%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET716+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n016.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 02:47:56 PM UTC 2026
% Result : Theorem 22.93s 20.50s
% Output : CNFRefutation 22.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 4
% Syntax : Number of formulae : 169 ( 27 unt; 0 def)
% Number of atoms : 743 ( 106 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 1014 ( 440 ~; 475 |; 76 &)
% ( 8 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-5 aty)
% Number of variables : 551 ( 0 sgn 525 !; 26 ?; 325 :)
% 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/sandbox2/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/sandbox2/benchmark/Axioms/SET006+1.ax',compose_function) ).
fof(f17,axiom,
! [X0,X1,X2] :
( injective(X0,X1,X2)
<=> ! [X3,X4,X5] :
( ( member(X5,X2)
& member(X4,X1)
& member(X3,X1) )
=> ( ( apply(X0,X4,X5)
& apply(X0,X3,X5) )
=> X3 = X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',injective) ).
fof(f29,conjecture,
! [X0,X1,X2,X3,X4] :
( ( injective(X1,X3,X4)
& injective(X0,X2,X3)
& maps(X1,X3,X4)
& maps(X0,X2,X3) )
=> injective(compose_function(X1,X0,X2,X3,X4),X2,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thII07) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( ( injective(X1,X3,X4)
& injective(X0,X2,X3)
& maps(X1,X3,X4)
& maps(X0,X2,X3) )
=> injective(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] :
( 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(f33,plain,
? [X0,X1,X2,X3,X4] :
( injective(X1,X3,X4)
& injective(X0,X2,X3)
& maps(X1,X3,X4)
& maps(X0,X2,X3)
& ~ injective(compose_function(X1,X0,X2,X3,X4),X2,X4) ),
inference(ennf_transformation,[],[f30]) ).
fof(f34,plain,
? [X0,X1,X2,X3,X4] :
( injective(X1,X3,X4)
& injective(X0,X2,X3)
& maps(X1,X3,X4)
& maps(X0,X2,X3)
& ~ injective(compose_function(X1,X0,X2,X3,X4),X2,X4) ),
inference(flattening,[],[f33]) ).
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(ennf_transformation,[],[f32]) ).
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(flattening,[],[f35]) ).
fof(f37,plain,
! [X0,X1,X2] :
( injective(X0,X1,X2)
<=> ! [X3,X4,X5] :
( ~ member(X5,X2)
| ~ member(X4,X1)
| ~ member(X3,X1)
| ~ apply(X0,X4,X5)
| ~ apply(X0,X3,X5)
| X3 = X4 ) ),
inference(ennf_transformation,[],[f17]) ).
fof(f38,plain,
! [X0,X1,X2] :
( injective(X0,X1,X2)
<=> ! [X3,X4,X5] :
( ~ member(X5,X2)
| ~ member(X4,X1)
| ~ member(X3,X1)
| ~ apply(X0,X4,X5)
| ~ apply(X0,X3,X5)
| X3 = X4 ) ),
inference(flattening,[],[f37]) ).
fof(f39,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(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(flattening,[],[f39]) ).
fof(f41,plain,
( injective(sK1,sK3,sK4)
& injective(sK0,sK2,sK3)
& maps(sK1,sK3,sK4)
& maps(sK0,sK2,sK3)
& ~ injective(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f34]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ~ maps(X0,X1,X2)
| ( ! [X5,X6,X7] :
( ~ member(X7,X2)
| ~ member(X6,X2)
| ~ member(X5,X1)
| ~ apply(X0,X5,X7)
| ~ apply(X0,X5,X6)
| X6 = X7 )
& ! [X3] :
( ~ member(X3,X1)
| ( apply(X0,X3,sK5(X0,X2,X3))
& member(sK5(X0,X2,X3),X2) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X4,sK5(X0,X2,X3))],[f36]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ( ~ injective(X0,X1,X2)
| ! [X3,X4,X5] :
( ~ member(X5,X2)
| ~ member(X4,X1)
| ~ member(X3,X1)
| ~ apply(X0,X4,X5)
| ~ apply(X0,X3,X5)
| X3 = X4 ) )
& ( ? [X3,X4,X5] :
( member(X5,X2)
& member(X4,X1)
& member(X3,X1)
& apply(X0,X4,X5)
& apply(X0,X3,X5)
& X3 != X4 )
| injective(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f38]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ( ~ injective(X0,X1,X2)
| ! [X6,X7,X8] :
( ~ member(X8,X2)
| ~ member(X7,X1)
| ~ member(X6,X1)
| ~ apply(X0,X7,X8)
| ~ apply(X0,X6,X8)
| X6 = X7 ) )
& ( ? [X3,X4,X5] :
( member(X5,X2)
& member(X4,X1)
& member(X3,X1)
& apply(X0,X4,X5)
& apply(X0,X3,X5)
& X3 != X4 )
| injective(X0,X1,X2) ) ),
inference(rectify,[],[f43]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ( ~ injective(X0,X1,X2)
| ! [X6,X7,X8] :
( ~ member(X8,X2)
| ~ member(X7,X1)
| ~ member(X6,X1)
| ~ apply(X0,X7,X8)
| ~ apply(X0,X6,X8)
| X6 = X7 ) )
& ( ( member(sK8(X0,X1,X2),X2)
& member(sK7(X0,X1,X2),X1)
& member(sK6(X0,X1,X2),X1)
& apply(X0,sK7(X0,X1,X2),sK8(X0,X1,X2))
& apply(X0,sK6(X0,X1,X2),sK8(X0,X1,X2))
& sK6(X0,X1,X2) != sK7(X0,X1,X2) )
| injective(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))],[f44]) ).
fof(f46,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,[],[f40]) ).
fof(f47,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,[],[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)
| ( apply(X0,sK9(X0,X1,X3,X5,X6),X6)
& apply(X1,X5,sK9(X0,X1,X3,X5,X6))
& member(sK9(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,[sK9]),skolemize(X8,sK9(X0,X1,X3,X5,X6))],[f47]) ).
fof(f49,plain,
injective(sK1,sK3,sK4),
inference(cnf_transformation,[],[f41]) ).
fof(f50,plain,
injective(sK0,sK2,sK3),
inference(cnf_transformation,[],[f41]) ).
fof(f51,plain,
maps(sK1,sK3,sK4),
inference(cnf_transformation,[],[f41]) ).
fof(f52,plain,
maps(sK0,sK2,sK3),
inference(cnf_transformation,[],[f41]) ).
fof(f53,plain,
~ injective(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),
inference(cnf_transformation,[],[f41]) ).
fof(f54,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,[],[f42]) ).
fof(f55,plain,
! [X2,X3,X0,X1] :
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| apply(X0,X3,sK5(X0,X2,X3)) ),
inference(cnf_transformation,[],[f42]) ).
fof(f56,plain,
! [X2,X3,X0,X1] :
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| member(sK5(X0,X2,X3),X2) ),
inference(cnf_transformation,[],[f42]) ).
fof(f57,plain,
! [X2,X0,X1,X8,X6,X7] :
( ~ injective(X0,X1,X2)
| ~ member(X8,X2)
| ~ member(X7,X1)
| ~ member(X6,X1)
| ~ apply(X0,X7,X8)
| ~ apply(X0,X6,X8)
| X6 = X7 ),
inference(cnf_transformation,[],[f45]) ).
fof(f58,plain,
! [X2,X0,X1] :
( member(sK8(X0,X1,X2),X2)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f45]) ).
fof(f59,plain,
! [X2,X0,X1] :
( member(sK7(X0,X1,X2),X1)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f45]) ).
fof(f60,plain,
! [X2,X0,X1] :
( member(sK6(X0,X1,X2),X1)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f45]) ).
fof(f61,plain,
! [X2,X0,X1] :
( apply(X0,sK7(X0,X1,X2),sK8(X0,X1,X2))
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f45]) ).
fof(f62,plain,
! [X2,X0,X1] :
( apply(X0,sK6(X0,X1,X2),sK8(X0,X1,X2))
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f45]) ).
fof(f63,plain,
! [X2,X0,X1] :
( sK6(X0,X1,X2) != sK7(X0,X1,X2)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f45]) ).
fof(f64,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,sK9(X0,X1,X3,X5,X6),X6) ),
inference(cnf_transformation,[],[f48]) ).
fof(f65,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,sK9(X0,X1,X3,X5,X6)) ),
inference(cnf_transformation,[],[f48]) ).
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)
| member(sK9(X0,X1,X3,X5,X6),X3) ),
inference(cnf_transformation,[],[f48]) ).
fof(f67,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,[],[f48]) ).
tcf(c_49,negated_conjecture,
~ injective(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),
inference(cnf_transformation,[],[f53]) ).
tcf(c_50,negated_conjecture,
maps(sK0,sK2,sK3),
inference(cnf_transformation,[],[f52]) ).
tcf(c_51,negated_conjecture,
maps(sK1,sK3,sK4),
inference(cnf_transformation,[],[f51]) ).
tcf(c_52,negated_conjecture,
injective(sK0,sK2,sK3),
inference(cnf_transformation,[],[f50]) ).
tcf(c_53,negated_conjecture,
injective(sK1,sK3,sK4),
inference(cnf_transformation,[],[f49]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK5(X0,X2,X3),X2)
| ~ member(X3,X1)
| ~ maps(X0,X1,X2) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,X3,sK5(X0,X2,X3))
| ~ member(X3,X1)
| ~ maps(X0,X1,X2) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_56,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,[],[f54]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( injective(X0,X1,X2)
| ( sK6(X0,X1,X2) != sK7(X0,X1,X2) ) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( injective(X0,X1,X2)
| apply(X0,sK6(X0,X1,X2),sK8(X0,X1,X2)) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( injective(X0,X1,X2)
| apply(X0,sK7(X0,X1,X2),sK8(X0,X1,X2)) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( injective(X0,X1,X2)
| member(sK6(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] :
( injective(X0,X1,X2)
| member(sK7(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f59]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] :
( injective(X0,X1,X2)
| member(sK8(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( X3 = X5 )
| ~ member(X5,X1)
| ~ member(X4,X2)
| ~ member(X3,X1)
| ~ apply(X0,X5,X4)
| ~ apply(X0,X3,X4)
| ~ injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f57]) ).
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,X6,X5),X4,X2)
| ~ member(X4,X7)
| ~ member(X2,X5)
| ~ member(X1,X6)
| ~ apply(X3,X4,X1)
| ~ apply(X0,X1,X2) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( member(sK9(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,[],[f66]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( apply(X1,X5,sK9(X0,X1,X3,X5,X6))
| ~ member(X6,X4)
| ~ member(X5,X2)
| ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( apply(X0,sK9(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,[],[f64]) ).
tcf(c_298,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 != sK3 )
| ( X1 != sK2 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_56]) ).
tcf(c_299,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ member(X2,sK3)
| ~ member(X1,sK3)
| ~ member(X0,sK2)
| ~ apply(sK0,X0,X2)
| ~ apply(sK0,X0,X1) ),
inference(unflattening,[status(thm)],[c_298]) ).
tcf(c_319,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,X3,sK5(X0,X2,X3))
| ~ member(X3,X1)
| ( X2 != sK3 )
| ( X1 != sK2 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_55]) ).
tcf(c_320,plain,
! [X0: $i] :
( apply(sK0,X0,sK5(sK0,sK3,X0))
| ~ member(X0,sK2) ),
inference(unflattening,[status(thm)],[c_319]) ).
tcf(c_328,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK5(X0,X2,X3),X2)
| ~ member(X3,X1)
| ( X2 != sK3 )
| ( X1 != sK2 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_54]) ).
tcf(c_329,plain,
! [X0: $i] :
( member(sK5(sK0,sK3,X0),sK3)
| ~ member(X0,sK2) ),
inference(unflattening,[status(thm)],[c_328]) ).
tcf(c_337,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( X4 = X5 )
| ~ member(X5,X2)
| ~ member(X4,X2)
| ~ member(X3,X1)
| ~ apply(X0,X3,X5)
| ~ apply(X0,X3,X4)
| ( X2 != sK4 )
| ( X1 != sK3 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_56]) ).
tcf(c_338,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(unflattening,[status(thm)],[c_337]) ).
tcf(c_358,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,X3,sK5(X0,X2,X3))
| ~ member(X3,X1)
| ( X2 != sK4 )
| ( X1 != sK3 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_55]) ).
tcf(c_359,plain,
! [X0: $i] :
( apply(sK1,X0,sK5(sK1,sK4,X0))
| ~ member(X0,sK3) ),
inference(unflattening,[status(thm)],[c_358]) ).
tcf(c_367,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK5(X0,X2,X3),X2)
| ~ member(X3,X1)
| ( X2 != sK4 )
| ( X1 != sK3 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_54]) ).
tcf(c_368,plain,
! [X0: $i] :
( member(sK5(sK1,sK4,X0),sK4)
| ~ member(X0,sK3) ),
inference(unflattening,[status(thm)],[c_367]) ).
tcf(c_560,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(sK8(X0,X1,X2),X2)
| ( X2 != sK4 )
| ( X1 != sK2 )
| ( compose_function(sK1,sK0,sK2,sK3,sK4) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_62]) ).
tcf(c_561,plain,
member(sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK4),
inference(unflattening,[status(thm)],[c_560]) ).
tcf(c_565,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(sK7(X0,X1,X2),X1)
| ( X2 != sK4 )
| ( X1 != sK2 )
| ( compose_function(sK1,sK0,sK2,sK3,sK4) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_61]) ).
tcf(c_566,plain,
member(sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK2),
inference(unflattening,[status(thm)],[c_565]) ).
tcf(c_570,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(sK6(X0,X1,X2),X1)
| ( X2 != sK4 )
| ( X1 != sK2 )
| ( compose_function(sK1,sK0,sK2,sK3,sK4) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_60]) ).
tcf(c_571,plain,
member(sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK2),
inference(unflattening,[status(thm)],[c_570]) ).
tcf(c_575,plain,
! [X0: $i,X1: $i,X2: $i] :
( apply(X0,sK7(X0,X1,X2),sK8(X0,X1,X2))
| ( X2 != sK4 )
| ( X1 != sK2 )
| ( compose_function(sK1,sK0,sK2,sK3,sK4) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_59]) ).
tcf(c_576,plain,
apply(compose_function(sK1,sK0,sK2,sK3,sK4),sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),
inference(unflattening,[status(thm)],[c_575]) ).
tcf(c_580,plain,
! [X0: $i,X1: $i,X2: $i] :
( apply(X0,sK6(X0,X1,X2),sK8(X0,X1,X2))
| ( X2 != sK4 )
| ( X1 != sK2 )
| ( compose_function(sK1,sK0,sK2,sK3,sK4) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_58]) ).
tcf(c_581,plain,
apply(compose_function(sK1,sK0,sK2,sK3,sK4),sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),
inference(unflattening,[status(thm)],[c_580]) ).
tcf(c_585,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 != sK4 )
| ( X1 != sK2 )
| ( sK6(X0,X1,X2) != sK7(X0,X1,X2) )
| ( compose_function(sK1,sK0,sK2,sK3,sK4) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_57]) ).
tcf(c_586,plain,
sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4) != sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),
inference(unflattening,[status(thm)],[c_585]) ).
tcf(c_1139,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( injective(compose_function(X0,X1,X2,X3,X4),X5,X6)
| member(sK9(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(sK8(compose_function(X0,X1,X2,X3,X4),X5,X6),X4)
| ~ member(sK6(compose_function(X0,X1,X2,X3,X4),X5,X6),X2) ),
inference(superposition,[status(thm)],[c_58,c_65]) ).
tcf(c_1194,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( injective(compose_function(X0,X1,X2,X3,X4),X5,X6)
| apply(X1,sK6(compose_function(X0,X1,X2,X3,X4),X5,X6),sK9(X0,X1,X3,sK6(compose_function(X0,X1,X2,X3,X4),X5,X6),sK8(compose_function(X0,X1,X2,X3,X4),X5,X6)))
| ~ member(sK8(compose_function(X0,X1,X2,X3,X4),X5,X6),X4)
| ~ member(sK6(compose_function(X0,X1,X2,X3,X4),X5,X6),X2) ),
inference(superposition,[status(thm)],[c_58,c_66]) ).
tcf(c_1195,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( injective(compose_function(X0,X1,X2,X3,X4),X5,X6)
| apply(X1,sK7(compose_function(X0,X1,X2,X3,X4),X5,X6),sK9(X0,X1,X3,sK7(compose_function(X0,X1,X2,X3,X4),X5,X6),sK8(compose_function(X0,X1,X2,X3,X4),X5,X6)))
| ~ member(sK8(compose_function(X0,X1,X2,X3,X4),X5,X6),X4)
| ~ member(sK7(compose_function(X0,X1,X2,X3,X4),X5,X6),X2) ),
inference(superposition,[status(thm)],[c_59,c_66]) ).
tcf(c_1390,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( injective(compose_function(X0,X1,X2,X3,X4),X5,X6)
| apply(X0,sK9(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(sK8(compose_function(X0,X1,X2,X3,X4),X5,X6),X4)
| ~ member(sK6(compose_function(X0,X1,X2,X3,X4),X5,X6),X2) ),
inference(superposition,[status(thm)],[c_58,c_67]) ).
tcf(c_1391,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( injective(compose_function(X0,X1,X2,X3,X4),X5,X6)
| apply(X0,sK9(X0,X1,X3,sK7(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(sK8(compose_function(X0,X1,X2,X3,X4),X5,X6),X4)
| ~ member(sK7(compose_function(X0,X1,X2,X3,X4),X5,X6),X2) ),
inference(superposition,[status(thm)],[c_59,c_67]) ).
tcf(c_1417,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( apply(compose_function(sK1,X2,X5,X4,X1),X3,sK5(sK1,sK4,X0))
| ~ member(X0,sK3)
| ~ member(X3,X5)
| ~ member(X0,X4)
| ~ apply(X2,X3,X0)
| ~ member(sK5(sK1,sK4,X0),X1) ),
inference(superposition,[status(thm)],[c_359,c_64]) ).
tcf(c_1610,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( apply(sK1,sK9(sK1,X2,X4,X3,sK5(sK1,sK4,X0)),sK5(sK1,sK4,X0))
| ~ member(X0,sK3)
| ~ member(X3,X5)
| ~ member(X0,X4)
| ~ apply(X2,X3,X0)
| ~ member(sK5(sK1,sK4,X0),X1) ),
inference(superposition,[status(thm)],[c_1417,c_67]) ).
tcf(c_1611,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( apply(X2,X3,sK9(sK1,X2,X4,X3,sK5(sK1,sK4,X0)))
| ~ member(X0,sK3)
| ~ member(X3,X5)
| ~ member(X0,X4)
| ~ apply(X2,X3,X0)
| ~ member(sK5(sK1,sK4,X0),X1) ),
inference(superposition,[status(thm)],[c_1417,c_66]) ).
tcf(c_1612,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( member(sK9(sK1,X2,X4,X3,sK5(sK1,sK4,X0)),X4)
| ~ member(X0,sK3)
| ~ member(X3,X5)
| ~ member(X0,X4)
| ~ apply(X2,X3,X0)
| ~ member(sK5(sK1,sK4,X0),X1) ),
inference(superposition,[status(thm)],[c_1417,c_65]) ).
tcf(c_1658,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(sK9(X0,X1,X2,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),X4),X2)
| ~ member(X4,X3)
| ~ member(sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK2)
| ~ apply(compose_function(X0,X1,sK2,X2,X3),sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),X4) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_1664,plain,
( apply(sK0,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)))
| ~ member(sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK2) ),
inference(instantiation,[status(thm)],[c_320]) ).
tcf(c_1665,plain,
( member(sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),sK3)
| ~ member(sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK2) ),
inference(instantiation,[status(thm)],[c_329]) ).
tcf(c_1779,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(sK9(X0,X1,X2,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),X4),X2)
| ~ member(X4,X3)
| ~ member(sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK2)
| ~ apply(compose_function(X0,X1,sK2,X2,X3),sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),X4) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_1878,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(sK9(sK1,X0,X3,X1,sK5(sK1,sK4,X2)),X3)
| ~ member(X2,sK3)
| ~ member(X2,X3)
| ~ member(X1,X4)
| ~ apply(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_368,c_1612]) ).
tcf(c_1900,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( injective(X1,X2,X3)
| member(sK9(sK1,X0,X5,sK6(X1,X2,X3),sK5(sK1,sK4,X4)),X5)
| ~ member(X4,sK3)
| ~ member(X4,X5)
| ~ apply(X0,sK6(X1,X2,X3),X4) ),
inference(superposition,[status(thm)],[c_60,c_1878]) ).
tcf(c_2104,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4) = sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4) )
| ~ member(X1,X3)
| ~ injective(X0,X2,X3)
| ~ member(sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),X2)
| ~ member(sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),X2)
| ~ apply(X0,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),X1)
| ~ apply(X0,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),X1) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_2484,plain,
( apply(sK1,sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),sK5(sK1,sK4,sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))))
| ~ member(sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),sK3) ),
inference(instantiation,[status(thm)],[c_359]) ).
tcf(c_2485,plain,
( member(sK5(sK1,sK4,sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))),sK4)
| ~ member(sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),sK3) ),
inference(instantiation,[status(thm)],[c_368]) ).
tcf(c_2890,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apply(X0,X1,sK9(sK1,X0,X3,X1,sK5(sK1,sK4,X2)))
| ~ member(X2,sK3)
| ~ member(X2,X3)
| ~ member(X1,X4)
| ~ apply(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_368,c_1611]) ).
tcf(c_3433,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( injective(X1,X2,X3)
| apply(X0,sK6(X1,X2,X3),sK9(sK1,X0,X5,sK6(X1,X2,X3),sK5(sK1,sK4,X4)))
| ~ member(X4,sK3)
| ~ member(X4,X5)
| ~ apply(X0,sK6(X1,X2,X3),X4) ),
inference(superposition,[status(thm)],[c_60,c_2890]) ).
tcf(c_3691,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( injective(X1,X2,X3)
| ( sK9(sK1,sK0,X0,sK6(X1,X2,X3),sK5(sK1,sK4,X4)) = X5 )
| ~ member(X5,sK3)
| ~ member(X4,sK3)
| ~ member(X4,X0)
| ~ member(sK6(X1,X2,X3),sK2)
| ~ apply(sK0,sK6(X1,X2,X3),X5)
| ~ apply(sK0,sK6(X1,X2,X3),X4)
| ~ member(sK9(sK1,sK0,X0,sK6(X1,X2,X3),sK5(sK1,sK4,X4)),sK3) ),
inference(superposition,[status(thm)],[c_3433,c_299]) ).
tcf(c_3802,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4) = sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4) )
| ~ member(X1,X2)
| ~ injective(X0,sK2,X2)
| ~ member(sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK2)
| ~ member(sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK2)
| ~ apply(X0,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),X1)
| ~ apply(X0,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),X1) ),
inference(instantiation,[status(thm)],[c_2104]) ).
tcf(c_3804,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(sK9(X0,X1,X2,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),X2)
| ~ member(sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK4)
| ~ member(sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK2)
| ~ apply(compose_function(X0,X1,sK2,X2,sK4),sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)) ),
inference(instantiation,[status(thm)],[c_1658]) ).
tcf(c_4220,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(sK9(X0,X1,X2,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),X2)
| ~ member(sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK4)
| ~ member(sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK2)
| ~ apply(compose_function(X0,X1,sK2,X2,sK4),sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)) ),
inference(instantiation,[status(thm)],[c_1779]) ).
tcf(c_5053,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apply(sK1,sK9(sK1,X0,X3,X1,sK5(sK1,sK4,X2)),sK5(sK1,sK4,X2))
| ~ member(X2,sK3)
| ~ member(X2,X3)
| ~ member(X1,X4)
| ~ apply(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_368,c_1610]) ).
tcf(c_5617,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( injective(X1,X2,X3)
| apply(sK1,sK9(sK1,X0,X5,sK6(X1,X2,X3),sK5(sK1,sK4,X4)),sK5(sK1,sK4,X4))
| ~ member(X4,sK3)
| ~ member(X4,X5)
| ~ apply(X0,sK6(X1,X2,X3),X4) ),
inference(superposition,[status(thm)],[c_60,c_5053]) ).
tcf(c_7598,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( injective(X0,X1,X2)
| ( sK9(sK1,sK0,sK3,sK6(X0,X1,X2),sK5(sK1,sK4,X3)) = X4 )
| ~ member(X4,sK3)
| ~ member(X3,sK3)
| ~ member(sK6(X0,X1,X2),sK2)
| ~ apply(sK0,sK6(X0,X1,X2),X4)
| ~ apply(sK0,sK6(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_1900,c_3691]) ).
tcf(c_8222,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( injective(X2,X3,X4)
| ( sK5(sK1,sK4,X5) = X6 )
| ~ member(X6,sK4)
| ~ member(X5,sK3)
| ~ member(X5,X1)
| ~ member(sK5(sK1,sK4,X5),sK4)
| ~ apply(X0,sK6(X2,X3,X4),X5)
| ~ member(sK9(sK1,X0,X1,sK6(X2,X3,X4),sK5(sK1,sK4,X5)),sK3)
| ~ apply(sK1,sK9(sK1,X0,X1,sK6(X2,X3,X4),sK5(sK1,sK4,X5)),X6) ),
inference(superposition,[status(thm)],[c_5617,c_338]) ).
tcf(c_8430,plain,
( member(sK9(sK1,sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),sK3)
| ~ member(sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK4)
| ~ member(sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK2)
| ~ apply(compose_function(sK1,sK0,sK2,sK3,sK4),sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)) ),
inference(instantiation,[status(thm)],[c_3804]) ).
tcf(c_8758,plain,
! [X0: $i,X1: $i] :
( member(sK9(X0,X1,sK3,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),sK3)
| ~ member(sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK4)
| ~ member(sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK2)
| ~ apply(compose_function(X0,X1,sK2,sK3,sK4),sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)) ),
inference(instantiation,[status(thm)],[c_4220]) ).
tcf(c_10861,plain,
! [X0: $i] :
( ( sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4) = sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4) )
| ~ injective(X0,sK2,sK3)
| ~ member(sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK2)
| ~ member(sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK2)
| ~ member(sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),sK3)
| ~ apply(X0,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)))
| ~ apply(X0,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))) ),
inference(instantiation,[status(thm)],[c_3802]) ).
tcf(c_12745,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( injective(X2,X3,X4)
| ( sK5(sK1,sK4,X5) = X6 )
| ~ member(X6,sK4)
| ~ member(X5,sK3)
| ~ member(X5,X1)
| ~ apply(X0,sK6(X2,X3,X4),X5)
| ~ member(sK9(sK1,X0,X1,sK6(X2,X3,X4),sK5(sK1,sK4,X5)),sK3)
| ~ apply(sK1,sK9(sK1,X0,X1,sK6(X2,X3,X4),sK5(sK1,sK4,X5)),X6) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8222,c_368]) ).
tcf(c_12770,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( injective(X2,X3,X4)
| ( sK5(sK1,sK4,sK9(sK1,X0,X1,sK6(X2,X3,X4),sK5(sK1,sK4,X5))) = sK5(sK1,sK4,X5) )
| ~ member(X5,sK3)
| ~ member(X5,X1)
| ~ apply(X0,sK6(X2,X3,X4),X5)
| ~ member(sK9(sK1,X0,X1,sK6(X2,X3,X4),sK5(sK1,sK4,X5)),sK3)
| ~ member(sK5(sK1,sK4,sK9(sK1,X0,X1,sK6(X2,X3,X4),sK5(sK1,sK4,X5))),sK4) ),
inference(superposition,[status(thm)],[c_359,c_12745]) ).
tcf(c_20987,plain,
( member(sK9(sK1,sK0,sK3,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),sK3)
| ~ member(sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK4)
| ~ member(sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK2)
| ~ apply(compose_function(sK1,sK0,sK2,sK3,sK4),sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)) ),
inference(instantiation,[status(thm)],[c_8758]) ).
tcf(c_23933,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( injective(X2,X3,X4)
| ( sK5(sK1,sK4,sK9(sK1,X0,X1,sK6(X2,X3,X4),sK5(sK1,sK4,X5))) = sK5(sK1,sK4,X5) )
| ~ member(X5,sK3)
| ~ member(X5,X1)
| ~ apply(X0,sK6(X2,X3,X4),X5)
| ~ member(sK9(sK1,X0,X1,sK6(X2,X3,X4),sK5(sK1,sK4,X5)),sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12770,c_368]) ).
tcf(c_23952,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( injective(X1,X2,X3)
| ( sK5(sK1,sK4,sK9(sK1,X0,sK3,sK6(X1,X2,X3),sK5(sK1,sK4,X4))) = sK5(sK1,sK4,X4) )
| ~ member(X4,sK3)
| ~ apply(X0,sK6(X1,X2,X3),X4) ),
inference(superposition,[status(thm)],[c_1900,c_23933]) ).
tcf(c_24152,plain,
( ( sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4) = sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4) )
| ~ injective(sK0,sK2,sK3)
| ~ member(sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK2)
| ~ member(sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK2)
| ~ member(sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),sK3)
| ~ apply(sK0,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)))
| ~ apply(sK0,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))) ),
inference(instantiation,[status(thm)],[c_10861]) ).
tcf(c_24960,plain,
! [X0: $i,X1: $i,X2: $i] :
( injective(X0,X1,X2)
| ( sK5(sK1,sK4,sK9(sK1,sK0,sK3,sK6(X0,X1,X2),sK5(sK1,sK4,sK5(sK0,sK3,sK6(X0,X1,X2))))) = sK5(sK1,sK4,sK5(sK0,sK3,sK6(X0,X1,X2))) )
| ~ member(sK6(X0,X1,X2),sK2)
| ~ member(sK5(sK0,sK3,sK6(X0,X1,X2)),sK3) ),
inference(superposition,[status(thm)],[c_320,c_23952]) ).
tcf(c_25224,plain,
! [X0: $i,X1: $i,X2: $i] :
( injective(X0,X1,X2)
| ( sK5(sK1,sK4,sK9(sK1,sK0,sK3,sK6(X0,X1,X2),sK5(sK1,sK4,sK5(sK0,sK3,sK6(X0,X1,X2))))) = sK5(sK1,sK4,sK5(sK0,sK3,sK6(X0,X1,X2))) )
| ~ member(sK6(X0,X1,X2),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_24960,c_329]) ).
tcf(c_25234,plain,
! [X0: $i,X1: $i] :
( injective(X0,sK2,X1)
| ( sK5(sK1,sK4,sK9(sK1,sK0,sK3,sK6(X0,sK2,X1),sK5(sK1,sK4,sK5(sK0,sK3,sK6(X0,sK2,X1))))) = sK5(sK1,sK4,sK5(sK0,sK3,sK6(X0,sK2,X1))) ) ),
inference(superposition,[status(thm)],[c_60,c_25224]) ).
tcf(c_25250,plain,
sK5(sK1,sK4,sK9(sK1,sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK5(sK1,sK4,sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))))) = sK5(sK1,sK4,sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))),
inference(superposition,[status(thm)],[c_25234,c_49]) ).
tcf(c_26402,plain,
( member(sK5(sK1,sK4,sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))),sK4)
| ~ member(sK9(sK1,sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK5(sK1,sK4,sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)))),sK3) ),
inference(superposition,[status(thm)],[c_25250,c_368]) ).
tcf(c_30207,plain,
member(sK5(sK1,sK4,sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))),sK4),
inference(global_subsumption_just,[status(thm)],[c_26402,c_571,c_1665,c_2485]) ).
tcf(c_33892,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( injective(X0,X1,X2)
| ( sK9(sK1,sK0,sK3,sK6(X0,X1,X2),sK5(sK1,sK4,sK5(sK0,sK3,sK6(X0,X1,X2)))) = X3 )
| ~ member(X3,sK3)
| ~ member(sK6(X0,X1,X2),sK2)
| ~ apply(sK0,sK6(X0,X1,X2),X3)
| ~ member(sK5(sK0,sK3,sK6(X0,X1,X2)),sK3) ),
inference(superposition,[status(thm)],[c_320,c_7598]) ).
tcf(c_33973,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( injective(X0,X1,X2)
| ( sK9(sK1,sK0,sK3,sK6(X0,X1,X2),sK5(sK1,sK4,sK5(sK0,sK3,sK6(X0,X1,X2)))) = X3 )
| ~ member(X3,sK3)
| ~ member(sK6(X0,X1,X2),sK2)
| ~ apply(sK0,sK6(X0,X1,X2),X3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_33892,c_329]) ).
tcf(c_33990,plain,
! [X0: $i,X1: $i,X2: $i] :
( injective(X0,X1,X2)
| ( sK9(sK1,sK0,sK3,sK6(X0,X1,X2),sK5(sK1,sK4,sK5(sK0,sK3,sK6(X0,X1,X2)))) = sK5(sK0,sK3,sK6(X0,X1,X2)) )
| ~ member(sK6(X0,X1,X2),sK2)
| ~ member(sK5(sK0,sK3,sK6(X0,X1,X2)),sK3) ),
inference(superposition,[status(thm)],[c_320,c_33973]) ).
tcf(c_34063,plain,
! [X0: $i,X1: $i,X2: $i] :
( injective(X0,X1,X2)
| ( sK9(sK1,sK0,sK3,sK6(X0,X1,X2),sK5(sK1,sK4,sK5(sK0,sK3,sK6(X0,X1,X2)))) = sK5(sK0,sK3,sK6(X0,X1,X2)) )
| ~ member(sK6(X0,X1,X2),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_33990,c_329]) ).
tcf(c_34073,plain,
! [X0: $i,X1: $i] :
( injective(X0,sK2,X1)
| ( sK9(sK1,sK0,sK3,sK6(X0,sK2,X1),sK5(sK1,sK4,sK5(sK0,sK3,sK6(X0,sK2,X1)))) = sK5(sK0,sK3,sK6(X0,sK2,X1)) ) ),
inference(superposition,[status(thm)],[c_60,c_34063]) ).
tcf(c_34288,plain,
sK9(sK1,sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK5(sK1,sK4,sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)))) = sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),
inference(superposition,[status(thm)],[c_34073,c_49]) ).
tcf(c_34310,plain,
( injective(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)
| apply(sK1,sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),sK5(sK1,sK4,sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))))
| ~ member(sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),sK3)
| ~ apply(sK0,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))) ),
inference(superposition,[status(thm)],[c_34288,c_5617]) ).
tcf(c_34314,plain,
! [X0: $i] :
( injective(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)
| ( sK5(sK1,sK4,sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))) = X0 )
| ~ member(X0,sK4)
| ~ member(sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),sK3)
| ~ apply(sK1,sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),X0)
| ~ apply(sK0,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)))
| ~ member(sK9(sK1,sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK5(sK1,sK4,sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)))),sK3) ),
inference(superposition,[status(thm)],[c_34288,c_12745]) ).
tcf(c_34315,plain,
! [X0: $i] :
( injective(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)
| ( sK9(sK1,sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK5(sK1,sK4,sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)))) = X0 )
| ~ member(X0,sK3)
| ~ member(sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK2)
| ~ apply(sK0,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),X0)
| ~ member(sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),sK3)
| ~ apply(sK0,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))) ),
inference(superposition,[status(thm)],[c_34288,c_3691]) ).
tcf(c_34316,plain,
( apply(sK1,sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),sK5(sK1,sK4,sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))))
| ~ member(sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),sK3)
| ~ apply(sK0,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34310,c_49]) ).
tcf(c_34321,plain,
! [X0: $i] :
( injective(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)
| ( sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)) = X0 )
| ~ member(X0,sK3)
| ~ member(sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK2)
| ~ apply(sK0,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),X0)
| ~ member(sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),sK3)
| ~ apply(sK0,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))) ),
inference(light_normalisation,[status(thm)],[c_34315,c_34288]) ).
tcf(c_34322,plain,
! [X0: $i] :
( ( sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)) = X0 )
| ~ member(X0,sK3)
| ~ member(sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK2)
| ~ apply(sK0,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),X0)
| ~ member(sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),sK3)
| ~ apply(sK0,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34321,c_49]) ).
tcf(c_34329,plain,
! [X0: $i] :
( injective(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)
| ( sK5(sK1,sK4,sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))) = X0 )
| ~ member(X0,sK4)
| ~ member(sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),sK3)
| ~ apply(sK1,sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),X0)
| ~ apply(sK0,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))) ),
inference(light_normalisation,[status(thm)],[c_34314,c_34288]) ).
tcf(c_34330,plain,
! [X0: $i] :
( ( sK5(sK1,sK4,sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))) = X0 )
| ~ member(X0,sK4)
| ~ member(sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),sK3)
| ~ apply(sK1,sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),X0)
| ~ apply(sK0,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34329,c_49]) ).
tcf(c_34709,plain,
apply(sK1,sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),sK5(sK1,sK4,sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)))),
inference(global_subsumption_just,[status(thm)],[c_34316,c_571,c_1665,c_2484]) ).
tcf(c_34714,plain,
! [X0: $i] :
( ( sK5(sK1,sK4,sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))) = X0 )
| ~ member(X0,sK4)
| ~ member(sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),sK3)
| ~ apply(sK1,sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),X0)
| ~ member(sK5(sK1,sK4,sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))),sK4) ),
inference(superposition,[status(thm)],[c_34709,c_338]) ).
tcf(c_34722,plain,
! [X0: $i] :
( ( sK5(sK1,sK4,sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))) = X0 )
| ~ member(X0,sK4)
| ~ member(sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),sK3)
| ~ apply(sK1,sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34714,c_30207]) ).
tcf(c_34863,plain,
! [X0: $i] :
( ( sK5(sK1,sK4,sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))) = X0 )
| ~ member(X0,sK4)
| ~ apply(sK1,sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),X0) ),
inference(global_subsumption_just,[status(thm)],[c_34330,c_571,c_1665,c_34722]) ).
tcf(c_34936,plain,
! [X0: $i] :
( ( sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)) = X0 )
| ~ member(X0,sK3)
| ~ apply(sK0,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),X0) ),
inference(global_subsumption_just,[status(thm)],[c_34322,c_571,c_1665,c_1664,c_34322]) ).
tcf(c_34946,plain,
( injective(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)
| ( sK9(sK1,sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)) = sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)) )
| ~ member(sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK4)
| ~ member(sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK2)
| ~ member(sK9(sK1,sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),sK3) ),
inference(superposition,[status(thm)],[c_1194,c_34936]) ).
tcf(c_34975,plain,
( ( sK9(sK1,sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)) = sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)) )
| ~ member(sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK4)
| ~ member(sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK2)
| ~ member(sK9(sK1,sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34946,c_49]) ).
tcf(c_36273,plain,
sK9(sK1,sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)) = sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),
inference(global_subsumption_just,[status(thm)],[c_34975,c_561,c_571,c_581,c_8430,c_34975]) ).
tcf(c_36275,plain,
( injective(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)
| apply(sK1,sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))
| ~ member(sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK4)
| ~ member(sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK2) ),
inference(superposition,[status(thm)],[c_36273,c_1390]) ).
tcf(c_36277,plain,
( injective(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)
| member(sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),sK3)
| ~ member(sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK4)
| ~ member(sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK2) ),
inference(superposition,[status(thm)],[c_36273,c_1139]) ).
tcf(c_36278,plain,
( member(sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),sK3)
| ~ member(sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK4)
| ~ member(sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_36277,c_49]) ).
tcf(c_36286,plain,
( apply(sK1,sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))
| ~ member(sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK4)
| ~ member(sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_36275,c_49]) ).
tcf(c_36290,plain,
member(sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),sK3),
inference(global_subsumption_just,[status(thm)],[c_36278,c_571,c_1665]) ).
tcf(c_36428,plain,
apply(sK1,sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),
inference(global_subsumption_just,[status(thm)],[c_36286,c_561,c_571,c_36286]) ).
tcf(c_36430,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)) = X1 )
| ~ member(X1,X0)
| ~ injective(sK1,X0,X2)
| ~ member(sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),X2)
| ~ apply(sK1,X1,sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))
| ~ member(sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),X0) ),
inference(superposition,[status(thm)],[c_36428,c_63]) ).
tcf(c_36440,plain,
( ( sK5(sK1,sK4,sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))) = sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4) )
| ~ member(sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK4) ),
inference(superposition,[status(thm)],[c_36428,c_34863]) ).
tcf(c_37388,plain,
! [X0: $i,X1: $i] :
( ( sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)) = X0 )
| ~ member(X0,sK3)
| ~ injective(sK1,sK3,X1)
| ~ member(sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),X1)
| ~ apply(sK1,X0,sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)) ),
inference(superposition,[status(thm)],[c_36290,c_36430]) ).
tcf(c_37402,plain,
sK5(sK1,sK4,sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))) = sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),
inference(global_subsumption_just,[status(thm)],[c_36440,c_561,c_36440]) ).
tcf(c_37408,plain,
member(sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK4),
inference(demodulation,[status(thm)],[c_30207,c_37402]) ).
tcf(c_46558,plain,
! [X0: $i] :
( injective(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)
| ( sK9(sK1,sK0,sK3,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)) = sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)) )
| ~ injective(sK1,sK3,X0)
| ~ member(sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK4)
| ~ member(sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK2)
| ~ member(sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),X0)
| ~ member(sK9(sK1,sK0,sK3,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),sK3) ),
inference(superposition,[status(thm)],[c_1391,c_37388]) ).
tcf(c_46560,plain,
! [X0: $i] :
( ( sK9(sK1,sK0,sK3,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)) = sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)) )
| ~ injective(sK1,sK3,X0)
| ~ member(sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK2)
| ~ member(sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),X0)
| ~ member(sK9(sK1,sK0,sK3,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_46558,c_49,c_37408]) ).
tcf(c_47498,plain,
! [X0: $i] :
( ( sK9(sK1,sK0,sK3,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)) = sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)) )
| ~ injective(sK1,sK3,X0)
| ~ member(sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),X0) ),
inference(global_subsumption_just,[status(thm)],[c_46560,c_561,c_566,c_576,c_20987,c_46560]) ).
tcf(c_47508,plain,
( ( sK9(sK1,sK0,sK3,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)) = sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)) )
| ~ injective(sK1,sK3,sK4) ),
inference(superposition,[status(thm)],[c_37408,c_47498]) ).
tcf(c_47509,plain,
sK9(sK1,sK0,sK3,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)) = sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),
inference(forward_subsumption_resolution,[status(thm)],[c_47508,c_53]) ).
tcf(c_47511,plain,
( injective(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)
| apply(sK0,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)))
| ~ member(sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK4)
| ~ member(sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK2) ),
inference(superposition,[status(thm)],[c_47509,c_1195]) ).
tcf(c_47513,plain,
( apply(sK0,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK5(sK0,sK3,sK6(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)))
| ~ member(sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_47511,c_49,c_37408]) ).
tcf(c_47516,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_47513,c_24152,c_1664,c_1665,c_586,c_571,c_566,c_52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET716+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/15.60 % Computer : n016.cluster.edu
% 0.10/15.60 % Model : x86_64 x86_64
% 0.10/15.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/15.60 % Memory : 8046.5625MB
% 0.10/15.60 % OS : Linux 6.8.0-71-generic
% 0.10/15.60 % CPULimit : 300
% 0.10/15.60 % WCLimit : 300
% 0.10/15.60 % DateTime : Thu Sep 24 11:50:16 UTC 2026
% 0.10/15.61 % CPUTime :
% 0.10/15.61 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/15.65 Running first-order theorem proving
% 0.10/15.65 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/15.66
% 0.10/15.66 % ======== iProver multi-core TPTP/SMT =========
% 0.10/15.66
% 0.10/15.66 % Detected problem language: tptp
% 0.10/15.67 % Proving...
% 22.93/20.50 % SZS status Started for theBenchmark.p
% 22.93/20.50 % SZS status Theorem for theBenchmark.p
% 22.93/20.50
% 22.93/20.50 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 22.93/20.50
% 22.93/20.50 % ------ iProver source info
% 22.93/20.50
% 22.93/20.50 % git: date: 2026-07-19 20:42:38 +0200
% 22.93/20.50 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 22.93/20.50 % git: non_committed_changes: false
% 22.93/20.50
% 22.93/20.50 % ------ Parsing...
% 22.93/20.50 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 22.93/20.50
% 22.93/20.50 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e %
% 22.93/20.50
% 22.93/20.50 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 22.93/20.50
% 22.93/20.50 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 22.93/20.50 % ------ Proving...
% 22.93/20.50 % ------ Problem Properties
% 22.93/20.50
% 22.93/20.50 %
% 22.93/20.50 % clauses 20
% 22.93/20.50 % conjectures 3
% 22.93/20.50 % EPR 5
% 22.93/20.50 % Horn 15
% 22.93/20.50 % unary 3
% 22.93/20.50 % binary 10
% 22.93/20.50 % lits 60
% 22.93/20.50 % lits eq 4
% 22.93/20.50 % fd_pure 0
% 22.93/20.50 % fd_pseudo 0
% 22.93/20.50 % fd_cond 0
% 22.93/20.50 % fd_pseudo_cond 3
% 22.93/20.50 % AC symbols 0
% 22.93/20.50
% 22.93/20.50 % ------ Schedule dynamic 5 is on
% 22.93/20.50
% 22.93/20.50 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 22.93/20.50
% 22.93/20.50
% 22.93/20.50 % ------
% 22.93/20.50 % Current options:
% 22.93/20.50 % ------
% 22.93/20.50
% 22.93/20.50
% 22.93/20.50 %
% 22.93/20.50
% 22.93/20.50 % ------ Proving...
% 22.93/20.50 %
% 22.93/20.50
% 22.93/20.50 % SZS status Theorem for theBenchmark.p
% 22.93/20.50
% 22.93/20.50 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 22.93/20.51
% 22.93/20.51
%------------------------------------------------------------------------------