%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET749+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 : n003.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 02:48:11 PM UTC 2026
% Result : Theorem 7.59s 1.99s
% Output : CNFRefutation 7.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 5
% Syntax : Number of formulae : 146 ( 35 unt; 0 def)
% Number of atoms : 615 ( 94 equ)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 806 ( 337 ~; 343 |; 100 &)
% ( 7 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 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 : 7 ( 5 usr; 1 prp; 0-5 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-5 aty)
% Number of variables : 507 ( 0 sgn 473 !; 34 ?; 217 :)
% 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(f26,axiom,
! [X0,X1,X2,X3,X4] :
( increasing(X0,X1,X2,X3,X4)
<=> ! [X5,X6,X7,X8] :
( ( apply(X0,X7,X8)
& apply(X0,X5,X6)
& apply(X2,X5,X7)
& member(X8,X3)
& member(X7,X1)
& member(X6,X3)
& member(X5,X1) )
=> apply(X4,X6,X8) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax',increasing_function) ).
fof(f27,axiom,
! [X0,X1,X2,X3,X4] :
( decreasing(X0,X1,X2,X3,X4)
<=> ! [X5,X6,X7,X8] :
( ( apply(X0,X7,X8)
& apply(X0,X5,X6)
& apply(X2,X5,X7)
& member(X8,X3)
& member(X7,X1)
& member(X6,X3)
& member(X5,X1) )
=> apply(X4,X8,X6) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax',decreasing_function) ).
fof(f29,conjecture,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ( decreasing(X1,X3,X6,X4,X7)
& decreasing(X0,X2,X5,X3,X6)
& maps(X1,X3,X4)
& maps(X0,X2,X3) )
=> increasing(compose_function(X1,X0,X2,X3,X4),X2,X5,X4,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thII40) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ( decreasing(X1,X3,X6,X4,X7)
& decreasing(X0,X2,X5,X3,X6)
& maps(X1,X3,X4)
& maps(X0,X2,X3) )
=> increasing(compose_function(X1,X0,X2,X3,X4),X2,X5,X4,X7) ),
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] :
( decreasing(X0,X1,X2,X3,X4)
=> ! [X5,X6,X7,X8] :
( ( apply(X0,X7,X8)
& apply(X0,X5,X6)
& apply(X2,X5,X7)
& member(X8,X3)
& member(X7,X1)
& member(X6,X3)
& member(X5,X1) )
=> apply(X4,X8,X6) ) ),
inference(unused_predicate_definition_removal,[],[f27]) ).
fof(f33,plain,
! [X0,X1,X2,X3,X4] :
( ! [X5,X6,X7,X8] :
( ( apply(X0,X7,X8)
& apply(X0,X5,X6)
& apply(X2,X5,X7)
& member(X8,X3)
& member(X7,X1)
& member(X6,X3)
& member(X5,X1) )
=> apply(X4,X6,X8) )
=> increasing(X0,X1,X2,X3,X4) ),
inference(unused_predicate_definition_removal,[],[f26]) ).
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(unused_predicate_definition_removal,[],[f31]) ).
fof(f35,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7] :
( decreasing(X1,X3,X6,X4,X7)
& decreasing(X0,X2,X5,X3,X6)
& maps(X1,X3,X4)
& maps(X0,X2,X3)
& ~ increasing(compose_function(X1,X0,X2,X3,X4),X2,X5,X4,X7) ),
inference(ennf_transformation,[],[f30]) ).
fof(f36,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7] :
( decreasing(X1,X3,X6,X4,X7)
& decreasing(X0,X2,X5,X3,X6)
& maps(X1,X3,X4)
& maps(X0,X2,X3)
& ~ increasing(compose_function(X1,X0,X2,X3,X4),X2,X5,X4,X7) ),
inference(flattening,[],[f35]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ~ maps(X0,X1,X2)
| ( ! [X5,X6,X7] :
( ~ member(X7,X2)
| ~ member(X6,X2)
| ~ member(X5,X1)
| ~ apply(X0,X5,X7)
| ~ apply(X0,X5,X6)
| X6 = X7 )
& ! [X3] :
( ~ member(X3,X1)
| ? [X4] :
( apply(X0,X3,X4)
& member(X4,X2) ) ) ) ),
inference(ennf_transformation,[],[f34]) ).
fof(f38,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,[],[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,
! [X0,X1,X2,X3,X4] :
( ? [X5,X6,X7,X8] :
( apply(X0,X7,X8)
& apply(X0,X5,X6)
& apply(X2,X5,X7)
& member(X8,X3)
& member(X7,X1)
& member(X6,X3)
& member(X5,X1)
& ~ apply(X4,X6,X8) )
| increasing(X0,X1,X2,X3,X4) ),
inference(ennf_transformation,[],[f33]) ).
fof(f42,plain,
! [X0,X1,X2,X3,X4] :
( ? [X5,X6,X7,X8] :
( apply(X0,X7,X8)
& apply(X0,X5,X6)
& apply(X2,X5,X7)
& member(X8,X3)
& member(X7,X1)
& member(X6,X3)
& member(X5,X1)
& ~ apply(X4,X6,X8) )
| increasing(X0,X1,X2,X3,X4) ),
inference(flattening,[],[f41]) ).
fof(f43,plain,
! [X0,X1,X2,X3,X4] :
( ~ decreasing(X0,X1,X2,X3,X4)
| ! [X5,X6,X7,X8] :
( ~ apply(X0,X7,X8)
| ~ apply(X0,X5,X6)
| ~ apply(X2,X5,X7)
| ~ member(X8,X3)
| ~ member(X7,X1)
| ~ member(X6,X3)
| ~ member(X5,X1)
| apply(X4,X8,X6) ) ),
inference(ennf_transformation,[],[f32]) ).
fof(f44,plain,
! [X0,X1,X2,X3,X4] :
( ~ decreasing(X0,X1,X2,X3,X4)
| ! [X5,X6,X7,X8] :
( ~ apply(X0,X7,X8)
| ~ apply(X0,X5,X6)
| ~ apply(X2,X5,X7)
| ~ member(X8,X3)
| ~ member(X7,X1)
| ~ member(X6,X3)
| ~ member(X5,X1)
| apply(X4,X8,X6) ) ),
inference(flattening,[],[f43]) ).
fof(f45,plain,
( decreasing(sK1,sK3,sK6,sK4,sK7)
& decreasing(sK0,sK2,sK5,sK3,sK6)
& maps(sK1,sK3,sK4)
& maps(sK0,sK2,sK3)
& ~ increasing(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5),skolemize(X6,sK6),skolemize(X7,sK7)],[f36]) ).
fof(f46,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,sK8(X0,X2,X3))
& member(sK8(X0,X2,X3),X2) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X4,sK8(X0,X2,X3))],[f38]) ).
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)
| ? [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(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)
| ? [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,[],[f47]) ).
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)
| ( 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))],[f48]) ).
fof(f50,plain,
! [X0,X1,X2,X3,X4] :
( ( apply(X0,sK12(X0,X1,X2,X3,X4),sK13(X0,X1,X2,X3,X4))
& apply(X0,sK10(X0,X1,X2,X3,X4),sK11(X0,X1,X2,X3,X4))
& apply(X2,sK10(X0,X1,X2,X3,X4),sK12(X0,X1,X2,X3,X4))
& member(sK13(X0,X1,X2,X3,X4),X3)
& member(sK12(X0,X1,X2,X3,X4),X1)
& member(sK11(X0,X1,X2,X3,X4),X3)
& member(sK10(X0,X1,X2,X3,X4),X1)
& ~ apply(X4,sK11(X0,X1,X2,X3,X4),sK13(X0,X1,X2,X3,X4)) )
| increasing(X0,X1,X2,X3,X4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13]),skolemize(X5,sK10(X0,X1,X2,X3,X4)),skolemize(X6,sK11(X0,X1,X2,X3,X4)),skolemize(X7,sK12(X0,X1,X2,X3,X4)),skolemize(X8,sK13(X0,X1,X2,X3,X4))],[f42]) ).
fof(f51,plain,
decreasing(sK1,sK3,sK6,sK4,sK7),
inference(cnf_transformation,[],[f45]) ).
fof(f52,plain,
decreasing(sK0,sK2,sK5,sK3,sK6),
inference(cnf_transformation,[],[f45]) ).
fof(f53,plain,
maps(sK1,sK3,sK4),
inference(cnf_transformation,[],[f45]) ).
fof(f54,plain,
maps(sK0,sK2,sK3),
inference(cnf_transformation,[],[f45]) ).
fof(f55,plain,
~ increasing(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),
inference(cnf_transformation,[],[f45]) ).
fof(f56,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,[],[f46]) ).
fof(f57,plain,
! [X2,X3,X0,X1] :
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| apply(X0,X3,sK8(X0,X2,X3)) ),
inference(cnf_transformation,[],[f46]) ).
fof(f58,plain,
! [X2,X3,X0,X1] :
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| member(sK8(X0,X2,X3),X2) ),
inference(cnf_transformation,[],[f46]) ).
fof(f59,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,[],[f49]) ).
fof(f60,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,[],[f49]) ).
fof(f61,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,[],[f49]) ).
fof(f63,plain,
! [X2,X3,X0,X1,X4] :
( apply(X0,sK12(X0,X1,X2,X3,X4),sK13(X0,X1,X2,X3,X4))
| increasing(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f50]) ).
fof(f64,plain,
! [X2,X3,X0,X1,X4] :
( apply(X0,sK10(X0,X1,X2,X3,X4),sK11(X0,X1,X2,X3,X4))
| increasing(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f50]) ).
fof(f65,plain,
! [X2,X3,X0,X1,X4] :
( apply(X2,sK10(X0,X1,X2,X3,X4),sK12(X0,X1,X2,X3,X4))
| increasing(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f50]) ).
fof(f66,plain,
! [X2,X3,X0,X1,X4] :
( member(sK13(X0,X1,X2,X3,X4),X3)
| increasing(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f50]) ).
fof(f67,plain,
! [X2,X3,X0,X1,X4] :
( member(sK12(X0,X1,X2,X3,X4),X1)
| increasing(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f50]) ).
fof(f68,plain,
! [X2,X3,X0,X1,X4] :
( member(sK11(X0,X1,X2,X3,X4),X3)
| increasing(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f50]) ).
fof(f69,plain,
! [X2,X3,X0,X1,X4] :
( member(sK10(X0,X1,X2,X3,X4),X1)
| increasing(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f50]) ).
fof(f70,plain,
! [X2,X3,X0,X1,X4] :
( ~ apply(X4,sK11(X0,X1,X2,X3,X4),sK13(X0,X1,X2,X3,X4))
| increasing(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f50]) ).
fof(f71,plain,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( ~ decreasing(X0,X1,X2,X3,X4)
| ~ apply(X0,X7,X8)
| ~ apply(X0,X5,X6)
| ~ apply(X2,X5,X7)
| ~ member(X8,X3)
| ~ member(X7,X1)
| ~ member(X6,X3)
| ~ member(X5,X1)
| apply(X4,X8,X6) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_49,negated_conjecture,
~ increasing(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),
inference(cnf_transformation,[],[f55]) ).
tcf(c_50,negated_conjecture,
maps(sK0,sK2,sK3),
inference(cnf_transformation,[],[f54]) ).
tcf(c_51,negated_conjecture,
maps(sK1,sK3,sK4),
inference(cnf_transformation,[],[f53]) ).
tcf(c_52,negated_conjecture,
decreasing(sK0,sK2,sK5,sK3,sK6),
inference(cnf_transformation,[],[f52]) ).
tcf(c_53,negated_conjecture,
decreasing(sK1,sK3,sK6,sK4,sK7),
inference(cnf_transformation,[],[f51]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK8(X0,X2,X3),X2)
| ~ member(X3,X1)
| ~ maps(X0,X1,X2) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,X3,sK8(X0,X2,X3))
| ~ member(X3,X1)
| ~ maps(X0,X1,X2) ),
inference(cnf_transformation,[],[f57]) ).
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,[],[f56]) ).
tcf(c_58,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,[],[f61]) ).
tcf(c_59,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,[],[f60]) ).
tcf(c_60,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,[],[f59]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( increasing(X1,X2,X3,X4,X0)
| ~ apply(X0,sK11(X1,X2,X3,X4,X0),sK13(X1,X2,X3,X4,X0)) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( increasing(X0,X1,X2,X3,X4)
| member(sK10(X0,X1,X2,X3,X4),X1) ),
inference(cnf_transformation,[],[f69]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( increasing(X0,X1,X2,X3,X4)
| member(sK11(X0,X1,X2,X3,X4),X3) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( increasing(X0,X1,X2,X3,X4)
| member(sK12(X0,X1,X2,X3,X4),X1) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( increasing(X0,X1,X2,X3,X4)
| member(sK13(X0,X1,X2,X3,X4),X3) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( increasing(X1,X2,X0,X3,X4)
| apply(X0,sK10(X1,X2,X0,X3,X4),sK12(X1,X2,X0,X3,X4)) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( increasing(X0,X1,X2,X3,X4)
| apply(X0,sK10(X0,X1,X2,X3,X4),sK11(X0,X1,X2,X3,X4)) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( increasing(X0,X1,X2,X3,X4)
| apply(X0,sK12(X0,X1,X2,X3,X4),sK13(X0,X1,X2,X3,X4)) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
( apply(X4,X6,X8)
| ~ member(X8,X3)
| ~ member(X7,X1)
| ~ member(X6,X3)
| ~ member(X5,X1)
| ~ apply(X2,X7,X5)
| ~ apply(X0,X7,X8)
| ~ apply(X0,X5,X6)
| ~ decreasing(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_326,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ apply(X4,sK11(X0,X1,X3,X2,X4),sK13(X0,X1,X3,X2,X4))
| ( X4 != sK7 )
| ( X3 != sK5 )
| ( X2 != sK4 )
| ( X1 != sK2 )
| ( compose_function(sK1,sK0,sK2,sK3,sK4) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_61]) ).
tcf(c_327,plain,
~ apply(sK7,sK11(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK13(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),
inference(unflattening,[status(thm)],[c_326]) ).
tcf(c_331,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apply(X0,sK12(X0,X1,X3,X2,X4),sK13(X0,X1,X3,X2,X4))
| ( X4 != sK7 )
| ( X3 != sK5 )
| ( X2 != sK4 )
| ( X1 != sK2 )
| ( compose_function(sK1,sK0,sK2,sK3,sK4) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_68]) ).
tcf(c_332,plain,
apply(compose_function(sK1,sK0,sK2,sK3,sK4),sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK13(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),
inference(unflattening,[status(thm)],[c_331]) ).
tcf(c_336,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apply(X0,sK10(X0,X1,X3,X2,X4),sK11(X0,X1,X3,X2,X4))
| ( X4 != sK7 )
| ( X3 != sK5 )
| ( X2 != sK4 )
| ( X1 != sK2 )
| ( compose_function(sK1,sK0,sK2,sK3,sK4) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_67]) ).
tcf(c_337,plain,
apply(compose_function(sK1,sK0,sK2,sK3,sK4),sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK11(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),
inference(unflattening,[status(thm)],[c_336]) ).
tcf(c_341,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(sK13(X0,X1,X3,X2,X4),X2)
| ( X4 != sK7 )
| ( X3 != sK5 )
| ( X2 != sK4 )
| ( X1 != sK2 )
| ( compose_function(sK1,sK0,sK2,sK3,sK4) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_65]) ).
tcf(c_342,plain,
member(sK13(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK4),
inference(unflattening,[status(thm)],[c_341]) ).
tcf(c_346,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(sK12(X0,X1,X3,X2,X4),X1)
| ( X4 != sK7 )
| ( X3 != sK5 )
| ( X2 != sK4 )
| ( X1 != sK2 )
| ( compose_function(sK1,sK0,sK2,sK3,sK4) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_64]) ).
tcf(c_347,plain,
member(sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK2),
inference(unflattening,[status(thm)],[c_346]) ).
tcf(c_351,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(sK11(X0,X1,X3,X2,X4),X2)
| ( X4 != sK7 )
| ( X3 != sK5 )
| ( X2 != sK4 )
| ( X1 != sK2 )
| ( compose_function(sK1,sK0,sK2,sK3,sK4) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_63]) ).
tcf(c_352,plain,
member(sK11(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK4),
inference(unflattening,[status(thm)],[c_351]) ).
tcf(c_356,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(sK10(X0,X1,X3,X2,X4),X1)
| ( X4 != sK7 )
| ( X3 != sK5 )
| ( X2 != sK4 )
| ( X1 != sK2 )
| ( compose_function(sK1,sK0,sK2,sK3,sK4) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_62]) ).
tcf(c_357,plain,
member(sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK2),
inference(unflattening,[status(thm)],[c_356]) ).
tcf(c_361,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apply(X3,sK10(X0,X1,X3,X2,X4),sK12(X0,X1,X3,X2,X4))
| ( X4 != sK7 )
| ( X3 != sK5 )
| ( X2 != sK4 )
| ( X1 != sK2 )
| ( compose_function(sK1,sK0,sK2,sK3,sK4) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_66]) ).
tcf(c_362,plain,
apply(sK5,sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),
inference(unflattening,[status(thm)],[c_361]) ).
tcf(c_374,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
( apply(X4,X6,X8)
| ~ member(X8,X2)
| ~ member(X7,X1)
| ~ member(X6,X2)
| ~ member(X5,X1)
| ~ apply(X3,X7,X5)
| ~ apply(X0,X7,X8)
| ~ apply(X0,X5,X6)
| ( X4 != sK6 )
| ( X3 != sK5 )
| ( X2 != sK3 )
| ( X1 != sK2 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_69]) ).
tcf(c_375,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(sK6,X1,X3)
| ~ member(X3,sK3)
| ~ member(X2,sK2)
| ~ member(X1,sK3)
| ~ member(X0,sK2)
| ~ apply(sK5,X2,X0)
| ~ apply(sK0,X2,X3)
| ~ apply(sK0,X0,X1) ),
inference(unflattening,[status(thm)],[c_374]) ).
tcf(c_401,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
( apply(X3,X6,X8)
| ~ member(X8,X2)
| ~ member(X7,X1)
| ~ member(X6,X2)
| ~ member(X5,X1)
| ~ apply(X4,X7,X5)
| ~ apply(X0,X7,X8)
| ~ apply(X0,X5,X6)
| ( X4 != sK6 )
| ( X3 != sK7 )
| ( X2 != sK4 )
| ( X1 != sK3 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_69]) ).
tcf(c_402,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(sK7,X1,X3)
| ~ member(X3,sK4)
| ~ member(X2,sK3)
| ~ member(X1,sK4)
| ~ member(X0,sK3)
| ~ apply(sK6,X2,X0)
| ~ apply(sK1,X2,X3)
| ~ apply(sK1,X0,X1) ),
inference(unflattening,[status(thm)],[c_401]) ).
tcf(c_444,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_445,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_444]) ).
tcf(c_465,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,X3,sK8(X0,X2,X3))
| ~ member(X3,X1)
| ( X2 != sK3 )
| ( X1 != sK2 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_55]) ).
tcf(c_466,plain,
! [X0: $i] :
( apply(sK0,X0,sK8(sK0,sK3,X0))
| ~ member(X0,sK2) ),
inference(unflattening,[status(thm)],[c_465]) ).
tcf(c_474,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK8(X0,X2,X3),X2)
| ~ member(X3,X1)
| ( X2 != sK3 )
| ( X1 != sK2 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_54]) ).
tcf(c_475,plain,
! [X0: $i] :
( member(sK8(sK0,sK3,X0),sK3)
| ~ member(X0,sK2) ),
inference(unflattening,[status(thm)],[c_474]) ).
tcf(c_483,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_484,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_483]) ).
tcf(c_504,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,X3,sK8(X0,X2,X3))
| ~ member(X3,X1)
| ( X2 != sK4 )
| ( X1 != sK3 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_55]) ).
tcf(c_505,plain,
! [X0: $i] :
( apply(sK1,X0,sK8(sK1,sK4,X0))
| ~ member(X0,sK3) ),
inference(unflattening,[status(thm)],[c_504]) ).
tcf(c_513,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK8(X0,X2,X3),X2)
| ~ member(X3,X1)
| ( X2 != sK4 )
| ( X1 != sK3 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_54]) ).
tcf(c_514,plain,
! [X0: $i] :
( member(sK8(sK1,sK4,X0),sK4)
| ~ member(X0,sK3) ),
inference(unflattening,[status(thm)],[c_513]) ).
tcf(c_1321,plain,
! [X0: $i,X1: $i] :
( ( sK8(sK0,sK3,X0) = X1 )
| ~ member(X1,sK3)
| ~ member(X0,sK2)
| ~ apply(sK0,X0,X1)
| ~ member(sK8(sK0,sK3,X0),sK3) ),
inference(superposition,[status(thm)],[c_466,c_445]) ).
tcf(c_1340,plain,
! [X0: $i,X1: $i] :
( ( sK8(sK1,sK4,X0) = X1 )
| ~ member(X1,sK4)
| ~ member(X0,sK3)
| ~ apply(sK1,X0,X1)
| ~ member(sK8(sK1,sK4,X0),sK4) ),
inference(superposition,[status(thm)],[c_505,c_484]) ).
tcf(c_1347,plain,
! [X0: $i,X1: $i] :
( ( sK8(sK0,sK3,X0) = X1 )
| ~ member(X1,sK3)
| ~ member(X0,sK2)
| ~ apply(sK0,X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_1321,c_475,c_1321]) ).
tcf(c_1360,plain,
( apply(sK1,sK9(sK1,sK0,sK3,sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK13(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),sK13(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7))
| ~ member(sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK2)
| ~ member(sK13(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK4) ),
inference(superposition,[status(thm)],[c_332,c_60]) ).
tcf(c_1361,plain,
( apply(sK0,sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK9(sK1,sK0,sK3,sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK13(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)))
| ~ member(sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK2)
| ~ member(sK13(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK4) ),
inference(superposition,[status(thm)],[c_332,c_59]) ).
tcf(c_1362,plain,
( member(sK9(sK1,sK0,sK3,sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK13(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),sK3)
| ~ member(sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK2)
| ~ member(sK13(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK4) ),
inference(superposition,[status(thm)],[c_332,c_58]) ).
tcf(c_1363,plain,
member(sK9(sK1,sK0,sK3,sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK13(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),sK3),
inference(forward_subsumption_resolution,[status(thm)],[c_1362,c_347,c_342]) ).
tcf(c_1364,plain,
apply(sK0,sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK9(sK1,sK0,sK3,sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK13(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7))),
inference(forward_subsumption_resolution,[status(thm)],[c_1361,c_347,c_342]) ).
tcf(c_1365,plain,
apply(sK1,sK9(sK1,sK0,sK3,sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK13(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),sK13(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),
inference(forward_subsumption_resolution,[status(thm)],[c_1360,c_347,c_342]) ).
tcf(c_1373,plain,
( apply(sK1,sK9(sK1,sK0,sK3,sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK11(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),sK11(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7))
| ~ member(sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK2)
| ~ member(sK11(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK4) ),
inference(superposition,[status(thm)],[c_337,c_60]) ).
tcf(c_1374,plain,
( apply(sK0,sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK9(sK1,sK0,sK3,sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK11(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)))
| ~ member(sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK2)
| ~ member(sK11(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK4) ),
inference(superposition,[status(thm)],[c_337,c_59]) ).
tcf(c_1375,plain,
( member(sK9(sK1,sK0,sK3,sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK11(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),sK3)
| ~ member(sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK2)
| ~ member(sK11(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK4) ),
inference(superposition,[status(thm)],[c_337,c_58]) ).
tcf(c_1376,plain,
member(sK9(sK1,sK0,sK3,sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK11(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),sK3),
inference(forward_subsumption_resolution,[status(thm)],[c_1375,c_357,c_352]) ).
tcf(c_1377,plain,
apply(sK0,sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK9(sK1,sK0,sK3,sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK11(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7))),
inference(forward_subsumption_resolution,[status(thm)],[c_1374,c_357,c_352]) ).
tcf(c_1378,plain,
apply(sK1,sK9(sK1,sK0,sK3,sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK11(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),sK11(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),
inference(forward_subsumption_resolution,[status(thm)],[c_1373,c_357,c_352]) ).
tcf(c_1426,plain,
! [X0: $i,X1: $i,X2: $i] :
( apply(sK7,sK8(sK1,sK4,X0),X2)
| ~ member(X2,sK4)
| ~ member(X1,sK3)
| ~ member(X0,sK3)
| ~ apply(sK6,X1,X0)
| ~ apply(sK1,X1,X2)
| ~ member(sK8(sK1,sK4,X0),sK4) ),
inference(superposition,[status(thm)],[c_505,c_402]) ).
tcf(c_1435,plain,
! [X0: $i,X1: $i] :
( ( sK8(sK1,sK4,X0) = X1 )
| ~ member(X1,sK4)
| ~ member(X0,sK3)
| ~ apply(sK1,X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_1340,c_514,c_1340]) ).
tcf(c_1699,plain,
( member(sK8(sK0,sK3,sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),sK3)
| ~ member(sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK2) ),
inference(instantiation,[status(thm)],[c_475]) ).
tcf(c_1700,plain,
( member(sK8(sK0,sK3,sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),sK3)
| ~ member(sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK2) ),
inference(instantiation,[status(thm)],[c_475]) ).
tcf(c_2278,plain,
! [X0: $i,X1: $i,X2: $i] :
( apply(sK7,sK8(sK1,sK4,X0),X2)
| ~ member(X2,sK4)
| ~ member(X1,sK3)
| ~ member(X0,sK3)
| ~ apply(sK6,X1,X0)
| ~ apply(sK1,X1,X2) ),
inference(global_subsumption_just,[status(thm)],[c_1426,c_514,c_1426]) ).
tcf(c_2279,plain,
! [X0: $i,X1: $i,X2: $i] :
( apply(sK7,sK8(sK1,sK4,X2),X1)
| ~ member(X2,sK3)
| ~ member(X1,sK4)
| ~ member(X0,sK3)
| ~ apply(sK6,X0,X2)
| ~ apply(sK1,X0,X1) ),
inference(renaming,[status(thm)],[c_2278]) ).
tcf(c_2293,plain,
! [X0: $i,X1: $i] :
( apply(sK7,sK8(sK1,sK4,X1),sK8(sK1,sK4,X0))
| ~ member(X1,sK3)
| ~ member(X0,sK3)
| ~ apply(sK6,X0,X1)
| ~ member(sK8(sK1,sK4,X0),sK4) ),
inference(superposition,[status(thm)],[c_505,c_2279]) ).
tcf(c_2300,plain,
! [X0: $i,X1: $i] :
( apply(sK7,sK8(sK1,sK4,X1),sK8(sK1,sK4,X0))
| ~ member(X1,sK3)
| ~ member(X0,sK3)
| ~ apply(sK6,X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_2293,c_514,c_2293]) ).
tcf(c_2407,plain,
( ( sK9(sK1,sK0,sK3,sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK13(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)) = sK8(sK0,sK3,sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)) )
| ~ member(sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK2)
| ~ member(sK9(sK1,sK0,sK3,sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK13(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),sK3) ),
inference(superposition,[status(thm)],[c_1364,c_1347]) ).
tcf(c_2409,plain,
sK9(sK1,sK0,sK3,sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK13(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)) = sK8(sK0,sK3,sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),
inference(forward_subsumption_resolution,[status(thm)],[c_2407,c_347,c_1363]) ).
tcf(c_2429,plain,
apply(sK0,sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK8(sK0,sK3,sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7))),
inference(demodulation,[status(thm)],[c_1364,c_2409]) ).
tcf(c_2430,plain,
member(sK8(sK0,sK3,sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),sK3),
inference(demodulation,[status(thm)],[c_1363,c_2409]) ).
tcf(c_2449,plain,
apply(sK1,sK8(sK0,sK3,sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),sK13(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),
inference(light_normalisation,[status(thm)],[c_1365,c_2409]) ).
tcf(c_2452,plain,
( ( sK8(sK1,sK4,sK8(sK0,sK3,sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7))) = sK13(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7) )
| ~ member(sK13(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK4)
| ~ member(sK8(sK0,sK3,sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),sK3) ),
inference(superposition,[status(thm)],[c_2449,c_1435]) ).
tcf(c_2455,plain,
( ( sK8(sK1,sK4,sK8(sK0,sK3,sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7))) = sK13(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7) )
| ~ member(sK8(sK0,sK3,sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2452,c_342]) ).
tcf(c_2487,plain,
( ( sK9(sK1,sK0,sK3,sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK11(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)) = sK8(sK0,sK3,sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)) )
| ~ member(sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK2)
| ~ member(sK9(sK1,sK0,sK3,sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK11(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),sK3) ),
inference(superposition,[status(thm)],[c_1377,c_1347]) ).
tcf(c_2489,plain,
sK9(sK1,sK0,sK3,sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK11(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)) = sK8(sK0,sK3,sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),
inference(forward_subsumption_resolution,[status(thm)],[c_2487,c_357,c_1376]) ).
tcf(c_2509,plain,
apply(sK0,sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK8(sK0,sK3,sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7))),
inference(demodulation,[status(thm)],[c_1377,c_2489]) ).
tcf(c_2510,plain,
member(sK8(sK0,sK3,sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),sK3),
inference(demodulation,[status(thm)],[c_1376,c_2489]) ).
tcf(c_2527,plain,
apply(sK1,sK8(sK0,sK3,sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),sK11(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),
inference(light_normalisation,[status(thm)],[c_1378,c_2489]) ).
tcf(c_2530,plain,
( ( sK8(sK1,sK4,sK8(sK0,sK3,sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7))) = sK11(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7) )
| ~ member(sK11(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK4)
| ~ member(sK8(sK0,sK3,sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),sK3) ),
inference(superposition,[status(thm)],[c_2527,c_1435]) ).
tcf(c_2533,plain,
( ( sK8(sK1,sK4,sK8(sK0,sK3,sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7))) = sK11(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7) )
| ~ member(sK8(sK0,sK3,sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2530,c_352]) ).
tcf(c_2682,plain,
! [X0: $i,X1: $i] :
( apply(sK6,sK8(sK0,sK3,sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),X1)
| ~ member(X1,sK3)
| ~ member(X0,sK2)
| ~ apply(sK0,X0,X1)
| ~ member(sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK2)
| ~ apply(sK5,X0,sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7))
| ~ member(sK8(sK0,sK3,sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),sK3) ),
inference(superposition,[status(thm)],[c_2429,c_375]) ).
tcf(c_2698,plain,
! [X0: $i,X1: $i] :
( apply(sK6,sK8(sK0,sK3,sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),X1)
| ~ member(X1,sK3)
| ~ member(X0,sK2)
| ~ apply(sK0,X0,X1)
| ~ apply(sK5,X0,sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2682,c_347,c_2430]) ).
tcf(c_6739,plain,
! [X0: $i] :
( apply(sK6,sK8(sK0,sK3,sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),X0)
| ~ member(X0,sK3)
| ~ member(sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK2)
| ~ apply(sK0,sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),X0) ),
inference(superposition,[status(thm)],[c_362,c_2698]) ).
tcf(c_6740,plain,
! [X0: $i] :
( apply(sK6,sK8(sK0,sK3,sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),X0)
| ~ member(X0,sK3)
| ~ apply(sK0,sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6739,c_357]) ).
tcf(c_8621,plain,
sK8(sK1,sK4,sK8(sK0,sK3,sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7))) = sK13(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),
inference(global_subsumption_just,[status(thm)],[c_2455,c_347,c_1699,c_2455]) ).
tcf(c_9025,plain,
sK8(sK1,sK4,sK8(sK0,sK3,sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7))) = sK11(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),
inference(global_subsumption_just,[status(thm)],[c_2533,c_357,c_1700,c_2533]) ).
tcf(c_9047,plain,
! [X0: $i] :
( apply(sK7,sK11(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK8(sK1,sK4,X0))
| ~ member(X0,sK3)
| ~ member(sK8(sK0,sK3,sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),sK3)
| ~ apply(sK6,X0,sK8(sK0,sK3,sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7))) ),
inference(superposition,[status(thm)],[c_9025,c_2300]) ).
tcf(c_9050,plain,
! [X0: $i] :
( apply(sK7,sK11(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK8(sK1,sK4,X0))
| ~ member(X0,sK3)
| ~ apply(sK6,X0,sK8(sK0,sK3,sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9047,c_2510]) ).
tcf(c_10426,plain,
( apply(sK7,sK11(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK8(sK1,sK4,sK8(sK0,sK3,sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7))))
| ~ member(sK8(sK0,sK3,sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),sK3)
| ~ member(sK8(sK0,sK3,sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),sK3)
| ~ apply(sK0,sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK8(sK0,sK3,sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7))) ),
inference(superposition,[status(thm)],[c_6740,c_9050]) ).
tcf(c_10433,plain,
( apply(sK7,sK11(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK13(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7))
| ~ member(sK8(sK0,sK3,sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),sK3)
| ~ member(sK8(sK0,sK3,sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),sK3)
| ~ apply(sK0,sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK8(sK0,sK3,sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7))) ),
inference(light_normalisation,[status(thm)],[c_10426,c_8621]) ).
tcf(c_10434,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_10433,c_327,c_2430,c_2510,c_2509]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET749+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.18/0.44 % Computer : n003.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Thu Sep 24 11:52:52 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.18/0.50 Running first-order theorem proving
% 0.18/0.50 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
% 0.26/0.52
% 0.26/0.52 % ======== iProver multi-core TPTP/SMT =========
% 0.26/0.52
% 0.26/0.52 % Detected problem language: tptp
% 0.26/0.54 % Proving...
% 7.59/1.99 % SZS status Started for theBenchmark.p
% 7.59/1.99 % SZS status Theorem for theBenchmark.p
% 7.59/1.99
% 7.59/1.99 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.59/1.99
% 7.59/1.99 % ------ iProver source info
% 7.59/1.99
% 7.59/1.99 % git: date: 2026-07-19 20:42:38 +0200
% 7.59/1.99 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.59/1.99 % git: non_committed_changes: false
% 7.59/1.99
% 7.59/1.99 % ------ Parsing...
% 7.59/1.99 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.59/1.99
% 7.59/1.99 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e %
% 7.59/1.99
% 7.59/1.99 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 7.59/1.99
% 7.59/1.99 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.59/1.99 % ------ Proving...
% 7.59/1.99 % ------ Problem Properties
% 7.59/1.99
% 7.59/1.99 %
% 7.59/1.99 % clauses 20
% 7.59/1.99 % conjectures 0
% 7.59/1.99 % EPR 4
% 7.59/1.99 % Horn 20
% 7.59/1.99 % unary 8
% 7.59/1.99 % binary 4
% 7.59/1.99 % lits 62
% 7.59/1.99 % lits eq 2
% 7.59/1.99 % fd_pure 0
% 7.59/1.99 % fd_pseudo 0
% 7.59/1.99 % fd_cond 0
% 7.59/1.99 % fd_pseudo_cond 2
% 7.59/1.99 % AC symbols 0
% 7.59/1.99
% 7.59/1.99 % ------ Schedule dynamic 5 is on
% 7.59/1.99
% 7.59/1.99 % ------ no conjectures: strip conj schedule
% 7.59/1.99
% 7.59/1.99 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 7.59/1.99
% 7.59/1.99
% 7.59/1.99 % ------
% 7.59/1.99 % Current options:
% 7.59/1.99 % ------
% 7.59/1.99
% 7.59/1.99
% 7.59/1.99 %
% 7.59/1.99
% 7.59/1.99 % ------ Proving...
% 7.59/1.99 %
% 7.59/1.99
% 7.59/1.99 % SZS status Theorem for theBenchmark.p
% 7.59/1.99
% 7.59/1.99 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.59/2.00
% 7.59/2.00
%------------------------------------------------------------------------------