%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET746+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 02:48:00 PM UTC 2026
% Result : Theorem 68.21s 10.83s
% Output : CNFRefutation 68.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 98 ( 15 unt; 0 def)
% Number of atoms : 439 ( 40 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 589 ( 248 ~; 267 |; 64 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 9 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-5 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-5 aty)
% Number of variables : 444 ( 0 sgn 415 !; 29 ?; 230 :)
% Comments :
%------------------------------------------------------------------------------
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(f29,conjecture,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ( increasing(X1,X3,X6,X4,X7)
& increasing(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',thII37) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ( increasing(X1,X3,X6,X4,X7)
& increasing(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(f37,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ member(X6,X4)
| ~ member(X5,X2)
| ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
<=> ? [X7] :
( apply(X0,X7,X6)
& apply(X1,X5,X7)
& member(X7,X3) ) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f38,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,[],[f37]) ).
fof(f41,plain,
! [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) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f42,plain,
! [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) ) ),
inference(flattening,[],[f41]) ).
fof(f43,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7] :
( increasing(X1,X3,X6,X4,X7)
& increasing(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(f44,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7] :
( increasing(X1,X3,X6,X4,X7)
& increasing(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,[],[f43]) ).
fof(f65,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,[],[f38]) ).
fof(f66,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,[],[f65]) ).
fof(f67,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,sK4(X0,X1,X3,X5,X6),X6)
& apply(X1,X5,sK4(X0,X1,X3,X5,X6))
& member(sK4(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,[sK4]),skolemize(X8,sK4(X0,X1,X3,X5,X6))],[f66]) ).
fof(f83,plain,
! [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) ) )
& ( ? [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(nnf_transformation,[],[f42]) ).
fof(f84,plain,
! [X0,X1,X2,X3,X4] :
( ( ~ increasing(X0,X1,X2,X3,X4)
| ! [X9,X10,X11,X12] :
( ~ apply(X0,X11,X12)
| ~ apply(X0,X9,X10)
| ~ apply(X2,X9,X11)
| ~ member(X12,X3)
| ~ member(X11,X1)
| ~ member(X10,X3)
| ~ member(X9,X1)
| apply(X4,X10,X12) ) )
& ( ? [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(rectify,[],[f83]) ).
fof(f85,plain,
! [X0,X1,X2,X3,X4] :
( ( ~ increasing(X0,X1,X2,X3,X4)
| ! [X9,X10,X11,X12] :
( ~ apply(X0,X11,X12)
| ~ apply(X0,X9,X10)
| ~ apply(X2,X9,X11)
| ~ member(X12,X3)
| ~ member(X11,X1)
| ~ member(X10,X3)
| ~ member(X9,X1)
| apply(X4,X10,X12) ) )
& ( ( apply(X0,sK11(X0,X1,X2,X3,X4),sK12(X0,X1,X2,X3,X4))
& apply(X0,sK9(X0,X1,X2,X3,X4),sK10(X0,X1,X2,X3,X4))
& apply(X2,sK9(X0,X1,X2,X3,X4),sK11(X0,X1,X2,X3,X4))
& member(sK12(X0,X1,X2,X3,X4),X3)
& member(sK11(X0,X1,X2,X3,X4),X1)
& member(sK10(X0,X1,X2,X3,X4),X3)
& member(sK9(X0,X1,X2,X3,X4),X1)
& ~ apply(X4,sK10(X0,X1,X2,X3,X4),sK12(X0,X1,X2,X3,X4)) )
| increasing(X0,X1,X2,X3,X4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12]),skolemize(X5,sK9(X0,X1,X2,X3,X4)),skolemize(X6,sK10(X0,X1,X2,X3,X4)),skolemize(X7,sK11(X0,X1,X2,X3,X4)),skolemize(X8,sK12(X0,X1,X2,X3,X4))],[f84]) ).
fof(f86,plain,
( increasing(sK14,sK16,sK19,sK17,sK20)
& increasing(sK13,sK15,sK18,sK16,sK19)
& maps(sK14,sK16,sK17)
& maps(sK13,sK15,sK16)
& ~ increasing(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14,sK15,sK16,sK17,sK18,sK19,sK20]),skolemize(X0,sK13),skolemize(X1,sK14),skolemize(X2,sK15),skolemize(X3,sK16),skolemize(X4,sK17),skolemize(X5,sK18),skolemize(X6,sK19),skolemize(X7,sK20)],[f44]) ).
fof(f116,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,sK4(X0,X1,X3,X5,X6),X6) ),
inference(cnf_transformation,[],[f67]) ).
fof(f117,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,sK4(X0,X1,X3,X5,X6)) ),
inference(cnf_transformation,[],[f67]) ).
fof(f118,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(sK4(X0,X1,X3,X5,X6),X3) ),
inference(cnf_transformation,[],[f67]) ).
fof(f136,plain,
! [X2,X3,X10,X0,X11,X1,X9,X4,X12] :
( ~ increasing(X0,X1,X2,X3,X4)
| ~ apply(X0,X11,X12)
| ~ apply(X0,X9,X10)
| ~ apply(X2,X9,X11)
| ~ member(X12,X3)
| ~ member(X11,X1)
| ~ member(X10,X3)
| ~ member(X9,X1)
| apply(X4,X10,X12) ),
inference(cnf_transformation,[],[f85]) ).
fof(f137,plain,
! [X2,X3,X0,X1,X4] :
( apply(X0,sK11(X0,X1,X2,X3,X4),sK12(X0,X1,X2,X3,X4))
| increasing(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f85]) ).
fof(f138,plain,
! [X2,X3,X0,X1,X4] :
( apply(X0,sK9(X0,X1,X2,X3,X4),sK10(X0,X1,X2,X3,X4))
| increasing(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f85]) ).
fof(f139,plain,
! [X2,X3,X0,X1,X4] :
( apply(X2,sK9(X0,X1,X2,X3,X4),sK11(X0,X1,X2,X3,X4))
| increasing(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f85]) ).
fof(f140,plain,
! [X2,X3,X0,X1,X4] :
( member(sK12(X0,X1,X2,X3,X4),X3)
| increasing(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f85]) ).
fof(f141,plain,
! [X2,X3,X0,X1,X4] :
( member(sK11(X0,X1,X2,X3,X4),X1)
| increasing(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f85]) ).
fof(f142,plain,
! [X2,X3,X0,X1,X4] :
( member(sK10(X0,X1,X2,X3,X4),X3)
| increasing(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f85]) ).
fof(f143,plain,
! [X2,X3,X0,X1,X4] :
( member(sK9(X0,X1,X2,X3,X4),X1)
| increasing(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f85]) ).
fof(f144,plain,
! [X2,X3,X0,X1,X4] :
( ~ apply(X4,sK10(X0,X1,X2,X3,X4),sK12(X0,X1,X2,X3,X4))
| increasing(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f85]) ).
fof(f145,plain,
increasing(sK14,sK16,sK19,sK17,sK20),
inference(cnf_transformation,[],[f86]) ).
fof(f146,plain,
increasing(sK13,sK15,sK18,sK16,sK19),
inference(cnf_transformation,[],[f86]) ).
fof(f149,plain,
~ increasing(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),
inference(cnf_transformation,[],[f86]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( member(sK4(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,[],[f118]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( apply(X1,X5,sK4(X0,X1,X3,X5,X6))
| ~ member(X6,X4)
| ~ member(X5,X2)
| ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6) ),
inference(cnf_transformation,[],[f117]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( apply(X0,sK4(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,[],[f116]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( increasing(X1,X2,X3,X4,X0)
| ~ apply(X0,sK10(X1,X2,X3,X4,X0),sK12(X1,X2,X3,X4,X0)) ),
inference(cnf_transformation,[],[f144]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( increasing(X0,X1,X2,X3,X4)
| member(sK9(X0,X1,X2,X3,X4),X1) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( increasing(X0,X1,X2,X3,X4)
| member(sK10(X0,X1,X2,X3,X4),X3) ),
inference(cnf_transformation,[],[f142]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( increasing(X0,X1,X2,X3,X4)
| member(sK11(X0,X1,X2,X3,X4),X1) ),
inference(cnf_transformation,[],[f141]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( increasing(X0,X1,X2,X3,X4)
| member(sK12(X0,X1,X2,X3,X4),X3) ),
inference(cnf_transformation,[],[f140]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( increasing(X1,X2,X0,X3,X4)
| apply(X0,sK9(X1,X2,X0,X3,X4),sK11(X1,X2,X0,X3,X4)) ),
inference(cnf_transformation,[],[f139]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( increasing(X0,X1,X2,X3,X4)
| apply(X0,sK9(X0,X1,X2,X3,X4),sK10(X0,X1,X2,X3,X4)) ),
inference(cnf_transformation,[],[f138]) ).
tcf(c_105,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( increasing(X0,X1,X2,X3,X4)
| apply(X0,sK11(X0,X1,X2,X3,X4),sK12(X0,X1,X2,X3,X4)) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_106,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,X5,X7)
| ~ apply(X0,X7,X8)
| ~ apply(X0,X5,X6)
| ~ increasing(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f136]) ).
tcf(c_107,negated_conjecture,
~ increasing(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),
inference(cnf_transformation,[],[f149]) ).
tcf(c_110,negated_conjecture,
increasing(sK13,sK15,sK18,sK16,sK19),
inference(cnf_transformation,[],[f146]) ).
tcf(c_111,negated_conjecture,
increasing(sK14,sK16,sK19,sK17,sK20),
inference(cnf_transformation,[],[f145]) ).
tcf(c_231,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( increasing(X1,X2,X3,X4,X0)
| ~ apply(X0,sK10(X1,X2,X3,X4,X0),sK12(X1,X2,X3,X4,X0)) ),
inference(prop_impl_just,[status(thm)],[c_98]) ).
tcf(c_233,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(sK9(X0,X1,X2,X3,X4),X1)
| increasing(X0,X1,X2,X3,X4) ),
inference(prop_impl_just,[status(thm)],[c_99]) ).
tcf(c_234,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( increasing(X0,X1,X2,X3,X4)
| member(sK9(X0,X1,X2,X3,X4),X1) ),
inference(renaming,[status(thm)],[c_233]) ).
tcf(c_235,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(sK10(X0,X1,X2,X3,X4),X3)
| increasing(X0,X1,X2,X3,X4) ),
inference(prop_impl_just,[status(thm)],[c_100]) ).
tcf(c_236,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( increasing(X0,X1,X2,X3,X4)
| member(sK10(X0,X1,X2,X3,X4),X3) ),
inference(renaming,[status(thm)],[c_235]) ).
tcf(c_237,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(sK11(X0,X1,X2,X3,X4),X1)
| increasing(X0,X1,X2,X3,X4) ),
inference(prop_impl_just,[status(thm)],[c_101]) ).
tcf(c_238,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( increasing(X0,X1,X2,X3,X4)
| member(sK11(X0,X1,X2,X3,X4),X1) ),
inference(renaming,[status(thm)],[c_237]) ).
tcf(c_239,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(sK12(X0,X1,X2,X3,X4),X3)
| increasing(X0,X1,X2,X3,X4) ),
inference(prop_impl_just,[status(thm)],[c_102]) ).
tcf(c_240,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( increasing(X0,X1,X2,X3,X4)
| member(sK12(X0,X1,X2,X3,X4),X3) ),
inference(renaming,[status(thm)],[c_239]) ).
tcf(c_241,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apply(X0,sK9(X0,X1,X2,X3,X4),sK10(X0,X1,X2,X3,X4))
| increasing(X0,X1,X2,X3,X4) ),
inference(prop_impl_just,[status(thm)],[c_104]) ).
tcf(c_242,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( increasing(X0,X1,X2,X3,X4)
| apply(X0,sK9(X0,X1,X2,X3,X4),sK10(X0,X1,X2,X3,X4)) ),
inference(renaming,[status(thm)],[c_241]) ).
tcf(c_243,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apply(X0,sK11(X0,X1,X2,X3,X4),sK12(X0,X1,X2,X3,X4))
| increasing(X0,X1,X2,X3,X4) ),
inference(prop_impl_just,[status(thm)],[c_105]) ).
tcf(c_244,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( increasing(X0,X1,X2,X3,X4)
| apply(X0,sK11(X0,X1,X2,X3,X4),sK12(X0,X1,X2,X3,X4)) ),
inference(renaming,[status(thm)],[c_243]) ).
tcf(c_285,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( increasing(X1,X2,X0,X3,X4)
| apply(X0,sK9(X1,X2,X0,X3,X4),sK11(X1,X2,X0,X3,X4)) ),
inference(prop_impl_just,[status(thm)],[c_103]) ).
tcf(c_1388,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ apply(X0,sK10(X1,X2,X3,X4,X0),sK12(X1,X2,X3,X4,X0))
| ( X4 != sK17 )
| ( X3 != sK18 )
| ( X2 != sK15 )
| ( X0 != sK20 )
| ( compose_function(sK14,sK13,sK15,sK16,sK17) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_231,c_107]) ).
tcf(c_1389,plain,
~ apply(sK20,sK10(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK12(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20)),
inference(unflattening,[status(thm)],[c_1388]) ).
tcf(c_1422,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apply(X0,sK11(X0,X1,X2,X3,X4),sK12(X0,X1,X2,X3,X4))
| ( X4 != sK20 )
| ( X3 != sK17 )
| ( X2 != sK18 )
| ( X1 != sK15 )
| ( compose_function(sK14,sK13,sK15,sK16,sK17) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_244,c_107]) ).
tcf(c_1423,plain,
apply(compose_function(sK14,sK13,sK15,sK16,sK17),sK11(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK12(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20)),
inference(unflattening,[status(thm)],[c_1422]) ).
tcf(c_1427,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apply(X0,sK9(X0,X1,X2,X3,X4),sK10(X0,X1,X2,X3,X4))
| ( X4 != sK20 )
| ( X3 != sK17 )
| ( X2 != sK18 )
| ( X1 != sK15 )
| ( compose_function(sK14,sK13,sK15,sK16,sK17) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_242,c_107]) ).
tcf(c_1428,plain,
apply(compose_function(sK14,sK13,sK15,sK16,sK17),sK9(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK10(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20)),
inference(unflattening,[status(thm)],[c_1427]) ).
tcf(c_1432,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(sK12(X0,X1,X2,X3,X4),X3)
| ( X4 != sK20 )
| ( X3 != sK17 )
| ( X2 != sK18 )
| ( X1 != sK15 )
| ( compose_function(sK14,sK13,sK15,sK16,sK17) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_240,c_107]) ).
tcf(c_1433,plain,
member(sK12(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK17),
inference(unflattening,[status(thm)],[c_1432]) ).
tcf(c_1437,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(sK11(X0,X1,X2,X3,X4),X1)
| ( X4 != sK20 )
| ( X3 != sK17 )
| ( X2 != sK18 )
| ( X1 != sK15 )
| ( compose_function(sK14,sK13,sK15,sK16,sK17) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_238,c_107]) ).
tcf(c_1438,plain,
member(sK11(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK15),
inference(unflattening,[status(thm)],[c_1437]) ).
tcf(c_1442,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(sK10(X0,X1,X2,X3,X4),X3)
| ( X4 != sK20 )
| ( X3 != sK17 )
| ( X2 != sK18 )
| ( X1 != sK15 )
| ( compose_function(sK14,sK13,sK15,sK16,sK17) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_236,c_107]) ).
tcf(c_1443,plain,
member(sK10(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK17),
inference(unflattening,[status(thm)],[c_1442]) ).
tcf(c_1447,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(sK9(X0,X1,X2,X3,X4),X1)
| ( X4 != sK20 )
| ( X3 != sK17 )
| ( X2 != sK18 )
| ( X1 != sK15 )
| ( compose_function(sK14,sK13,sK15,sK16,sK17) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_234,c_107]) ).
tcf(c_1448,plain,
member(sK9(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK15),
inference(unflattening,[status(thm)],[c_1447]) ).
tcf(c_1506,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apply(X0,sK9(X1,X2,X0,X3,X4),sK11(X1,X2,X0,X3,X4))
| ( X4 != sK20 )
| ( X3 != sK17 )
| ( X2 != sK15 )
| ( X0 != sK18 )
| ( compose_function(sK14,sK13,sK15,sK16,sK17) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_285,c_107]) ).
tcf(c_1507,plain,
apply(sK18,sK9(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK11(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20)),
inference(unflattening,[status(thm)],[c_1506]) ).
tcf(c_3404,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apply(X0,sK4(X0,X1,X3,X4,sK10(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20)),sK10(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20))
| ~ member(X4,X2)
| ~ member(sK10(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK17)
| ~ apply(compose_function(X0,X1,X2,X3,sK17),X4,sK10(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20)) ),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_3405,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apply(X1,X4,sK4(X0,X1,X3,X4,sK10(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20)))
| ~ member(X4,X2)
| ~ member(sK10(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK17)
| ~ apply(compose_function(X0,X1,X2,X3,sK17),X4,sK10(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20)) ),
inference(instantiation,[status(thm)],[c_80]) ).
tcf(c_3406,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(sK4(X0,X1,X3,X4,sK10(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20)),X3)
| ~ member(X4,X2)
| ~ member(sK10(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK17)
| ~ apply(compose_function(X0,X1,X2,X3,sK17),X4,sK10(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20)) ),
inference(instantiation,[status(thm)],[c_79]) ).
tcf(c_3679,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apply(X0,sK4(X0,X1,X3,X4,sK12(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20)),sK12(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20))
| ~ member(X4,X2)
| ~ member(sK12(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK17)
| ~ apply(compose_function(X0,X1,X2,X3,sK17),X4,sK12(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20)) ),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_3680,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apply(X1,X4,sK4(X0,X1,X3,X4,sK12(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20)))
| ~ member(X4,X2)
| ~ member(sK12(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK17)
| ~ apply(compose_function(X0,X1,X2,X3,sK17),X4,sK12(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20)) ),
inference(instantiation,[status(thm)],[c_80]) ).
tcf(c_3681,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(sK4(X0,X1,X3,X4,sK12(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20)),X3)
| ~ member(X4,X2)
| ~ member(sK12(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK17)
| ~ apply(compose_function(X0,X1,X2,X3,sK17),X4,sK12(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20)) ),
inference(instantiation,[status(thm)],[c_79]) ).
tcf(c_3687,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( apply(X4,X6,sK12(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20))
| ~ member(X6,sK17)
| ~ member(X5,X2)
| ~ member(X1,X2)
| ~ apply(X3,X5,X1)
| ~ apply(X0,X5,X6)
| ~ increasing(X0,X2,X3,sK17,X4)
| ~ member(sK12(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK17)
| ~ apply(X0,X1,sK12(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20)) ),
inference(instantiation,[status(thm)],[c_106]) ).
tcf(c_8374,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( apply(X5,X1,X2)
| ~ member(X2,X4)
| ~ member(X1,X4)
| ~ increasing(X0,X3,sK18,X4,X5)
| ~ member(sK11(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),X3)
| ~ member(sK9(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),X3)
| ~ apply(X0,sK11(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),X2)
| ~ apply(X0,sK9(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),X1)
| ~ apply(sK18,sK9(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK11(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20)) ),
inference(instantiation,[status(thm)],[c_106]) ).
tcf(c_16483,plain,
( apply(sK14,sK4(sK14,sK13,sK16,sK9(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK10(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20)),sK10(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20))
| ~ member(sK9(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK15)
| ~ member(sK10(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK17)
| ~ apply(compose_function(sK14,sK13,sK15,sK16,sK17),sK9(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK10(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20)) ),
inference(instantiation,[status(thm)],[c_3404]) ).
tcf(c_16486,plain,
( member(sK4(sK14,sK13,sK16,sK9(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK10(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20)),sK16)
| ~ member(sK9(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK15)
| ~ member(sK10(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK17)
| ~ apply(compose_function(sK14,sK13,sK15,sK16,sK17),sK9(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK10(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20)) ),
inference(instantiation,[status(thm)],[c_3406]) ).
tcf(c_16493,plain,
( apply(sK14,sK4(sK14,sK13,sK16,sK11(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK12(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20)),sK12(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20))
| ~ member(sK11(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK15)
| ~ member(sK12(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK17)
| ~ apply(compose_function(sK14,sK13,sK15,sK16,sK17),sK11(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK12(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20)) ),
inference(instantiation,[status(thm)],[c_3679]) ).
tcf(c_16496,plain,
( member(sK4(sK14,sK13,sK16,sK11(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK12(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20)),sK16)
| ~ member(sK11(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK15)
| ~ member(sK12(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK17)
| ~ apply(compose_function(sK14,sK13,sK15,sK16,sK17),sK11(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK12(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20)) ),
inference(instantiation,[status(thm)],[c_3681]) ).
tcf(c_16529,plain,
( apply(sK13,sK9(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK4(sK14,sK13,sK16,sK9(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK10(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20)))
| ~ member(sK9(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK15)
| ~ member(sK10(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK17)
| ~ apply(compose_function(sK14,sK13,sK15,sK16,sK17),sK9(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK10(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20)) ),
inference(instantiation,[status(thm)],[c_3405]) ).
tcf(c_16534,plain,
( apply(sK13,sK11(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK4(sK14,sK13,sK16,sK11(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK12(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20)))
| ~ member(sK11(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK15)
| ~ member(sK12(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK17)
| ~ apply(compose_function(sK14,sK13,sK15,sK16,sK17),sK11(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK12(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20)) ),
inference(instantiation,[status(thm)],[c_3680]) ).
tcf(c_21068,plain,
! [X0: $i,X1: $i] :
( apply(sK19,X0,X1)
| ~ member(X1,sK16)
| ~ member(X0,sK16)
| ~ increasing(sK13,sK15,sK18,sK16,sK19)
| ~ member(sK11(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK15)
| ~ member(sK9(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK15)
| ~ apply(sK13,sK11(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),X1)
| ~ apply(sK13,sK9(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),X0)
| ~ apply(sK18,sK9(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK11(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20)) ),
inference(instantiation,[status(thm)],[c_8374]) ).
tcf(c_21241,plain,
! [X0: $i,X1: $i,X2: $i] :
( apply(sK20,X2,sK12(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20))
| ~ member(X2,sK17)
| ~ member(X1,sK16)
| ~ member(X0,sK16)
| ~ apply(sK19,X1,X0)
| ~ apply(sK14,X1,X2)
| ~ increasing(sK14,sK16,sK19,sK17,sK20)
| ~ member(sK12(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK17)
| ~ apply(sK14,X0,sK12(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20)) ),
inference(instantiation,[status(thm)],[c_3687]) ).
tcf(c_22932,plain,
! [X0: $i] :
( apply(sK19,X0,sK4(sK14,sK13,sK16,sK11(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK12(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20)))
| ~ member(X0,sK16)
| ~ increasing(sK13,sK15,sK18,sK16,sK19)
| ~ member(sK11(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK15)
| ~ member(sK9(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK15)
| ~ apply(sK13,sK9(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),X0)
| ~ apply(sK18,sK9(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK11(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20))
| ~ member(sK4(sK14,sK13,sK16,sK11(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK12(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20)),sK16)
| ~ apply(sK13,sK11(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK4(sK14,sK13,sK16,sK11(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK12(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20))) ),
inference(instantiation,[status(thm)],[c_21068]) ).
tcf(c_35945,plain,
( apply(sK19,sK4(sK14,sK13,sK16,sK9(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK10(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20)),sK4(sK14,sK13,sK16,sK11(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK12(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20)))
| ~ increasing(sK13,sK15,sK18,sK16,sK19)
| ~ member(sK11(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK15)
| ~ member(sK9(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK15)
| ~ apply(sK18,sK9(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK11(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20))
| ~ member(sK4(sK14,sK13,sK16,sK11(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK12(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20)),sK16)
| ~ member(sK4(sK14,sK13,sK16,sK9(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK10(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20)),sK16)
| ~ apply(sK13,sK11(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK4(sK14,sK13,sK16,sK11(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK12(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20)))
| ~ apply(sK13,sK9(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK4(sK14,sK13,sK16,sK9(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK10(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20))) ),
inference(instantiation,[status(thm)],[c_22932]) ).
tcf(c_46086,plain,
! [X0: $i] :
( apply(sK20,X0,sK12(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20))
| ~ member(X0,sK17)
| ~ increasing(sK14,sK16,sK19,sK17,sK20)
| ~ member(sK12(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK17)
| ~ member(sK4(sK14,sK13,sK16,sK11(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK12(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20)),sK16)
| ~ member(sK4(sK14,sK13,sK16,sK9(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK10(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20)),sK16)
| ~ apply(sK14,sK4(sK14,sK13,sK16,sK9(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK10(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20)),X0)
| ~ apply(sK14,sK4(sK14,sK13,sK16,sK11(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK12(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20)),sK12(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20))
| ~ apply(sK19,sK4(sK14,sK13,sK16,sK9(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK10(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20)),sK4(sK14,sK13,sK16,sK11(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK12(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20))) ),
inference(instantiation,[status(thm)],[c_21241]) ).
tcf(c_58062,plain,
( apply(sK20,sK10(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK12(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20))
| ~ increasing(sK14,sK16,sK19,sK17,sK20)
| ~ member(sK12(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK17)
| ~ member(sK10(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK17)
| ~ member(sK4(sK14,sK13,sK16,sK11(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK12(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20)),sK16)
| ~ member(sK4(sK14,sK13,sK16,sK9(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK10(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20)),sK16)
| ~ apply(sK14,sK4(sK14,sK13,sK16,sK11(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK12(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20)),sK12(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20))
| ~ apply(sK14,sK4(sK14,sK13,sK16,sK9(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK10(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20)),sK10(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20))
| ~ apply(sK19,sK4(sK14,sK13,sK16,sK9(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK10(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20)),sK4(sK14,sK13,sK16,sK11(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20),sK12(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK18,sK17,sK20))) ),
inference(instantiation,[status(thm)],[c_46086]) ).
tcf(c_58063,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_58062,c_35945,c_16534,c_16529,c_16496,c_16493,c_16486,c_16483,c_1507,c_1448,c_1443,c_1438,c_1433,c_1428,c_1423,c_1389,c_110,c_111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET746+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n003.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 11:52:21 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.44 % Proving...
% 68.21/10.83 % SZS status Started for theBenchmark.p
% 68.21/10.83 % SZS status Theorem for theBenchmark.p
% 68.21/10.83
% 68.21/10.83 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 68.21/10.83
% 68.21/10.83 % ------ iProver source info
% 68.21/10.83
% 68.21/10.83 % git: date: 2026-07-19 20:42:38 +0200
% 68.21/10.83 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 68.21/10.83 % git: non_committed_changes: false
% 68.21/10.83
% 68.21/10.83 % ------ Parsing...
% 68.21/10.83 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 68.21/10.83
% 68.21/10.83 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e %
% 68.21/10.83
% 68.21/10.83 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 68.21/10.83
% 68.21/10.83 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 68.21/10.83 % ------ Proving...
% 68.21/10.83 % ------ Problem Properties
% 68.21/10.83
% 68.21/10.83 %
% 68.21/10.83 % clauses 64
% 68.21/10.83 % conjectures 3
% 68.21/10.83 % EPR 7
% 68.21/10.83 % Horn 52
% 68.21/10.83 % unary 7
% 68.21/10.83 % binary 37
% 68.21/10.83 % lits 163
% 68.21/10.83 % lits eq 5
% 68.21/10.83 % fd_pure 0
% 68.21/10.83 % fd_pseudo 0
% 68.21/10.83 % fd_cond 0
% 68.21/10.83 % fd_pseudo_cond 4
% 68.21/10.83 % AC symbols 0
% 68.21/10.83
% 68.21/10.83 % ------ Input Options Time Limit: Unbounded
% 68.21/10.83
% 68.21/10.83
% 68.21/10.83 % ------
% 68.21/10.83 % Current options:
% 68.21/10.83 % ------
% 68.21/10.83
% 68.21/10.83
% 68.21/10.83 %
% 68.21/10.83
% 68.21/10.83 % ------ Proving...
% 68.21/10.83 %
% 68.21/10.83
% 68.21/10.83 % SZS status Theorem for theBenchmark.p
% 68.21/10.83
% 68.21/10.83 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 68.21/10.83
% 68.21/10.83
%------------------------------------------------------------------------------