%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET709+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 : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:47:51 PM UTC 2026
% Result : Theorem 46.92s 12.38s
% Output : CNFRefutation 46.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 4
% Syntax : Number of formulae : 169 ( 18 unt; 1 def)
% Number of atoms : 950 ( 51 equ)
% Maximal formula atoms : 14 ( 5 avg)
% Number of connectives : 977 ( 428 ~; 457 |; 74 &)
% ( 9 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 avg)
% Maximal term depth : 5 ( 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 : 9 ( 9 usr; 5 con; 0-5 aty)
% Number of variables : 565 ( 0 sgn 533 !; 32 ?; 331 :)
% 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(f29,conjecture,
! [X0,X1,X2,X3,X4] :
( ( maps(X1,X3,X4)
& maps(X0,X2,X3) )
=> maps(compose_function(X1,X0,X2,X3,X4),X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thII01) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( ( maps(X1,X3,X4)
& maps(X0,X2,X3) )
=> maps(compose_function(X1,X0,X2,X3,X4),X2,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,X3,X4] :
( maps(X1,X3,X4)
& maps(X0,X2,X3)
& ~ maps(compose_function(X1,X0,X2,X3,X4),X2,X4) ),
inference(ennf_transformation,[],[f30]) ).
fof(f33,plain,
? [X0,X1,X2,X3,X4] :
( maps(X1,X3,X4)
& maps(X0,X2,X3)
& ~ maps(compose_function(X1,X0,X2,X3,X4),X2,X4) ),
inference(flattening,[],[f32]) ).
fof(f34,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,[],[f31]) ).
fof(f35,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,[],[f34]) ).
fof(f36,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(f37,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,[],[f36]) ).
fof(f40,plain,
( maps(sK2,sK4,sK5)
& maps(sK1,sK3,sK4)
& ~ maps(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3),skolemize(X3,sK4),skolemize(X4,sK5)],[f33]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ( ~ maps(X0,X1,X2)
| ( sP0(X0,X1,X2)
& ! [X3] :
( ~ member(X3,X1)
| ? [X4] :
( apply(X0,X3,X4)
& member(X4,X2) ) ) ) )
& ( ~ sP0(X0,X1,X2)
| ? [X3] :
( member(X3,X1)
& ! [X4] :
( ~ apply(X0,X3,X4)
| ~ member(X4,X2) ) )
| maps(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f39]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ( ~ maps(X0,X1,X2)
| ( sP0(X0,X1,X2)
& ! [X3] :
( ~ member(X3,X1)
| ? [X4] :
( apply(X0,X3,X4)
& member(X4,X2) ) ) ) )
& ( ~ sP0(X0,X1,X2)
| ? [X3] :
( member(X3,X1)
& ! [X4] :
( ~ apply(X0,X3,X4)
| ~ member(X4,X2) ) )
| maps(X0,X1,X2) ) ),
inference(flattening,[],[f44]) ).
fof(f46,plain,
! [X0,X1,X2] :
( ( ~ maps(X0,X1,X2)
| ( sP0(X0,X1,X2)
& ! [X5] :
( ~ member(X5,X1)
| ? [X6] :
( apply(X0,X5,X6)
& member(X6,X2) ) ) ) )
& ( ~ sP0(X0,X1,X2)
| ? [X3] :
( member(X3,X1)
& ! [X4] :
( ~ apply(X0,X3,X4)
| ~ member(X4,X2) ) )
| maps(X0,X1,X2) ) ),
inference(rectify,[],[f45]) ).
fof(f47,plain,
! [X0,X1,X2] :
( ( ~ maps(X0,X1,X2)
| ( sP0(X0,X1,X2)
& ! [X5] :
( ~ member(X5,X1)
| ( apply(X0,X5,sK10(X0,X2,X5))
& member(sK10(X0,X2,X5),X2) ) ) ) )
& ( ~ sP0(X0,X1,X2)
| ( member(sK9(X0,X1,X2),X1)
& ! [X4] :
( ~ apply(X0,sK9(X0,X1,X2),X4)
| ~ member(X4,X2) ) )
| maps(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10]),skolemize(X3,sK9(X0,X1,X2)),skolemize(X6,sK10(X0,X2,X5))],[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,[],[f37]) ).
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,sK11(X0,X1,X3,X5,X6),X6)
& apply(X1,X5,sK11(X0,X1,X3,X5,X6))
& member(sK11(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,[sK11]),skolemize(X8,sK11(X0,X1,X3,X5,X6))],[f49]) ).
fof(f51,plain,
maps(sK2,sK4,sK5),
inference(cnf_transformation,[],[f40]) ).
fof(f52,plain,
maps(sK1,sK3,sK4),
inference(cnf_transformation,[],[f40]) ).
fof(f53,plain,
~ maps(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),
inference(cnf_transformation,[],[f40]) ).
fof(f61,plain,
! [X2,X0,X1] :
( ~ maps(X0,X1,X2)
| sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f47]) ).
fof(f62,plain,
! [X2,X0,X1,X5] :
( ~ maps(X0,X1,X2)
| ~ member(X5,X1)
| apply(X0,X5,sK10(X0,X2,X5)) ),
inference(cnf_transformation,[],[f47]) ).
fof(f63,plain,
! [X2,X0,X1,X5] :
( ~ maps(X0,X1,X2)
| ~ member(X5,X1)
| member(sK10(X0,X2,X5),X2) ),
inference(cnf_transformation,[],[f47]) ).
fof(f64,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1,X2)
| member(sK9(X0,X1,X2),X1)
| maps(X0,X1,X2) ),
inference(cnf_transformation,[],[f47]) ).
fof(f65,plain,
! [X2,X0,X1,X4] :
( ~ sP0(X0,X1,X2)
| ~ apply(X0,sK9(X0,X1,X2),X4)
| ~ member(X4,X2)
| maps(X0,X1,X2) ),
inference(cnf_transformation,[],[f47]) ).
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,sK11(X0,X1,X3,X5,X6),X6) ),
inference(cnf_transformation,[],[f50]) ).
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,sK11(X0,X1,X3,X5,X6)) ),
inference(cnf_transformation,[],[f50]) ).
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(sK11(X0,X1,X3,X5,X6),X3) ),
inference(cnf_transformation,[],[f50]) ).
fof(f69,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]) ).
tcf(c_49,negated_conjecture,
~ maps(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),
inference(cnf_transformation,[],[f53]) ).
tcf(c_50,negated_conjecture,
maps(sK1,sK3,sK4),
inference(cnf_transformation,[],[f52]) ).
tcf(c_51,negated_conjecture,
maps(sK2,sK4,sK5),
inference(cnf_transformation,[],[f51]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( maps(X0,X1,X2)
| ~ member(X3,X2)
| ~ sP0(X0,X1,X2)
| ~ apply(X0,sK9(X0,X1,X2),X3) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( maps(X0,X1,X2)
| member(sK9(X0,X1,X2),X1)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK10(X0,X2,X3),X2)
| ~ member(X3,X1)
| ~ maps(X0,X1,X2) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,X3,sK10(X0,X2,X3))
| ~ member(X3,X1)
| ~ maps(X0,X1,X2) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X0,X1,X2)
| ~ maps(X0,X1,X2) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( apply(compose_function(X0,X3,X7,X5,X6),X4,X2)
| ~ member(X4,X7)
| ~ member(X2,X6)
| ~ member(X1,X5)
| ~ apply(X3,X4,X1)
| ~ apply(X0,X1,X2) ),
inference(cnf_transformation,[],[f69]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( member(sK11(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_66,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( apply(X1,X5,sK11(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_67,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( apply(X0,sK11(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_427,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK10(X0,X2,X3),X2)
| ~ member(X3,X1)
| ( X2 != sK4 )
| ( X1 != sK3 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_61]) ).
tcf(c_428,plain,
! [X0: $i] :
( member(sK10(sK1,sK4,X0),sK4)
| ~ member(X0,sK3) ),
inference(unflattening,[status(thm)],[c_427]) ).
tcf(c_450,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK10(X0,X2,X3),X2)
| ~ member(X3,X1)
| ( X2 != sK5 )
| ( X1 != sK4 )
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_61]) ).
tcf(c_451,plain,
! [X0: $i] :
( member(sK10(sK2,sK5,X0),sK5)
| ~ member(X0,sK4) ),
inference(unflattening,[status(thm)],[c_450]) ).
tcf(c_1249,plain,
sP0(sK1,sK3,sK4),
inference(superposition,[status(thm)],[c_50,c_63]) ).
tcf(c_1250,plain,
sP0(sK2,sK4,sK5),
inference(superposition,[status(thm)],[c_51,c_63]) ).
tcf(c_1295,plain,
! [X0: $i] :
( member(sK10(sK1,sK4,X0),sK4)
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_50,c_61]) ).
tcf(c_1296,plain,
! [X0: $i] :
( member(sK10(sK2,sK5,X0),sK5)
| ~ member(X0,sK4) ),
inference(superposition,[status(thm)],[c_51,c_61]) ).
tcf(c_1315,plain,
! [X0: $i] :
( apply(sK1,X0,sK10(sK1,sK4,X0))
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_50,c_62]) ).
tcf(c_1316,plain,
! [X0: $i] :
( apply(sK2,X0,sK10(sK2,sK5,X0))
| ~ member(X0,sK4) ),
inference(superposition,[status(thm)],[c_51,c_62]) ).
tcf(c_1483,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( apply(compose_function(sK2,X2,X5,X4,X1),X3,sK10(sK2,sK5,X0))
| ~ member(X0,sK4)
| ~ member(X3,X5)
| ~ member(X0,X4)
| ~ apply(X2,X3,X0)
| ~ member(sK10(sK2,sK5,X0),X1) ),
inference(superposition,[status(thm)],[c_1316,c_64]) ).
tcf(c_1730,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( maps(compose_function(sK2,X0,X1,X2,X3),X4,X5)
| ~ member(X6,sK4)
| ~ member(X6,X2)
| ~ member(sK10(sK2,sK5,X6),X5)
| ~ member(sK10(sK2,sK5,X6),X3)
| ~ sP0(compose_function(sK2,X0,X1,X2,X3),X4,X5)
| ~ member(sK9(compose_function(sK2,X0,X1,X2,X3),X4,X5),X1)
| ~ apply(X0,sK9(compose_function(sK2,X0,X1,X2,X3),X4,X5),X6) ),
inference(superposition,[status(thm)],[c_1483,c_59]) ).
tcf(c_1733,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( apply(X2,X3,sK11(sK2,X2,X4,X3,sK10(sK2,sK5,X0)))
| ~ member(X0,sK4)
| ~ member(X3,X5)
| ~ member(X0,X4)
| ~ apply(X2,X3,X0)
| ~ member(sK10(sK2,sK5,X0),X1) ),
inference(superposition,[status(thm)],[c_1483,c_66]) ).
tcf(c_1734,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( member(sK11(sK2,X2,X4,X3,sK10(sK2,sK5,X0)),X4)
| ~ member(X0,sK4)
| ~ member(X3,X5)
| ~ member(X0,X4)
| ~ apply(X2,X3,X0)
| ~ member(sK10(sK2,sK5,X0),X1) ),
inference(superposition,[status(thm)],[c_1483,c_65]) ).
tcf(c_2072,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(sK11(sK2,X0,X3,X1,sK10(sK2,sK5,X2)),X3)
| ~ member(X2,sK4)
| ~ member(X2,X3)
| ~ member(X1,X4)
| ~ apply(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_1296,c_1734]) ).
tcf(c_2532,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apply(X0,X1,sK11(sK2,X0,X3,X1,sK10(sK2,sK5,X2)))
| ~ member(X2,sK4)
| ~ member(X2,X3)
| ~ member(X1,X4)
| ~ apply(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_1296,c_1733]) ).
tcf(c_2804,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( member(sK11(X0,X1,X3,sK6(X5,X2,X6),X7),X3)
| ~ member(X7,X4)
| ~ member(sK6(X5,X2,X6),X2)
| ~ apply(compose_function(X0,X1,X2,X3,X4),sK6(X5,X2,X6),X7) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_2808,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apply(X3,sK6(X0,X1,X2),sK10(X3,X4,sK6(X0,X1,X2)))
| ~ maps(X3,X1,X4)
| ~ member(sK6(X0,X1,X2),X1) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_2809,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(sK10(X3,X4,sK6(X0,X1,X2)),X4)
| ~ maps(X3,X1,X4)
| ~ member(sK6(X0,X1,X2),X1) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_4491,plain,
! [X0: $i,X1: $i] :
( member(sK10(sK1,sK4,sK6(X0,sK3,X1)),sK4)
| ~ maps(sK1,sK3,sK4)
| ~ member(sK6(X0,sK3,X1),sK3) ),
inference(instantiation,[status(thm)],[c_2809]) ).
tcf(c_4702,plain,
! [X0: $i,X1: $i] :
( apply(sK1,sK6(X0,sK3,X1),sK10(sK1,sK4,sK6(X0,sK3,X1)))
| ~ maps(sK1,sK3,sK4)
| ~ member(sK6(X0,sK3,X1),sK3) ),
inference(instantiation,[status(thm)],[c_2808]) ).
tcf(c_4969,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
( member(sK11(X0,X1,X3,sK6(X5,X2,X6),sK7(X7,X8,X4)),X3)
| ~ member(sK6(X5,X2,X6),X2)
| ~ member(sK7(X7,X8,X4),X4)
| ~ apply(compose_function(X0,X1,X2,X3,X4),sK6(X5,X2,X6),sK7(X7,X8,X4)) ),
inference(instantiation,[status(thm)],[c_2804]) ).
tcf(c_4971,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
( member(sK11(X0,X1,X3,sK6(X5,X2,X6),sK8(X7,X8,X4)),X3)
| ~ member(sK6(X5,X2,X6),X2)
| ~ member(sK8(X7,X8,X4),X4)
| ~ apply(compose_function(X0,X1,X2,X3,X4),sK6(X5,X2,X6),sK8(X7,X8,X4)) ),
inference(instantiation,[status(thm)],[c_2804]) ).
tcf(c_7114,plain,
( member(sK10(sK1,sK4,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)),sK4)
| ~ maps(sK1,sK3,sK4)
| ~ member(sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK3) ),
inference(instantiation,[status(thm)],[c_4491]) ).
tcf(c_7115,plain,
( apply(sK1,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK10(sK1,sK4,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)))
| ~ maps(sK1,sK3,sK4)
| ~ member(sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK3) ),
inference(instantiation,[status(thm)],[c_4702]) ).
tcf(c_19537,plain,
! [X0: $i] :
( member(sK10(sK1,sK4,X0),sK4)
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_50,c_61]) ).
tcf(c_19538,plain,
! [X0: $i] :
( member(sK10(sK2,sK5,X0),sK5)
| ~ member(X0,sK4) ),
inference(superposition,[status(thm)],[c_51,c_61]) ).
tcf(c_19549,plain,
! [X0: $i] :
( apply(sK1,X0,sK10(sK1,sK4,X0))
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_50,c_62]) ).
tcf(c_19550,plain,
! [X0: $i] :
( apply(sK2,X0,sK10(sK2,sK5,X0))
| ~ member(X0,sK4) ),
inference(superposition,[status(thm)],[c_51,c_62]) ).
tcf(c_19790,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( apply(compose_function(sK2,X2,X5,X4,X1),X3,sK10(sK2,sK5,X0))
| ~ member(X0,sK4)
| ~ member(X3,X5)
| ~ member(X0,X4)
| ~ apply(X2,X3,X0)
| ~ member(sK10(sK2,sK5,X0),X1) ),
inference(superposition,[status(thm)],[c_19550,c_64]) ).
tcf(c_19956,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( maps(compose_function(sK2,X0,X1,X2,X3),X4,X5)
| ~ member(X6,sK4)
| ~ member(X6,X2)
| ~ member(sK10(sK2,sK5,X6),X5)
| ~ member(sK10(sK2,sK5,X6),X3)
| ~ sP0(compose_function(sK2,X0,X1,X2,X3),X4,X5)
| ~ member(sK9(compose_function(sK2,X0,X1,X2,X3),X4,X5),X1)
| ~ apply(X0,sK9(compose_function(sK2,X0,X1,X2,X3),X4,X5),X6) ),
inference(superposition,[status(thm)],[c_19790,c_59]) ).
tcf(c_20640,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( maps(compose_function(sK2,sK1,X0,X1,X2),X3,X4)
| ~ sP0(compose_function(sK2,sK1,X0,X1,X2),X3,X4)
| ~ member(sK9(compose_function(sK2,sK1,X0,X1,X2),X3,X4),sK3)
| ~ member(sK9(compose_function(sK2,sK1,X0,X1,X2),X3,X4),X0)
| ~ member(sK10(sK1,sK4,sK9(compose_function(sK2,sK1,X0,X1,X2),X3,X4)),sK4)
| ~ member(sK10(sK1,sK4,sK9(compose_function(sK2,sK1,X0,X1,X2),X3,X4)),X1)
| ~ member(sK10(sK2,sK5,sK10(sK1,sK4,sK9(compose_function(sK2,sK1,X0,X1,X2),X3,X4))),X4)
| ~ member(sK10(sK2,sK5,sK10(sK1,sK4,sK9(compose_function(sK2,sK1,X0,X1,X2),X3,X4))),X2) ),
inference(superposition,[status(thm)],[c_19549,c_19956]) ).
tcf(c_21453,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( member(sK11(X0,X1,X3,sK6(X4,X2,X5),sK7(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)),X3)
| ~ member(sK6(X4,X2,X5),X2)
| ~ member(sK7(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK5)
| ~ apply(compose_function(X0,X1,X2,X3,sK5),sK6(X4,X2,X5),sK7(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)) ),
inference(instantiation,[status(thm)],[c_4969]) ).
tcf(c_21472,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( member(sK11(X0,X1,X3,sK6(X4,X2,X5),sK8(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)),X3)
| ~ member(sK6(X4,X2,X5),X2)
| ~ member(sK8(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK5)
| ~ apply(compose_function(X0,X1,X2,X3,sK5),sK6(X4,X2,X5),sK8(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)) ),
inference(instantiation,[status(thm)],[c_4971]) ).
tcf(c_22196,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( maps(compose_function(sK2,sK1,X0,X1,X2),X3,X4)
| ~ sP0(compose_function(sK2,sK1,X0,X1,X2),X3,X4)
| ~ member(sK9(compose_function(sK2,sK1,X0,X1,X2),X3,X4),sK3)
| ~ member(sK9(compose_function(sK2,sK1,X0,X1,X2),X3,X4),X0)
| ~ member(sK10(sK1,sK4,sK9(compose_function(sK2,sK1,X0,X1,X2),X3,X4)),X1)
| ~ member(sK10(sK2,sK5,sK10(sK1,sK4,sK9(compose_function(sK2,sK1,X0,X1,X2),X3,X4))),X4)
| ~ member(sK10(sK2,sK5,sK10(sK1,sK4,sK9(compose_function(sK2,sK1,X0,X1,X2),X3,X4))),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20640,c_19537]) ).
tcf(c_22218,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( maps(compose_function(sK2,sK1,X0,X1,sK5),X2,X3)
| ~ sP0(compose_function(sK2,sK1,X0,X1,sK5),X2,X3)
| ~ member(sK9(compose_function(sK2,sK1,X0,X1,sK5),X2,X3),sK3)
| ~ member(sK9(compose_function(sK2,sK1,X0,X1,sK5),X2,X3),X0)
| ~ member(sK10(sK1,sK4,sK9(compose_function(sK2,sK1,X0,X1,sK5),X2,X3)),sK4)
| ~ member(sK10(sK1,sK4,sK9(compose_function(sK2,sK1,X0,X1,sK5),X2,X3)),X1)
| ~ member(sK10(sK2,sK5,sK10(sK1,sK4,sK9(compose_function(sK2,sK1,X0,X1,sK5),X2,X3))),X3) ),
inference(superposition,[status(thm)],[c_19538,c_22196]) ).
tcf(c_22234,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( maps(compose_function(sK2,sK1,X0,X1,sK5),X2,X3)
| ~ sP0(compose_function(sK2,sK1,X0,X1,sK5),X2,X3)
| ~ member(sK9(compose_function(sK2,sK1,X0,X1,sK5),X2,X3),sK3)
| ~ member(sK9(compose_function(sK2,sK1,X0,X1,sK5),X2,X3),X0)
| ~ member(sK10(sK1,sK4,sK9(compose_function(sK2,sK1,X0,X1,sK5),X2,X3)),X1)
| ~ member(sK10(sK2,sK5,sK10(sK1,sK4,sK9(compose_function(sK2,sK1,X0,X1,sK5),X2,X3))),X3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22218,c_19537]) ).
tcf(c_22253,plain,
! [X0: $i,X1: $i,X2: $i] :
( maps(compose_function(sK2,sK1,X0,X1,sK5),X2,sK5)
| ~ sP0(compose_function(sK2,sK1,X0,X1,sK5),X2,sK5)
| ~ member(sK9(compose_function(sK2,sK1,X0,X1,sK5),X2,sK5),sK3)
| ~ member(sK9(compose_function(sK2,sK1,X0,X1,sK5),X2,sK5),X0)
| ~ member(sK10(sK1,sK4,sK9(compose_function(sK2,sK1,X0,X1,sK5),X2,sK5)),sK4)
| ~ member(sK10(sK1,sK4,sK9(compose_function(sK2,sK1,X0,X1,sK5),X2,sK5)),X1) ),
inference(superposition,[status(thm)],[c_19538,c_22234]) ).
tcf(c_24376,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( maps(compose_function(sK2,sK1,X0,X1,X2),X3,X4)
| ~ sP0(compose_function(sK2,sK1,X0,X1,X2),X3,X4)
| ~ member(sK9(compose_function(sK2,sK1,X0,X1,X2),X3,X4),sK3)
| ~ member(sK9(compose_function(sK2,sK1,X0,X1,X2),X3,X4),X0)
| ~ member(sK10(sK1,sK4,sK9(compose_function(sK2,sK1,X0,X1,X2),X3,X4)),sK4)
| ~ member(sK10(sK1,sK4,sK9(compose_function(sK2,sK1,X0,X1,X2),X3,X4)),X1)
| ~ member(sK10(sK2,sK5,sK10(sK1,sK4,sK9(compose_function(sK2,sK1,X0,X1,X2),X3,X4))),X4)
| ~ member(sK10(sK2,sK5,sK10(sK1,sK4,sK9(compose_function(sK2,sK1,X0,X1,X2),X3,X4))),X2) ),
inference(superposition,[status(thm)],[c_1315,c_1730]) ).
tcf(c_25620,plain,
! [X0: $i,X1: $i,X2: $i] :
( maps(compose_function(sK2,sK1,X0,X1,sK5),X2,sK5)
| ~ sP0(compose_function(sK2,sK1,X0,X1,sK5),X2,sK5)
| ~ member(sK9(compose_function(sK2,sK1,X0,X1,sK5),X2,sK5),sK3)
| ~ member(sK9(compose_function(sK2,sK1,X0,X1,sK5),X2,sK5),X0)
| ~ member(sK10(sK1,sK4,sK9(compose_function(sK2,sK1,X0,X1,sK5),X2,sK5)),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22253,c_19537]) ).
tcf(c_25636,plain,
! [X0: $i,X1: $i] :
( maps(compose_function(sK2,sK1,X0,sK4,sK5),X1,sK5)
| ~ sP0(compose_function(sK2,sK1,X0,sK4,sK5),X1,sK5)
| ~ member(sK9(compose_function(sK2,sK1,X0,sK4,sK5),X1,sK5),sK3)
| ~ member(sK9(compose_function(sK2,sK1,X0,sK4,sK5),X1,sK5),X0) ),
inference(superposition,[status(thm)],[c_19537,c_25620]) ).
tcf(c_25650,plain,
! [X0: $i] :
( maps(compose_function(sK2,sK1,X0,sK4,sK5),sK3,sK5)
| ~ sP0(compose_function(sK2,sK1,X0,sK4,sK5),sK3,sK5)
| ~ member(sK9(compose_function(sK2,sK1,X0,sK4,sK5),sK3,sK5),X0) ),
inference(superposition,[status(thm)],[c_60,c_25636]) ).
tcf(c_25903,plain,
( maps(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)
| ~ sP0(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5) ),
inference(superposition,[status(thm)],[c_60,c_25650]) ).
tcf(c_25904,plain,
~ sP0(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),
inference(forward_subsumption_resolution,[status(thm)],[c_25903,c_49]) ).
tcf(c_26693,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( maps(compose_function(sK2,sK1,X0,X1,X2),X3,X4)
| ~ sP0(compose_function(sK2,sK1,X0,X1,X2),X3,X4)
| ~ member(sK9(compose_function(sK2,sK1,X0,X1,X2),X3,X4),sK3)
| ~ member(sK9(compose_function(sK2,sK1,X0,X1,X2),X3,X4),X0)
| ~ member(sK10(sK1,sK4,sK9(compose_function(sK2,sK1,X0,X1,X2),X3,X4)),X1)
| ~ member(sK10(sK2,sK5,sK10(sK1,sK4,sK9(compose_function(sK2,sK1,X0,X1,X2),X3,X4))),X4)
| ~ member(sK10(sK2,sK5,sK10(sK1,sK4,sK9(compose_function(sK2,sK1,X0,X1,X2),X3,X4))),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_24376,c_1295]) ).
tcf(c_26715,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( maps(compose_function(sK2,sK1,X0,X1,sK5),X2,X3)
| ~ sP0(compose_function(sK2,sK1,X0,X1,sK5),X2,X3)
| ~ member(sK9(compose_function(sK2,sK1,X0,X1,sK5),X2,X3),sK3)
| ~ member(sK9(compose_function(sK2,sK1,X0,X1,sK5),X2,X3),X0)
| ~ member(sK10(sK1,sK4,sK9(compose_function(sK2,sK1,X0,X1,sK5),X2,X3)),sK4)
| ~ member(sK10(sK1,sK4,sK9(compose_function(sK2,sK1,X0,X1,sK5),X2,X3)),X1)
| ~ member(sK10(sK2,sK5,sK10(sK1,sK4,sK9(compose_function(sK2,sK1,X0,X1,sK5),X2,X3))),X3) ),
inference(superposition,[status(thm)],[c_1296,c_26693]) ).
tcf(c_26730,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( maps(compose_function(sK2,sK1,X0,X1,sK5),X2,X3)
| ~ sP0(compose_function(sK2,sK1,X0,X1,sK5),X2,X3)
| ~ member(sK9(compose_function(sK2,sK1,X0,X1,sK5),X2,X3),sK3)
| ~ member(sK9(compose_function(sK2,sK1,X0,X1,sK5),X2,X3),X0)
| ~ member(sK10(sK1,sK4,sK9(compose_function(sK2,sK1,X0,X1,sK5),X2,X3)),X1)
| ~ member(sK10(sK2,sK5,sK10(sK1,sK4,sK9(compose_function(sK2,sK1,X0,X1,sK5),X2,X3))),X3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26715,c_1295]) ).
tcf(c_26749,plain,
! [X0: $i,X1: $i,X2: $i] :
( maps(compose_function(sK2,sK1,X0,X1,sK5),X2,sK5)
| ~ sP0(compose_function(sK2,sK1,X0,X1,sK5),X2,sK5)
| ~ member(sK9(compose_function(sK2,sK1,X0,X1,sK5),X2,sK5),sK3)
| ~ member(sK9(compose_function(sK2,sK1,X0,X1,sK5),X2,sK5),X0)
| ~ member(sK10(sK1,sK4,sK9(compose_function(sK2,sK1,X0,X1,sK5),X2,sK5)),sK4)
| ~ member(sK10(sK1,sK4,sK9(compose_function(sK2,sK1,X0,X1,sK5),X2,sK5)),X1) ),
inference(superposition,[status(thm)],[c_1296,c_26730]) ).
tcf(c_26762,plain,
! [X0: $i,X1: $i,X2: $i] :
( maps(compose_function(sK2,sK1,X0,X1,sK5),X2,sK5)
| ~ sP0(compose_function(sK2,sK1,X0,X1,sK5),X2,sK5)
| ~ member(sK9(compose_function(sK2,sK1,X0,X1,sK5),X2,sK5),sK3)
| ~ member(sK9(compose_function(sK2,sK1,X0,X1,sK5),X2,sK5),X0)
| ~ member(sK10(sK1,sK4,sK9(compose_function(sK2,sK1,X0,X1,sK5),X2,sK5)),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26749,c_1295]) ).
tcf(c_26778,plain,
! [X0: $i,X1: $i] :
( maps(compose_function(sK2,sK1,X0,sK4,sK5),X1,sK5)
| ~ sP0(compose_function(sK2,sK1,X0,sK4,sK5),X1,sK5)
| ~ member(sK9(compose_function(sK2,sK1,X0,sK4,sK5),X1,sK5),sK3)
| ~ member(sK9(compose_function(sK2,sK1,X0,sK4,sK5),X1,sK5),X0) ),
inference(superposition,[status(thm)],[c_1295,c_26762]) ).
tcf(c_26791,plain,
! [X0: $i] :
( maps(compose_function(sK2,sK1,X0,sK4,sK5),sK3,sK5)
| ~ sP0(compose_function(sK2,sK1,X0,sK4,sK5),sK3,sK5)
| ~ member(sK9(compose_function(sK2,sK1,X0,sK4,sK5),sK3,sK5),X0) ),
inference(superposition,[status(thm)],[c_60,c_26778]) ).
tcf(c_26982,plain,
( maps(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)
| ~ sP0(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5) ),
inference(superposition,[status(thm)],[c_60,c_26791]) ).
tcf(c_26983,plain,
~ sP0(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),
inference(forward_subsumption_resolution,[status(thm)],[c_26982,c_49]) ).
tcf(c_35608,plain,
( member(sK11(sK2,sK1,sK4,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK7(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)),sK4)
| ~ member(sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK3)
| ~ member(sK7(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK5)
| ~ apply(compose_function(sK2,sK1,sK3,sK4,sK5),sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK7(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)) ),
inference(instantiation,[status(thm)],[c_21453]) ).
tcf(c_35611,plain,
( member(sK11(sK2,sK1,sK4,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK8(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)),sK4)
| ~ member(sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK3)
| ~ member(sK8(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK5)
| ~ apply(compose_function(sK2,sK1,sK3,sK4,sK5),sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK8(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)) ),
inference(instantiation,[status(thm)],[c_21472]) ).
fof(f38,definition,
! [X0,X1,X2] :
( sP0(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 ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f39,plain,
! [X0,X1,X2] :
( maps(X0,X1,X2)
<=> ( sP0(X0,X1,X2)
& ! [X3] :
( ~ member(X3,X1)
| ? [X4] :
( apply(X0,X3,X4)
& member(X4,X2) ) ) ) ),
inference(definition_folding,[],[f35,f38]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ( ~ sP0(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 ) )
& ( ? [X5,X6,X7] :
( member(X7,X2)
& member(X6,X2)
& member(X5,X1)
& apply(X0,X5,X7)
& apply(X0,X5,X6)
& X6 != X7 )
| sP0(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f38]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ( ~ sP0(X0,X1,X2)
| ! [X6,X7,X8] :
( ~ member(X8,X2)
| ~ member(X7,X2)
| ~ member(X6,X1)
| ~ apply(X0,X6,X8)
| ~ apply(X0,X6,X7)
| X7 = X8 ) )
& ( ? [X3,X4,X5] :
( member(X5,X2)
& member(X4,X2)
& member(X3,X1)
& apply(X0,X3,X5)
& apply(X0,X3,X4)
& X4 != X5 )
| sP0(X0,X1,X2) ) ),
inference(rectify,[],[f41]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ( ~ sP0(X0,X1,X2)
| ! [X6,X7,X8] :
( ~ member(X8,X2)
| ~ member(X7,X2)
| ~ member(X6,X1)
| ~ apply(X0,X6,X8)
| ~ apply(X0,X6,X7)
| X7 = X8 ) )
& ( ( member(sK8(X0,X1,X2),X2)
& member(sK7(X0,X1,X2),X2)
& member(sK6(X0,X1,X2),X1)
& apply(X0,sK6(X0,X1,X2),sK8(X0,X1,X2))
& apply(X0,sK6(X0,X1,X2),sK7(X0,X1,X2))
& sK7(X0,X1,X2) != sK8(X0,X1,X2) )
| sP0(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8]),skolemize(X3,sK6(X0,X1,X2)),skolemize(X4,sK7(X0,X1,X2)),skolemize(X5,sK8(X0,X1,X2))],[f42]) ).
fof(f54,plain,
! [X2,X0,X1,X8,X6,X7] :
( ~ sP0(X0,X1,X2)
| ~ member(X8,X2)
| ~ member(X7,X2)
| ~ member(X6,X1)
| ~ apply(X0,X6,X8)
| ~ apply(X0,X6,X7)
| X7 = X8 ),
inference(cnf_transformation,[],[f43]) ).
fof(f55,plain,
! [X2,X0,X1] :
( member(sK8(X0,X1,X2),X2)
| sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f43]) ).
fof(f56,plain,
! [X2,X0,X1] :
( member(sK7(X0,X1,X2),X2)
| sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f43]) ).
fof(f57,plain,
! [X2,X0,X1] :
( member(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f43]) ).
fof(f58,plain,
! [X2,X0,X1] :
( apply(X0,sK6(X0,X1,X2),sK8(X0,X1,X2))
| sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f43]) ).
fof(f59,plain,
! [X2,X0,X1] :
( apply(X0,sK6(X0,X1,X2),sK7(X0,X1,X2))
| sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f43]) ).
fof(f60,plain,
! [X2,X0,X1] :
( sK7(X0,X1,X2) != sK8(X0,X1,X2)
| sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X0,X1,X2)
| ( sK7(X0,X1,X2) != sK8(X0,X1,X2) ) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X0,X1,X2)
| apply(X0,sK6(X0,X1,X2),sK7(X0,X1,X2)) ),
inference(cnf_transformation,[],[f59]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X0,X1,X2)
| apply(X0,sK6(X0,X1,X2),sK8(X0,X1,X2)) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X0,X1,X2)
| member(sK6(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X0,X1,X2)
| member(sK7(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X0,X1,X2)
| member(sK8(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_58,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)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_1389,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( sP0(compose_function(X0,X1,X2,X3,X4),X5,X6)
| member(sK11(X0,X1,X3,sK6(compose_function(X0,X1,X2,X3,X4),X5,X6),sK8(compose_function(X0,X1,X2,X3,X4),X5,X6)),X3)
| ~ member(sK6(compose_function(X0,X1,X2,X3,X4),X5,X6),X2)
| ~ member(sK8(compose_function(X0,X1,X2,X3,X4),X5,X6),X4) ),
inference(superposition,[status(thm)],[c_54,c_65]) ).
tcf(c_1414,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ member(X2,sK4)
| ~ member(X1,sK4)
| ~ member(X0,sK3)
| ~ apply(sK1,X0,X2)
| ~ apply(sK1,X0,X1) ),
inference(superposition,[status(thm)],[c_1249,c_58]) ).
tcf(c_1415,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(superposition,[status(thm)],[c_1250,c_58]) ).
tcf(c_1436,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( sP0(compose_function(X0,X1,X2,X3,X4),X5,X6)
| apply(X1,sK6(compose_function(X0,X1,X2,X3,X4),X5,X6),sK11(X0,X1,X3,sK6(compose_function(X0,X1,X2,X3,X4),X5,X6),sK7(compose_function(X0,X1,X2,X3,X4),X5,X6)))
| ~ member(sK6(compose_function(X0,X1,X2,X3,X4),X5,X6),X2)
| ~ member(sK7(compose_function(X0,X1,X2,X3,X4),X5,X6),X4) ),
inference(superposition,[status(thm)],[c_53,c_66]) ).
tcf(c_1437,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( sP0(compose_function(X0,X1,X2,X3,X4),X5,X6)
| apply(X1,sK6(compose_function(X0,X1,X2,X3,X4),X5,X6),sK11(X0,X1,X3,sK6(compose_function(X0,X1,X2,X3,X4),X5,X6),sK8(compose_function(X0,X1,X2,X3,X4),X5,X6)))
| ~ member(sK6(compose_function(X0,X1,X2,X3,X4),X5,X6),X2)
| ~ member(sK8(compose_function(X0,X1,X2,X3,X4),X5,X6),X4) ),
inference(superposition,[status(thm)],[c_54,c_66]) ).
tcf(c_1456,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( sP0(compose_function(X0,X1,X2,X3,X4),X5,X6)
| apply(X0,sK11(X0,X1,X3,sK6(compose_function(X0,X1,X2,X3,X4),X5,X6),sK7(compose_function(X0,X1,X2,X3,X4),X5,X6)),sK7(compose_function(X0,X1,X2,X3,X4),X5,X6))
| ~ member(sK6(compose_function(X0,X1,X2,X3,X4),X5,X6),X2)
| ~ member(sK7(compose_function(X0,X1,X2,X3,X4),X5,X6),X4) ),
inference(superposition,[status(thm)],[c_53,c_67]) ).
tcf(c_1457,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( sP0(compose_function(X0,X1,X2,X3,X4),X5,X6)
| apply(X0,sK11(X0,X1,X3,sK6(compose_function(X0,X1,X2,X3,X4),X5,X6),sK8(compose_function(X0,X1,X2,X3,X4),X5,X6)),sK8(compose_function(X0,X1,X2,X3,X4),X5,X6))
| ~ member(sK6(compose_function(X0,X1,X2,X3,X4),X5,X6),X2)
| ~ member(sK8(compose_function(X0,X1,X2,X3,X4),X5,X6),X4) ),
inference(superposition,[status(thm)],[c_54,c_67]) ).
tcf(c_1526,plain,
! [X0: $i,X1: $i] :
( ( sK10(sK1,sK4,X0) = X1 )
| ~ member(X1,sK4)
| ~ member(X0,sK3)
| ~ apply(sK1,X0,X1)
| ~ member(sK10(sK1,sK4,X0),sK4) ),
inference(superposition,[status(thm)],[c_1315,c_1414]) ).
tcf(c_1562,plain,
! [X0: $i,X1: $i] :
( ( sK10(sK2,sK5,X0) = X1 )
| ~ member(X1,sK5)
| ~ member(X0,sK4)
| ~ apply(sK2,X0,X1)
| ~ member(sK10(sK2,sK5,X0),sK5) ),
inference(superposition,[status(thm)],[c_1316,c_1415]) ).
tcf(c_1586,plain,
! [X0: $i,X1: $i] :
( ( sK10(sK1,sK4,X0) = X1 )
| ~ member(X1,sK4)
| ~ member(X0,sK3)
| ~ apply(sK1,X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_1526,c_428,c_1526]) ).
tcf(c_1610,plain,
( sP0(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)
| apply(compose_function(sK2,sK1,sK3,sK4,sK5),sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK8(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_1611,plain,
( sP0(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)
| apply(compose_function(sK2,sK1,sK3,sK4,sK5),sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK7(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_1612,plain,
( sP0(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)
| ( sK7(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5) != sK8(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5) ) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_1613,plain,
( sP0(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)
| member(sK8(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK5) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_1614,plain,
( sP0(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)
| member(sK7(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK5) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_1615,plain,
( sP0(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)
| member(sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK3) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_1617,plain,
! [X0: $i,X1: $i] :
( ( sK10(sK2,sK5,X0) = X1 )
| ~ member(X1,sK5)
| ~ member(X0,sK4)
| ~ apply(sK2,X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_1562,c_451,c_1562]) ).
tcf(c_2094,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sP0(X1,X2,X3)
| member(sK11(sK2,X0,X5,sK6(X1,X2,X3),sK10(sK2,sK5,X4)),X5)
| ~ member(X4,sK4)
| ~ member(X4,X5)
| ~ apply(X0,sK6(X1,X2,X3),X4) ),
inference(superposition,[status(thm)],[c_55,c_2072]) ).
tcf(c_2845,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sP0(X1,X2,X3)
| apply(X0,sK6(X1,X2,X3),sK11(sK2,X0,X5,sK6(X1,X2,X3),sK10(sK2,sK5,X4)))
| ~ member(X4,sK4)
| ~ member(X4,X5)
| ~ apply(X0,sK6(X1,X2,X3),X4) ),
inference(superposition,[status(thm)],[c_55,c_2532]) ).
tcf(c_4315,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sP0(X1,X2,X3)
| ( sK11(sK2,sK1,X0,sK6(X1,X2,X3),sK10(sK2,sK5,X4)) = sK10(sK1,sK4,sK6(X1,X2,X3)) )
| ~ member(X4,sK4)
| ~ member(X4,X0)
| ~ member(sK6(X1,X2,X3),sK3)
| ~ apply(sK1,sK6(X1,X2,X3),X4)
| ~ member(sK11(sK2,sK1,X0,sK6(X1,X2,X3),sK10(sK2,sK5,X4)),sK4) ),
inference(superposition,[status(thm)],[c_2845,c_1586]) ).
tcf(c_4316,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sP0(X1,X2,X3)
| ( sK11(sK2,sK1,X0,sK6(X1,X2,X3),sK10(sK2,sK5,X4)) = X5 )
| ~ member(X5,sK4)
| ~ member(X4,sK4)
| ~ member(X4,X0)
| ~ member(sK6(X1,X2,X3),sK3)
| ~ apply(sK1,sK6(X1,X2,X3),X5)
| ~ apply(sK1,sK6(X1,X2,X3),X4)
| ~ member(sK11(sK2,sK1,X0,sK6(X1,X2,X3),sK10(sK2,sK5,X4)),sK4) ),
inference(superposition,[status(thm)],[c_2845,c_1414]) ).
tcf(c_36038,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP0(X0,X1,X2)
| ( sK11(sK2,sK1,sK4,sK6(X0,X1,X2),sK10(sK2,sK5,X3)) = sK10(sK1,sK4,sK6(X0,X1,X2)) )
| ~ member(X3,sK4)
| ~ member(sK6(X0,X1,X2),sK3)
| ~ apply(sK1,sK6(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_2094,c_4315]) ).
tcf(c_36497,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X0,X1,X2)
| ( sK11(sK2,sK1,sK4,sK6(X0,X1,X2),sK10(sK2,sK5,sK10(sK1,sK4,sK6(X0,X1,X2)))) = sK10(sK1,sK4,sK6(X0,X1,X2)) )
| ~ member(sK6(X0,X1,X2),sK3)
| ~ member(sK10(sK1,sK4,sK6(X0,X1,X2)),sK4) ),
inference(superposition,[status(thm)],[c_1315,c_36038]) ).
tcf(c_36624,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X0,X1,X2)
| ( sK11(sK2,sK1,sK4,sK6(X0,X1,X2),sK10(sK2,sK5,sK10(sK1,sK4,sK6(X0,X1,X2)))) = sK10(sK1,sK4,sK6(X0,X1,X2)) )
| ~ member(sK6(X0,X1,X2),sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_36497,c_1295]) ).
tcf(c_36634,plain,
! [X0: $i,X1: $i] :
( sP0(X0,sK3,X1)
| ( sK11(sK2,sK1,sK4,sK6(X0,sK3,X1),sK10(sK2,sK5,sK10(sK1,sK4,sK6(X0,sK3,X1)))) = sK10(sK1,sK4,sK6(X0,sK3,X1)) ) ),
inference(superposition,[status(thm)],[c_55,c_36624]) ).
tcf(c_36643,plain,
sK11(sK2,sK1,sK4,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK10(sK2,sK5,sK10(sK1,sK4,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)))) = sK10(sK1,sK4,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)),
inference(superposition,[status(thm)],[c_36634,c_26983]) ).
tcf(c_77316,plain,
! [X0: $i] :
( sP0(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)
| ( sK11(sK2,sK1,sK4,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK10(sK2,sK5,sK10(sK1,sK4,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)))) = X0 )
| ~ member(X0,sK4)
| ~ member(sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK3)
| ~ apply(sK1,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),X0)
| ~ member(sK10(sK1,sK4,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)),sK4)
| ~ apply(sK1,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK10(sK1,sK4,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5))) ),
inference(superposition,[status(thm)],[c_36643,c_4316]) ).
tcf(c_77324,plain,
! [X0: $i] :
( sP0(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)
| ( sK10(sK1,sK4,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)) = X0 )
| ~ member(X0,sK4)
| ~ member(sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK3)
| ~ apply(sK1,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),X0)
| ~ member(sK10(sK1,sK4,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)),sK4)
| ~ apply(sK1,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK10(sK1,sK4,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5))) ),
inference(light_normalisation,[status(thm)],[c_77316,c_36643]) ).
tcf(c_77325,plain,
! [X0: $i] :
( ( sK10(sK1,sK4,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)) = X0 )
| ~ member(X0,sK4)
| ~ member(sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK3)
| ~ apply(sK1,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),X0)
| ~ member(sK10(sK1,sK4,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)),sK4)
| ~ apply(sK1,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK10(sK1,sK4,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_77324,c_26983]) ).
tcf(c_77356,plain,
! [X0: $i] :
( ( sK10(sK1,sK4,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)) = X0 )
| ~ member(X0,sK4)
| ~ apply(sK1,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),X0) ),
inference(global_subsumption_just,[status(thm)],[c_77325,c_50,c_1615,c_7114,c_7115,c_25904,c_77325]) ).
tcf(c_77366,plain,
( sP0(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)
| ( sK11(sK2,sK1,sK4,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK7(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)) = sK10(sK1,sK4,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)) )
| ~ member(sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK3)
| ~ member(sK7(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK5)
| ~ member(sK11(sK2,sK1,sK4,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK7(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)),sK4) ),
inference(superposition,[status(thm)],[c_1436,c_77356]) ).
tcf(c_77367,plain,
( sP0(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)
| ( sK11(sK2,sK1,sK4,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK8(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)) = sK10(sK1,sK4,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)) )
| ~ member(sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK3)
| ~ member(sK8(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK5)
| ~ member(sK11(sK2,sK1,sK4,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK8(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)),sK4) ),
inference(superposition,[status(thm)],[c_1437,c_77356]) ).
tcf(c_77398,plain,
( ( sK11(sK2,sK1,sK4,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK8(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)) = sK10(sK1,sK4,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)) )
| ~ member(sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK3)
| ~ member(sK8(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK5)
| ~ member(sK11(sK2,sK1,sK4,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK8(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)),sK4) ),
inference(forward_subsumption_resolution,[status(thm)],[c_77367,c_26983]) ).
tcf(c_77403,plain,
( ( sK11(sK2,sK1,sK4,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK7(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)) = sK10(sK1,sK4,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)) )
| ~ member(sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK3)
| ~ member(sK7(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK5)
| ~ member(sK11(sK2,sK1,sK4,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK7(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)),sK4) ),
inference(forward_subsumption_resolution,[status(thm)],[c_77366,c_26983]) ).
tcf(c_78852,plain,
sK11(sK2,sK1,sK4,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK8(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)) = sK10(sK1,sK4,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)),
inference(global_subsumption_just,[status(thm)],[c_77398,c_1615,c_1613,c_1610,c_25904,c_35611,c_77398]) ).
tcf(c_78854,plain,
( sP0(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)
| apply(sK2,sK10(sK1,sK4,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)),sK8(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5))
| ~ member(sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK3)
| ~ member(sK8(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK5) ),
inference(superposition,[status(thm)],[c_78852,c_1457]) ).
tcf(c_78856,plain,
( sP0(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)
| member(sK10(sK1,sK4,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)),sK4)
| ~ member(sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK3)
| ~ member(sK8(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK5) ),
inference(superposition,[status(thm)],[c_78852,c_1389]) ).
tcf(c_78859,plain,
( member(sK10(sK1,sK4,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)),sK4)
| ~ member(sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK3)
| ~ member(sK8(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK5) ),
inference(forward_subsumption_resolution,[status(thm)],[c_78856,c_26983]) ).
tcf(c_78867,plain,
( apply(sK2,sK10(sK1,sK4,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)),sK8(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5))
| ~ member(sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK3)
| ~ member(sK8(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK5) ),
inference(forward_subsumption_resolution,[status(thm)],[c_78854,c_26983]) ).
tcf(c_79036,plain,
member(sK10(sK1,sK4,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)),sK4),
inference(global_subsumption_just,[status(thm)],[c_78859,c_50,c_1615,c_7114,c_25904]) ).
tcf(c_79312,plain,
apply(sK2,sK10(sK1,sK4,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)),sK8(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)),
inference(global_subsumption_just,[status(thm)],[c_78867,c_1615,c_1613,c_25904,c_78867]) ).
tcf(c_79325,plain,
( ( sK10(sK2,sK5,sK10(sK1,sK4,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5))) = sK8(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5) )
| ~ member(sK8(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK5)
| ~ member(sK10(sK1,sK4,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)),sK4) ),
inference(superposition,[status(thm)],[c_79312,c_1617]) ).
tcf(c_79337,plain,
( ( sK10(sK2,sK5,sK10(sK1,sK4,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5))) = sK8(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5) )
| ~ member(sK8(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK5) ),
inference(forward_subsumption_resolution,[status(thm)],[c_79325,c_79036]) ).
tcf(c_79710,plain,
sK10(sK2,sK5,sK10(sK1,sK4,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5))) = sK8(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),
inference(global_subsumption_just,[status(thm)],[c_79337,c_1613,c_25904,c_79337]) ).
tcf(c_82237,plain,
sK11(sK2,sK1,sK4,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK7(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)) = sK10(sK1,sK4,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)),
inference(global_subsumption_just,[status(thm)],[c_77403,c_1615,c_1614,c_1611,c_25904,c_35608,c_77403]) ).
tcf(c_82239,plain,
( sP0(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)
| apply(sK2,sK10(sK1,sK4,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)),sK7(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5))
| ~ member(sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK3)
| ~ member(sK7(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK5) ),
inference(superposition,[status(thm)],[c_82237,c_1456]) ).
tcf(c_82244,plain,
( apply(sK2,sK10(sK1,sK4,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)),sK7(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5))
| ~ member(sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK3)
| ~ member(sK7(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK5) ),
inference(forward_subsumption_resolution,[status(thm)],[c_82239,c_26983]) ).
tcf(c_82266,plain,
apply(sK2,sK10(sK1,sK4,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)),sK7(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)),
inference(global_subsumption_just,[status(thm)],[c_82244,c_1615,c_1614,c_25904,c_82244]) ).
tcf(c_82279,plain,
( ( sK10(sK2,sK5,sK10(sK1,sK4,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5))) = sK7(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5) )
| ~ member(sK7(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK5)
| ~ member(sK10(sK1,sK4,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)),sK4) ),
inference(superposition,[status(thm)],[c_82266,c_1617]) ).
tcf(c_82291,plain,
( ( sK7(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5) = sK8(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5) )
| ~ member(sK7(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK5)
| ~ member(sK10(sK1,sK4,sK6(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5)),sK4) ),
inference(light_normalisation,[status(thm)],[c_82279,c_79710]) ).
tcf(c_82292,plain,
( ( sK7(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5) = sK8(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5) )
| ~ member(sK7(compose_function(sK2,sK1,sK3,sK4,sK5),sK3,sK5),sK5) ),
inference(forward_subsumption_resolution,[status(thm)],[c_82291,c_79036]) ).
tcf(c_82415,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_82292,c_25904,c_1612,c_1614]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET709+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/5.38 % Computer : n001.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.09/5.38 % CPULimit : 300
% 0.09/5.39 % WCLimit : 300
% 0.09/5.39 % DateTime : Thu Sep 24 11:49:43 UTC 2026
% 0.09/5.39 % CPUTime :
% 0.09/5.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/5.43 Running first-order theorem proving
% 0.15/5.43 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
% 0.15/5.44
% 0.15/5.44 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.44
% 0.15/5.44 % Detected problem language: tptp
% 0.15/5.45 % Proving...
% 46.92/12.38 % SZS status Started for theBenchmark.p
% 46.92/12.38 % SZS status Theorem for theBenchmark.p
% 46.92/12.38
% 46.92/12.38 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 46.92/12.38
% 46.92/12.38 % ------ iProver source info
% 46.92/12.38
% 46.92/12.38 % git: date: 2026-07-19 20:42:38 +0200
% 46.92/12.38 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 46.92/12.38 % git: non_committed_changes: false
% 46.92/12.38
% 46.92/12.38 % ------ Parsing...
% 46.92/12.38 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 46.92/12.38
% 46.92/12.38 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 46.92/12.38
% 46.92/12.38 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 46.92/12.38
% 46.92/12.38 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 46.92/12.38 % ------ Proving...
% 46.92/12.38 % ------ Problem Properties
% 46.92/12.38
% 46.92/12.38 %
% 46.92/12.38 % clauses 19
% 46.92/12.38 % conjectures 3
% 46.92/12.38 % EPR 4
% 46.92/12.38 % Horn 13
% 46.92/12.38 % unary 3
% 46.92/12.38 % binary 7
% 46.92/12.38 % lits 55
% 46.92/12.38 % lits eq 2
% 46.92/12.38 % fd_pure 0
% 46.92/12.38 % fd_pseudo 0
% 46.92/12.38 % fd_cond 0
% 46.92/12.38 % fd_pseudo_cond 1
% 46.92/12.38 % AC symbols 0
% 46.92/12.38
% 46.92/12.38 % ------ Schedule dynamic 5 is on
% 46.92/12.38
% 46.92/12.38 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 46.92/12.38
% 46.92/12.38
% 46.92/12.38 % ------
% 46.92/12.38 % Current options:
% 46.92/12.38 % ------
% 46.92/12.38
% 46.92/12.38
% 46.92/12.38 %
% 46.92/12.38
% 46.92/12.38 % ------ Proving...
% 46.92/12.38 %
% 46.92/12.38
% 46.92/12.38 % SZS status Theorem for theBenchmark.p
% 46.92/12.38
% 46.92/12.38 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 46.92/12.38
% 46.92/12.38
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