plain,
( apply(sK2,sK7(sK2,sK1,sK4,sK5),sK8(sK2,sK1,sK4,sK5))
| ~ member(sK7(sK2,sK1,sK4,sK5),sK4) ),
inference(superposition,[status(thm)],[c_39241,c_452]) ).
tcf(c_39248,plain,
( member(sK8(sK2,sK1,sK4,sK5),sK5)
| ~ member(sK7(sK2,sK1,sK4,sK5),sK4) ),
inference(superposition,[status(thm)],[c_39241,c_461]) ).
tcf(c_39723,plain,
( equal_maps(sK2,sK1,sK4,sK5)
| member(sK8(sK2,sK1,sK4,sK5),sK5) ),
inference(superposition,[status(thm)],[c_61,c_39248]) ).
tcf(c_39777,plain,
( apply(sK1,sK7(sK2,sK1,sK4,sK5),sK9(sK2,sK1,sK4,sK5))
| ~ member(sK7(sK2,sK1,sK4,sK5),sK4) ),
inference(superposition,[status(thm)],[c_38817,c_413]) ).
tcf(c_39778,plain,
( member(sK9(sK2,sK1,sK4,sK5),sK5)
| ~ member(sK7(sK2,sK1,sK4,sK5),sK4) ),
inference(superposition,[status(thm)],[c_38817,c_422]) ).
tcf(c_40329,plain,
member(sK8(sK2,sK1,sK4,sK5),sK5),
inference(global_subsumption_just,[status(thm)],[c_39723,c_633,c_638,c_643,c_648,c_653,c_658,c_2747,c_2748,c_36030,c_39723]) ).
tcf(c_40959,plain,
( equal_maps(sK2,sK1,sK4,sK5)
| member(sK9(sK2,sK1,sK4,sK5),sK5) ),
inference(superposition,[status(thm)],[c_61,c_39778]) ).
tcf(c_40962,plain,
member(sK9(sK2,sK1,sK4,sK5),sK5),
inference(global_subsumption_just,[status(thm)],[c_40959,c_633,c_638,c_643,c_648,c_653,c_658,c_2747,c_2748,c_36030,c_40959]) ).
tcf(c_52606,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK6(sK2,sK5,X0) = X3 )
| ( sK6(sK0,sK4,sK11(sK0,sK3,sK7(sK2,X2,sK4,X1))) = sK7(sK2,X2,sK4,X1) )
| ~ member(X0,sK4)
| ~ member(X3,X1)
| ~ apply(X2,X0,X3)
| ~ member(sK6(sK2,sK5,X0),X1) ),
inference(superposition,[status(thm)],[c_452,c_1635]) ).
tcf(c_59914,plain,
! [X0: $i] :
( equal_maps(sK2,sK1,X0,sK5)
| ( sK8(sK2,sK1,X0,sK5) != sK9(sK2,sK1,X0,sK5) ) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_59917,plain,
! [X0: $i] :
( equal_maps(sK2,sK1,X0,sK5)
| member(sK7(sK2,sK1,X0,sK5),X0) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_59918,plain,
( equal_maps(sK2,sK1,sK4,sK5)
| member(sK7(sK2,sK1,sK4,sK5),sK4) ),
inference(instantiation,[status(thm)],[c_59917]) ).
tcf(c_59919,plain,
( equal_maps(sK2,sK1,sK4,sK5)
| ( sK8(sK2,sK1,sK4,sK5) != sK9(sK2,sK1,sK4,sK5) ) ),
inference(instantiation,[status(thm)],[c_59914]) ).
tcf(c_70912,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK6(sK2,sK5,X1) = X2 )
| ( sK6(sK0,sK4,sK11(sK0,sK3,sK7(sK2,X0,sK4,sK5))) = sK7(sK2,X0,sK4,sK5) )
| ~ member(X2,sK5)
| ~ member(X1,sK4)
| ~ apply(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_461,c_52606]) ).
tcf(c_71245,plain,
! [X0: $i] :
( ( sK6(sK1,sK5,X0) = sK6(sK2,sK5,X0) )
| ( sK6(sK0,sK4,sK11(sK0,sK3,sK7(sK2,sK1,sK4,sK5))) = sK7(sK2,sK1,sK4,sK5) )
| ~ member(X0,sK4)
| ~ member(sK6(sK1,sK5,X0),sK5) ),
inference(superposition,[status(thm)],[c_413,c_70912]) ).
tcf(c_71247,plain,
( ( sK6(sK2,sK5,sK7(sK1,sK2,sK4,sK5)) = sK8(sK1,sK2,sK4,sK5) )
| ( sK6(sK0,sK4,sK11(sK0,sK3,sK7(sK2,sK1,sK4,sK5))) = sK7(sK2,sK1,sK4,sK5) )
| ~ member(sK7(sK1,sK2,sK4,sK5),sK4)
| ~ member(sK8(sK1,sK2,sK4,sK5),sK5) ),
inference(superposition,[status(thm)],[c_4427,c_70912]) ).
tcf(c_71346,plain,
( ( sK8(sK1,sK2,sK4,sK5) = sK9(sK1,sK2,sK4,sK5) )
| ( sK6(sK0,sK4,sK11(sK0,sK3,sK7(sK2,sK1,sK4,sK5))) = sK7(sK2,sK1,sK4,sK5) )
| ~ member(sK7(sK1,sK2,sK4,sK5),sK4)
| ~ member(sK8(sK1,sK2,sK4,sK5),sK5) ),
inference(light_normalisation,[status(thm)],[c_71247,c_7623]) ).
tcf(c_71347,plain,
( ( sK8(sK1,sK2,sK4,sK5) = sK9(sK1,sK2,sK4,sK5) )
| ( sK6(sK0,sK4,sK11(sK0,sK3,sK7(sK2,sK1,sK4,sK5))) = sK7(sK2,sK1,sK4,sK5) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_71346,c_1655,c_4426]) ).
tcf(c_72041,plain,
sK6(sK0,sK4,sK11(sK0,sK3,sK7(sK2,sK1,sK4,sK5))) = sK7(sK2,sK1,sK4,sK5),
inference(global_subsumption_just,[status(thm)],[c_71245,c_653,c_71347]) ).
tcf(c_72049,plain,
( apply(sK0,sK11(sK0,sK3,sK7(sK2,sK1,sK4,sK5)),sK7(sK2,sK1,sK4,sK5))
| ~ member(sK11(sK0,sK3,sK7(sK2,sK1,sK4,sK5)),sK3) ),
inference(superposition,[status(thm)],[c_72041,c_374]) ).
tcf(c_72050,plain,
( member(sK7(sK2,sK1,sK4,sK5),sK4)
| ~ member(sK11(sK0,sK3,sK7(sK2,sK1,sK4,sK5)),sK3) ),
inference(superposition,[status(thm)],[c_72041,c_383]) ).
tcf(c_72753,plain,
member(sK7(sK2,sK1,sK4,sK5),sK4),
inference(global_subsumption_just,[status(thm)],[c_72050,c_633,c_638,c_643,c_648,c_653,c_658,c_2747,c_2748,c_36030,c_59918]) ).
tcf(c_72756,plain,
apply(sK1,sK7(sK2,sK1,sK4,sK5),sK9(sK2,sK1,sK4,sK5)),
inference(backward_subsumption_resolution,[status(thm)],[c_39777,c_72753]) ).
tcf(c_72758,plain,
apply(sK2,sK7(sK2,sK1,sK4,sK5),sK8(sK2,sK1,sK4,sK5)),
inference(backward_subsumption_resolution,[status(thm)],[c_39247,c_72753]) ).
tcf(c_75088,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apply(compose_function(sK1,X0,X4,X3,X2),X1,sK9(sK2,sK1,sK4,sK5))
| ~ member(X1,X4)
| ~ member(sK7(sK2,sK1,sK4,sK5),X3)
| ~ member(sK9(sK2,sK1,sK4,sK5),X2)
| ~ apply(X0,X1,sK7(sK2,sK1,sK4,sK5)) ),
inference(superposition,[status(thm)],[c_72756,c_65]) ).
tcf(c_75141,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apply(compose_function(sK2,X0,X4,X3,X2),X1,sK8(sK2,sK1,sK4,sK5))
| ~ member(X1,X4)
| ~ member(sK7(sK2,sK1,sK4,sK5),X3)
| ~ member(sK8(sK2,sK1,sK4,sK5),X2)
| ~ apply(X0,X1,sK7(sK2,sK1,sK4,sK5)) ),
inference(superposition,[status(thm)],[c_72758,c_65]) ).
tcf(c_77504,plain,
! [X0: $i,X1: $i] :
( ( sK9(sK2,sK1,sK4,sK5) = X1 )
| ~ member(X1,sK5)
| ~ member(X0,sK3)
| ~ member(sK7(sK2,sK1,sK4,sK5),sK4)
| ~ member(sK9(sK2,sK1,sK4,sK5),sK5)
| ~ apply(sK0,X0,sK7(sK2,sK1,sK4,sK5))
| ~ apply(compose_function(sK2,sK0,sK3,sK4,sK5),X0,X1) ),
inference(superposition,[status(thm)],[c_75088,c_1634]) ).
tcf(c_77522,plain,
! [X0: $i,X1: $i] :
( ( sK9(sK2,sK1,sK4,sK5) = X1 )
| ~ member(X1,sK5)
| ~ member(X0,sK3)
| ~ apply(sK0,X0,sK7(sK2,sK1,sK4,sK5))
| ~ apply(compose_function(sK2,sK0,sK3,sK4,sK5),X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_77504,c_72753,c_40962]) ).
tcf(c_95349,plain,
! [X0: $i] :
( ( sK8(sK2,sK1,sK4,sK5) = sK9(sK2,sK1,sK4,sK5) )
| ~ member(X0,sK3)
| ~ member(sK7(sK2,sK1,sK4,sK5),sK4)
| ~ member(sK8(sK2,sK1,sK4,sK5),sK5)
| ~ apply(sK0,X0,sK7(sK2,sK1,sK4,sK5)) ),
inference(superposition,[status(thm)],[c_75141,c_77522]) ).
tcf(c_95367,plain,
! [X0: $i] :
( ( sK8(sK2,sK1,sK4,sK5) = sK9(sK2,sK1,sK4,sK5) )
| ~ member(X0,sK3)
| ~ apply(sK0,X0,sK7(sK2,sK1,sK4,sK5)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_95349,c_72753,c_40329]) ).
tcf(c_96027,plain,
! [X0: $i] :
( ~ apply(sK0,X0,sK7(sK2,sK1,sK4,sK5))
| ~ member(X0,sK3) ),
inference(global_subsumption_just,[status(thm)],[c_95367,c_633,c_638,c_643,c_648,c_653,c_658,c_2747,c_2748,c_36030,c_59919,c_95367]) ).
tcf(c_96028,plain,
! [X0: $i] :
( ~ member(X0,sK3)
| ~ apply(sK0,X0,sK7(sK2,sK1,sK4,sK5)) ),
inference(renaming,[status(thm)],[c_96027]) ).
tcf(c_96034,plain,
~ member(sK11(sK0,sK3,sK7(sK2,sK1,sK4,sK5)),sK3),
inference(backward_subsumption_resolution,[status(thm)],[c_72049,c_96028]) ).
tcf(c_96036,plain,
~ member(sK7(sK2,sK1,sK4,sK5),sK4),
inference(superposition,[status(thm)],[c_340,c_96034]) ).
tcf(c_96037,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_96036,c_72753]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET724+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n004.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 11:46:35 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 33.82/7.30 % SZS status Started for theBenchmark.p
% 33.82/7.30 % SZS status Theorem for theBenchmark.p
% 33.82/7.30
% 33.82/7.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 33.82/7.30
% 33.82/7.30 % ------ iProver source info
% 33.82/7.30
% 33.82/7.30 % git: date: 2026-07-19 20:42:38 +0200
% 33.82/7.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 33.82/7.30 % git: non_committed_changes: false
% 33.82/7.30
% 33.82/7.30 % ------ Parsing...
% 33.82/7.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 33.82/7.30
% 33.82/7.30 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e %
% 33.82/7.30
% 33.82/7.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 33.82/7.30
% 33.82/7.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 33.82/7.30 % ------ Proving...
% 33.82/7.30 % ------ Problem Properties
% 33.82/7.30
% 33.82/7.30 %
% 33.82/7.30 % clauses 24
% 33.82/7.30 % conjectures 2
% 33.82/7.30 % EPR 5
% 33.82/7.30 % Horn 19
% 33.82/7.30 % unary 2
% 33.82/7.30 % binary 14
% 33.82/7.30 % lits 73
% 33.82/7.30 % lits eq 5
% 33.82/7.30 % fd_pure 0
% 33.82/7.30 % fd_pseudo 0
% 33.82/7.30 % fd_cond 0
% 33.82/7.30 % fd_pseudo_cond 4
% 33.82/7.30 % AC symbols 0
% 33.82/7.30
% 33.82/7.30 % ------ Schedule dynamic 5 is on
% 33.82/7.30
% 33.82/7.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 33.82/7.30
% 33.82/7.30
% 33.82/7.30 % ------
% 33.82/7.30 % Current options:
% 33.82/7.30 % ------
% 33.82/7.30
% 33.82/7.30
% 33.82/7.30 %
% 33.82/7.30
% 33.82/7.30 % ------ Proving...
% 33.82/7.30 %
% 33.82/7.30
% 33.82/7.30 % SZS status Theorem for theBenchmark.p
% 33.82/7.30
% 33.82/7.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 34.13/7.30
% 34.13/7.30
%------------------------------------------------------------------------------