%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET773+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:48:33 PM UTC 2026
% Result : Theorem 8.35s 1.74s
% Output : CNFRefutation 8.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 124 ( 12 unt; 2 def)
% Number of atoms : 648 ( 0 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 779 ( 311 ~; 347 |; 96 &)
% ( 11 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 271 ( 0 sgn 240 !; 31 ?; 85 :)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [X0,X1] :
( equivalence(X1,X0)
<=> ( ! [X2,X3,X4] :
( ( member(X4,X0)
& member(X3,X0)
& member(X2,X0) )
=> ( ( apply(X1,X3,X4)
& apply(X1,X2,X3) )
=> apply(X1,X2,X4) ) )
& ! [X2,X3] :
( ( member(X3,X0)
& member(X2,X0) )
=> ( apply(X1,X2,X3)
=> apply(X1,X3,X2) ) )
& ! [X2] :
( member(X2,X0)
=> apply(X1,X2,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+2.ax',equivalence) ).
fof(f17,conjecture,
! [X0,X1,X2,X3] :
( ( ! [X4,X5] :
( ( member(X5,X0)
& member(X4,X0) )
=> ( apply(X3,X4,X5)
<=> ( apply(X2,X4,X5)
& apply(X1,X4,X5) ) ) )
& equivalence(X2,X0)
& equivalence(X1,X0) )
=> equivalence(X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIII09) ).
fof(f18,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( ! [X4,X5] :
( ( member(X5,X0)
& member(X4,X0) )
=> ( apply(X3,X4,X5)
<=> ( apply(X2,X4,X5)
& apply(X1,X4,X5) ) ) )
& equivalence(X2,X0)
& equivalence(X1,X0) )
=> equivalence(X3,X0) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( equivalence(X1,X0)
<=> ( ! [X5,X6,X7] :
( ( member(X7,X0)
& member(X6,X0)
& member(X5,X0) )
=> ( ( apply(X1,X6,X7)
& apply(X1,X5,X6) )
=> apply(X1,X5,X7) ) )
& ! [X3,X4] :
( ( member(X4,X0)
& member(X3,X0) )
=> ( apply(X1,X3,X4)
=> apply(X1,X4,X3) ) )
& ! [X2] :
( member(X2,X0)
=> apply(X1,X2,X2) ) ) ),
inference(rectify,[],[f14]) ).
fof(f20,plain,
? [X0,X1,X2,X3] :
( ! [X4,X5] :
( ~ member(X5,X0)
| ~ member(X4,X0)
| ( apply(X3,X4,X5)
<=> ( apply(X2,X4,X5)
& apply(X1,X4,X5) ) ) )
& equivalence(X2,X0)
& equivalence(X1,X0)
& ~ equivalence(X3,X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f21,plain,
? [X0,X1,X2,X3] :
( ! [X4,X5] :
( ~ member(X5,X0)
| ~ member(X4,X0)
| ( apply(X3,X4,X5)
<=> ( apply(X2,X4,X5)
& apply(X1,X4,X5) ) ) )
& equivalence(X2,X0)
& equivalence(X1,X0)
& ~ equivalence(X3,X0) ),
inference(flattening,[],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( equivalence(X1,X0)
<=> ( ! [X5,X6,X7] :
( ~ member(X7,X0)
| ~ member(X6,X0)
| ~ member(X5,X0)
| ~ apply(X1,X6,X7)
| ~ apply(X1,X5,X6)
| apply(X1,X5,X7) )
& ! [X3,X4] :
( ~ member(X4,X0)
| ~ member(X3,X0)
| ~ apply(X1,X3,X4)
| apply(X1,X4,X3) )
& ! [X2] :
( ~ member(X2,X0)
| apply(X1,X2,X2) ) ) ),
inference(ennf_transformation,[],[f19]) ).
fof(f23,plain,
! [X0,X1] :
( equivalence(X1,X0)
<=> ( ! [X5,X6,X7] :
( ~ member(X7,X0)
| ~ member(X6,X0)
| ~ member(X5,X0)
| ~ apply(X1,X6,X7)
| ~ apply(X1,X5,X6)
| apply(X1,X5,X7) )
& ! [X3,X4] :
( ~ member(X4,X0)
| ~ member(X3,X0)
| ~ apply(X1,X3,X4)
| apply(X1,X4,X3) )
& ! [X2] :
( ~ member(X2,X0)
| apply(X1,X2,X2) ) ) ),
inference(flattening,[],[f22]) ).
fof(f27,plain,
? [X0,X1,X2,X3] :
( ! [X4,X5] :
( ~ member(X5,X0)
| ~ member(X4,X0)
| ( ( ~ apply(X3,X4,X5)
| ( apply(X2,X4,X5)
& apply(X1,X4,X5) ) )
& ( ~ apply(X2,X4,X5)
| ~ apply(X1,X4,X5)
| apply(X3,X4,X5) ) ) )
& equivalence(X2,X0)
& equivalence(X1,X0)
& ~ equivalence(X3,X0) ),
inference(nnf_transformation,[],[f21]) ).
fof(f28,plain,
? [X0,X1,X2,X3] :
( ! [X4,X5] :
( ~ member(X5,X0)
| ~ member(X4,X0)
| ( ( ~ apply(X3,X4,X5)
| ( apply(X2,X4,X5)
& apply(X1,X4,X5) ) )
& ( ~ apply(X2,X4,X5)
| ~ apply(X1,X4,X5)
| apply(X3,X4,X5) ) ) )
& equivalence(X2,X0)
& equivalence(X1,X0)
& ~ equivalence(X3,X0) ),
inference(flattening,[],[f27]) ).
fof(f29,plain,
( ! [X4,X5] :
( ~ member(X5,sK2)
| ~ member(X4,sK2)
| ( ( ~ apply(sK5,X4,X5)
| ( apply(sK4,X4,X5)
& apply(sK3,X4,X5) ) )
& ( ~ apply(sK4,X4,X5)
| ~ apply(sK3,X4,X5)
| apply(sK5,X4,X5) ) ) )
& equivalence(sK4,sK2)
& equivalence(sK3,sK2)
& ~ equivalence(sK5,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4),skolemize(X3,sK5)],[f28]) ).
fof(f30,plain,
! [X1,X0] :
( ( ~ sP1(X1,X0)
| ( sP0(X1,X0)
& ! [X3,X4] :
( ~ member(X4,X0)
| ~ member(X3,X0)
| ~ apply(X1,X3,X4)
| apply(X1,X4,X3) )
& ! [X2] :
( ~ member(X2,X0)
| apply(X1,X2,X2) ) ) )
& ( ~ sP0(X1,X0)
| ? [X3,X4] :
( member(X4,X0)
& member(X3,X0)
& apply(X1,X3,X4)
& ~ apply(X1,X4,X3) )
| ? [X2] :
( member(X2,X0)
& ~ apply(X1,X2,X2) )
| sP1(X1,X0) ) ),
inference(nnf_transformation,[],[f25]) ).
fof(f31,plain,
! [X1,X0] :
( ( ~ sP1(X1,X0)
| ( sP0(X1,X0)
& ! [X3,X4] :
( ~ member(X4,X0)
| ~ member(X3,X0)
| ~ apply(X1,X3,X4)
| apply(X1,X4,X3) )
& ! [X2] :
( ~ member(X2,X0)
| apply(X1,X2,X2) ) ) )
& ( ~ sP0(X1,X0)
| ? [X3,X4] :
( member(X4,X0)
& member(X3,X0)
& apply(X1,X3,X4)
& ~ apply(X1,X4,X3) )
| ? [X2] :
( member(X2,X0)
& ~ apply(X1,X2,X2) )
| sP1(X1,X0) ) ),
inference(flattening,[],[f30]) ).
fof(f32,plain,
! [X0,X1] :
( ( ~ sP1(X0,X1)
| ( sP0(X0,X1)
& ! [X6,X7] :
( ~ member(X7,X1)
| ~ member(X6,X1)
| ~ apply(X0,X6,X7)
| apply(X0,X7,X6) )
& ! [X5] :
( ~ member(X5,X1)
| apply(X0,X5,X5) ) ) )
& ( ~ sP0(X0,X1)
| ? [X3,X4] :
( member(X4,X1)
& member(X3,X1)
& apply(X0,X3,X4)
& ~ apply(X0,X4,X3) )
| ? [X2] :
( member(X2,X1)
& ~ apply(X0,X2,X2) )
| sP1(X0,X1) ) ),
inference(rectify,[],[f31]) ).
fof(f33,plain,
! [X0,X1] :
( ( ~ sP1(X0,X1)
| ( sP0(X0,X1)
& ! [X6,X7] :
( ~ member(X7,X1)
| ~ member(X6,X1)
| ~ apply(X0,X6,X7)
| apply(X0,X7,X6) )
& ! [X5] :
( ~ member(X5,X1)
| apply(X0,X5,X5) ) ) )
& ( ~ sP0(X0,X1)
| ( member(sK8(X0,X1),X1)
& member(sK7(X0,X1),X1)
& apply(X0,sK7(X0,X1),sK8(X0,X1))
& ~ apply(X0,sK8(X0,X1),sK7(X0,X1)) )
| ( member(sK6(X0,X1),X1)
& ~ apply(X0,sK6(X0,X1),sK6(X0,X1)) )
| sP1(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8]),skolemize(X2,sK6(X0,X1)),skolemize(X3,sK7(X0,X1)),skolemize(X4,sK8(X0,X1))],[f32]) ).
fof(f37,plain,
! [X0,X1] :
( ( ~ equivalence(X1,X0)
| sP1(X1,X0) )
& ( ~ sP1(X1,X0)
| equivalence(X1,X0) ) ),
inference(nnf_transformation,[],[f26]) ).
fof(f38,plain,
! [X4,X5] :
( ~ member(X5,sK2)
| ~ member(X4,sK2)
| ~ apply(sK5,X4,X5)
| apply(sK4,X4,X5) ),
inference(cnf_transformation,[],[f29]) ).
fof(f39,plain,
! [X4,X5] :
( ~ member(X5,sK2)
| ~ member(X4,sK2)
| ~ apply(sK5,X4,X5)
| apply(sK3,X4,X5) ),
inference(cnf_transformation,[],[f29]) ).
fof(f40,plain,
! [X4,X5] :
( ~ member(X5,sK2)
| ~ member(X4,sK2)
| ~ apply(sK4,X4,X5)
| ~ apply(sK3,X4,X5)
| apply(sK5,X4,X5) ),
inference(cnf_transformation,[],[f29]) ).
fof(f41,plain,
equivalence(sK4,sK2),
inference(cnf_transformation,[],[f29]) ).
fof(f42,plain,
equivalence(sK3,sK2),
inference(cnf_transformation,[],[f29]) ).
fof(f43,plain,
~ equivalence(sK5,sK2),
inference(cnf_transformation,[],[f29]) ).
fof(f44,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f45,plain,
! [X0,X1,X6,X7] :
( ~ sP1(X0,X1)
| ~ member(X7,X1)
| ~ member(X6,X1)
| ~ apply(X0,X6,X7)
| apply(X0,X7,X6) ),
inference(cnf_transformation,[],[f33]) ).
fof(f46,plain,
! [X0,X1,X5] :
( ~ sP1(X0,X1)
| ~ member(X5,X1)
| apply(X0,X5,X5) ),
inference(cnf_transformation,[],[f33]) ).
fof(f47,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| member(sK8(X0,X1),X1)
| member(sK6(X0,X1),X1)
| sP1(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f48,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| member(sK7(X0,X1),X1)
| member(sK6(X0,X1),X1)
| sP1(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f49,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| apply(X0,sK7(X0,X1),sK8(X0,X1))
| member(sK6(X0,X1),X1)
| sP1(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f50,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ~ apply(X0,sK8(X0,X1),sK7(X0,X1))
| member(sK6(X0,X1),X1)
| sP1(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f51,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| member(sK8(X0,X1),X1)
| ~ apply(X0,sK6(X0,X1),sK6(X0,X1))
| sP1(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f52,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| member(sK7(X0,X1),X1)
| ~ apply(X0,sK6(X0,X1),sK6(X0,X1))
| sP1(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f53,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| apply(X0,sK7(X0,X1),sK8(X0,X1))
| ~ apply(X0,sK6(X0,X1),sK6(X0,X1))
| sP1(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f54,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ~ apply(X0,sK8(X0,X1),sK7(X0,X1))
| ~ apply(X0,sK6(X0,X1),sK6(X0,X1))
| sP1(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f62,plain,
! [X0,X1] :
( ~ equivalence(X1,X0)
| sP1(X1,X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f63,plain,
! [X0,X1] :
( ~ sP1(X1,X0)
| equivalence(X1,X0) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_49,negated_conjecture,
~ equivalence(sK5,sK2),
inference(cnf_transformation,[],[f43]) ).
tcf(c_50,negated_conjecture,
equivalence(sK3,sK2),
inference(cnf_transformation,[],[f42]) ).
tcf(c_51,negated_conjecture,
equivalence(sK4,sK2),
inference(cnf_transformation,[],[f41]) ).
tcf(c_52,negated_conjecture,
! [X0: $i,X1: $i] :
( apply(sK5,X0,X1)
| ~ member(X1,sK2)
| ~ member(X0,sK2)
| ~ apply(sK4,X0,X1)
| ~ apply(sK3,X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_53,negated_conjecture,
! [X0: $i,X1: $i] :
( apply(sK3,X0,X1)
| ~ member(X1,sK2)
| ~ member(X0,sK2)
| ~ apply(sK5,X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_54,negated_conjecture,
! [X0: $i,X1: $i] :
( apply(sK4,X0,X1)
| ~ member(X1,sK2)
| ~ member(X0,sK2)
| ~ apply(sK5,X0,X1) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( sP1(X0,X1)
| ~ sP0(X0,X1)
| ~ apply(X0,sK8(X0,X1),sK7(X0,X1))
| ~ apply(X0,sK6(X0,X1),sK6(X0,X1)) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( sP1(X0,X1)
| apply(X0,sK7(X0,X1),sK8(X0,X1))
| ~ sP0(X0,X1)
| ~ apply(X0,sK6(X0,X1),sK6(X0,X1)) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( sP1(X0,X1)
| member(sK7(X0,X1),X1)
| ~ sP0(X0,X1)
| ~ apply(X0,sK6(X0,X1),sK6(X0,X1)) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( sP1(X0,X1)
| member(sK8(X0,X1),X1)
| ~ sP0(X0,X1)
| ~ apply(X0,sK6(X0,X1),sK6(X0,X1)) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( sP1(X0,X1)
| member(sK6(X0,X1),X1)
| ~ sP0(X0,X1)
| ~ apply(X0,sK8(X0,X1),sK7(X0,X1)) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( sP1(X0,X1)
| member(sK6(X0,X1),X1)
| apply(X0,sK7(X0,X1),sK8(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( sP1(X0,X1)
| member(sK7(X0,X1),X1)
| member(sK6(X0,X1),X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( sP1(X0,X1)
| member(sK8(X0,X1),X1)
| member(sK6(X0,X1),X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( apply(X2,X0,X0)
| ~ sP1(X2,X1)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,X2,X1)
| ~ sP1(X0,X3)
| ~ member(X2,X3)
| ~ member(X1,X3)
| ~ apply(X0,X1,X2) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( sP0(X0,X1)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( equivalence(X0,X1)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] :
( sP1(X0,X1)
| ~ equivalence(X0,X1) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i] :
( ~ equivalence(X0,X1)
| sP1(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_74]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i] :
( sP1(X0,X1)
| ~ equivalence(X0,X1) ),
inference(renaming,[status(thm)],[c_96]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i] :
( equivalence(X0,X1)
| ~ sP1(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_73]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i] :
( ~ sP1(X0,X1)
| sP0(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_65]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i] :
( sP0(X0,X1)
| ~ sP1(X0,X1) ),
inference(renaming,[status(thm)],[c_100]) ).
tcf(c_336,plain,
~ sP1(sK5,sK2),
inference(resolution,[status(thm)],[c_49,c_98]) ).
tcf(c_340,plain,
sP1(sK3,sK2),
inference(resolution,[status(thm)],[c_50,c_97]) ).
tcf(c_344,plain,
sP1(sK4,sK2),
inference(resolution,[status(thm)],[c_51,c_97]) ).
tcf(c_671,plain,
( member(sK8(sK5,sK2),sK2)
| member(sK6(sK5,sK2),sK2)
| ~ sP0(sK5,sK2) ),
inference(resolution,[status(thm)],[c_62,c_336]) ).
tcf(c_681,plain,
( member(sK7(sK5,sK2),sK2)
| member(sK6(sK5,sK2),sK2)
| ~ sP0(sK5,sK2) ),
inference(resolution,[status(thm)],[c_61,c_336]) ).
tcf(c_691,plain,
( member(sK6(sK5,sK2),sK2)
| apply(sK5,sK7(sK5,sK2),sK8(sK5,sK2))
| ~ sP0(sK5,sK2) ),
inference(resolution,[status(thm)],[c_60,c_336]) ).
tcf(c_701,plain,
( member(sK6(sK5,sK2),sK2)
| ~ sP0(sK5,sK2)
| ~ apply(sK5,sK8(sK5,sK2),sK7(sK5,sK2)) ),
inference(resolution,[status(thm)],[c_59,c_336]) ).
tcf(c_711,plain,
( member(sK8(sK5,sK2),sK2)
| ~ sP0(sK5,sK2)
| ~ apply(sK5,sK6(sK5,sK2),sK6(sK5,sK2)) ),
inference(resolution,[status(thm)],[c_58,c_336]) ).
tcf(c_721,plain,
( member(sK7(sK5,sK2),sK2)
| ~ sP0(sK5,sK2)
| ~ apply(sK5,sK6(sK5,sK2),sK6(sK5,sK2)) ),
inference(resolution,[status(thm)],[c_57,c_336]) ).
tcf(c_731,plain,
( apply(sK5,sK7(sK5,sK2),sK8(sK5,sK2))
| ~ sP0(sK5,sK2)
| ~ apply(sK5,sK6(sK5,sK2),sK6(sK5,sK2)) ),
inference(resolution,[status(thm)],[c_56,c_336]) ).
tcf(c_741,plain,
( ~ sP0(sK5,sK2)
| ~ apply(sK5,sK8(sK5,sK2),sK7(sK5,sK2))
| ~ apply(sK5,sK6(sK5,sK2),sK6(sK5,sK2)) ),
inference(resolution,[status(thm)],[c_55,c_336]) ).
tcf(c_751,plain,
sP0(sK3,sK2),
inference(resolution,[status(thm)],[c_101,c_340]) ).
tcf(c_755,plain,
sP0(sK4,sK2),
inference(resolution,[status(thm)],[c_101,c_344]) ).
tcf(c_3829,plain,
! [X0: $i] :
( apply(sK5,sK6(sK5,sK2),X0)
| ~ member(X0,sK2)
| ~ member(sK6(sK5,sK2),sK2)
| ~ apply(sK4,sK6(sK5,sK2),X0)
| ~ apply(sK3,sK6(sK5,sK2),X0) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_3837,plain,
! [X0: $i] :
( apply(X0,sK6(sK5,sK2),sK6(sK5,sK2))
| ~ sP1(X0,sK2)
| ~ member(sK6(sK5,sK2),sK2) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_3858,plain,
( apply(sK5,sK6(sK5,sK2),sK6(sK5,sK2))
| ~ member(sK6(sK5,sK2),sK2)
| ~ apply(sK4,sK6(sK5,sK2),sK6(sK5,sK2))
| ~ apply(sK3,sK6(sK5,sK2),sK6(sK5,sK2)) ),
inference(instantiation,[status(thm)],[c_3829]) ).
tcf(c_3863,plain,
( apply(sK3,sK6(sK5,sK2),sK6(sK5,sK2))
| ~ sP1(sK3,sK2)
| ~ member(sK6(sK5,sK2),sK2) ),
inference(instantiation,[status(thm)],[c_3837]) ).
tcf(c_3864,plain,
( apply(sK4,sK6(sK5,sK2),sK6(sK5,sK2))
| ~ sP1(sK4,sK2)
| ~ member(sK6(sK5,sK2),sK2) ),
inference(instantiation,[status(thm)],[c_3837]) ).
tcf(c_3907,plain,
! [X0: $i] :
( apply(sK4,sK7(sK5,sK2),X0)
| ~ member(X0,sK2)
| ~ member(sK7(sK5,sK2),sK2)
| ~ apply(sK5,sK7(sK5,sK2),X0) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_3908,plain,
! [X0: $i] :
( apply(sK3,sK7(sK5,sK2),X0)
| ~ member(X0,sK2)
| ~ member(sK7(sK5,sK2),sK2)
| ~ apply(sK5,sK7(sK5,sK2),X0) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_3916,plain,
! [X0: $i,X1: $i] :
( apply(X0,X1,sK7(sK5,sK2))
| ~ sP1(X0,sK2)
| ~ member(X1,sK2)
| ~ member(sK7(sK5,sK2),sK2)
| ~ apply(X0,sK7(sK5,sK2),X1) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_3923,plain,
! [X0: $i] :
( apply(sK5,sK8(sK5,sK2),X0)
| ~ member(X0,sK2)
| ~ member(sK8(sK5,sK2),sK2)
| ~ apply(sK4,sK8(sK5,sK2),X0)
| ~ apply(sK3,sK8(sK5,sK2),X0) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_3975,plain,
( apply(sK5,sK8(sK5,sK2),sK7(sK5,sK2))
| ~ member(sK7(sK5,sK2),sK2)
| ~ member(sK8(sK5,sK2),sK2)
| ~ apply(sK4,sK8(sK5,sK2),sK7(sK5,sK2))
| ~ apply(sK3,sK8(sK5,sK2),sK7(sK5,sK2)) ),
inference(instantiation,[status(thm)],[c_3923]) ).
tcf(c_4203,plain,
! [X0: $i] :
( apply(X0,sK8(sK5,sK2),sK7(sK5,sK2))
| ~ sP1(X0,sK2)
| ~ member(sK7(sK5,sK2),sK2)
| ~ member(sK8(sK5,sK2),sK2)
| ~ apply(X0,sK7(sK5,sK2),sK8(sK5,sK2)) ),
inference(instantiation,[status(thm)],[c_3916]) ).
tcf(c_4856,plain,
( apply(sK3,sK8(sK5,sK2),sK7(sK5,sK2))
| ~ sP1(sK3,sK2)
| ~ member(sK7(sK5,sK2),sK2)
| ~ member(sK8(sK5,sK2),sK2)
| ~ apply(sK3,sK7(sK5,sK2),sK8(sK5,sK2)) ),
inference(instantiation,[status(thm)],[c_4203]) ).
tcf(c_5038,plain,
( apply(sK4,sK7(sK5,sK2),sK8(sK5,sK2))
| ~ member(sK7(sK5,sK2),sK2)
| ~ member(sK8(sK5,sK2),sK2)
| ~ apply(sK5,sK7(sK5,sK2),sK8(sK5,sK2)) ),
inference(instantiation,[status(thm)],[c_3907]) ).
tcf(c_5040,plain,
( apply(sK3,sK7(sK5,sK2),sK8(sK5,sK2))
| ~ member(sK7(sK5,sK2),sK2)
| ~ member(sK8(sK5,sK2),sK2)
| ~ apply(sK5,sK7(sK5,sK2),sK8(sK5,sK2)) ),
inference(instantiation,[status(thm)],[c_3908]) ).
tcf(c_5131,plain,
( apply(sK4,sK8(sK5,sK2),sK7(sK5,sK2))
| ~ sP1(sK4,sK2)
| ~ member(sK7(sK5,sK2),sK2)
| ~ member(sK8(sK5,sK2),sK2)
| ~ apply(sK4,sK7(sK5,sK2),sK8(sK5,sK2)) ),
inference(instantiation,[status(thm)],[c_4203]) ).
tcf(c_5895,plain,
! [X0: $i] :
( apply(sK5,sK9(sK5,sK2),X0)
| ~ member(X0,sK2)
| ~ member(sK9(sK5,sK2),sK2)
| ~ apply(sK4,sK9(sK5,sK2),X0)
| ~ apply(sK3,sK9(sK5,sK2),X0) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_6320,plain,
( apply(sK5,sK9(sK5,sK2),sK11(sK5,sK2))
| ~ member(sK11(sK5,sK2),sK2)
| ~ member(sK9(sK5,sK2),sK2)
| ~ apply(sK4,sK9(sK5,sK2),sK11(sK5,sK2))
| ~ apply(sK3,sK9(sK5,sK2),sK11(sK5,sK2)) ),
inference(instantiation,[status(thm)],[c_5895]) ).
fof(f24,definition,
! [X1,X0] :
( sP0(X1,X0)
<=> ! [X5,X6,X7] :
( ~ member(X7,X0)
| ~ member(X6,X0)
| ~ member(X5,X0)
| ~ apply(X1,X6,X7)
| ~ apply(X1,X5,X6)
| apply(X1,X5,X7) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f25,definition,
! [X1,X0] :
( sP1(X1,X0)
<=> ( sP0(X1,X0)
& ! [X3,X4] :
( ~ member(X4,X0)
| ~ member(X3,X0)
| ~ apply(X1,X3,X4)
| apply(X1,X4,X3) )
& ! [X2] :
( ~ member(X2,X0)
| apply(X1,X2,X2) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f26,plain,
! [X0,X1] :
( equivalence(X1,X0)
<=> sP1(X1,X0) ),
inference(definition_folding,[],[f23,f25,f24]) ).
fof(f34,plain,
! [X1,X0] :
( ( ~ sP0(X1,X0)
| ! [X5,X6,X7] :
( ~ member(X7,X0)
| ~ member(X6,X0)
| ~ member(X5,X0)
| ~ apply(X1,X6,X7)
| ~ apply(X1,X5,X6)
| apply(X1,X5,X7) ) )
& ( ? [X5,X6,X7] :
( member(X7,X0)
& member(X6,X0)
& member(X5,X0)
& apply(X1,X6,X7)
& apply(X1,X5,X6)
& ~ apply(X1,X5,X7) )
| sP0(X1,X0) ) ),
inference(nnf_transformation,[],[f24]) ).
fof(f35,plain,
! [X0,X1] :
( ( ~ sP0(X0,X1)
| ! [X5,X6,X7] :
( ~ member(X7,X1)
| ~ member(X6,X1)
| ~ member(X5,X1)
| ~ apply(X0,X6,X7)
| ~ apply(X0,X5,X6)
| apply(X0,X5,X7) ) )
& ( ? [X2,X3,X4] :
( member(X4,X1)
& member(X3,X1)
& member(X2,X1)
& apply(X0,X3,X4)
& apply(X0,X2,X3)
& ~ apply(X0,X2,X4) )
| sP0(X0,X1) ) ),
inference(rectify,[],[f34]) ).
fof(f36,plain,
! [X0,X1] :
( ( ~ sP0(X0,X1)
| ! [X5,X6,X7] :
( ~ member(X7,X1)
| ~ member(X6,X1)
| ~ member(X5,X1)
| ~ apply(X0,X6,X7)
| ~ apply(X0,X5,X6)
| apply(X0,X5,X7) ) )
& ( ( member(sK11(X0,X1),X1)
& member(sK10(X0,X1),X1)
& member(sK9(X0,X1),X1)
& apply(X0,sK10(X0,X1),sK11(X0,X1))
& apply(X0,sK9(X0,X1),sK10(X0,X1))
& ~ apply(X0,sK9(X0,X1),sK11(X0,X1)) )
| sP0(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11]),skolemize(X2,sK9(X0,X1)),skolemize(X3,sK10(X0,X1)),skolemize(X4,sK11(X0,X1))],[f35]) ).
fof(f55,plain,
! [X0,X1,X6,X7,X5] :
( ~ sP0(X0,X1)
| ~ member(X7,X1)
| ~ member(X6,X1)
| ~ member(X5,X1)
| ~ apply(X0,X6,X7)
| ~ apply(X0,X5,X6)
| apply(X0,X5,X7) ),
inference(cnf_transformation,[],[f36]) ).
fof(f56,plain,
! [X0,X1] :
( member(sK11(X0,X1),X1)
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f57,plain,
! [X0,X1] :
( member(sK10(X0,X1),X1)
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f58,plain,
! [X0,X1] :
( member(sK9(X0,X1),X1)
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f59,plain,
! [X0,X1] :
( apply(X0,sK10(X0,X1),sK11(X0,X1))
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f60,plain,
! [X0,X1] :
( apply(X0,sK9(X0,X1),sK10(X0,X1))
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f61,plain,
! [X0,X1] :
( ~ apply(X0,sK9(X0,X1),sK11(X0,X1))
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( sP0(X0,X1)
| ~ apply(X0,sK9(X0,X1),sK11(X0,X1)) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( sP0(X0,X1)
| apply(X0,sK9(X0,X1),sK10(X0,X1)) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( sP0(X0,X1)
| apply(X0,sK10(X0,X1),sK11(X0,X1)) ),
inference(cnf_transformation,[],[f59]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] :
( sP0(X0,X1)
| member(sK9(X0,X1),X1) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] :
( sP0(X0,X1)
| member(sK10(X0,X1),X1) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( sP0(X0,X1)
| member(sK11(X0,X1),X1) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apply(X0,X1,X3)
| ~ sP0(X0,X4)
| ~ member(X3,X4)
| ~ member(X2,X4)
| ~ member(X1,X4)
| ~ apply(X0,X2,X3)
| ~ apply(X0,X1,X2) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_3776,plain,
( sP0(sK5,sK2)
| ~ apply(sK5,sK9(sK5,sK2),sK11(sK5,sK2)) ),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_3777,plain,
( sP0(sK5,sK2)
| member(sK11(sK5,sK2),sK2) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_3778,plain,
( sP0(sK5,sK2)
| member(sK10(sK5,sK2),sK2) ),
inference(instantiation,[status(thm)],[c_70]) ).
tcf(c_3779,plain,
( sP0(sK5,sK2)
| member(sK9(sK5,sK2),sK2) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_4260,plain,
! [X0: $i] :
( sP0(sK5,X0)
| apply(sK4,sK9(sK5,X0),sK10(sK5,X0))
| ~ member(sK10(sK5,X0),sK2)
| ~ member(sK9(sK5,X0),sK2) ),
inference(superposition,[status(thm)],[c_67,c_54]) ).
tcf(c_4261,plain,
! [X0: $i] :
( sP0(sK5,X0)
| apply(sK3,sK9(sK5,X0),sK10(sK5,X0))
| ~ member(sK10(sK5,X0),sK2)
| ~ member(sK9(sK5,X0),sK2) ),
inference(superposition,[status(thm)],[c_67,c_53]) ).
tcf(c_4362,plain,
! [X0: $i] :
( sP0(sK5,X0)
| apply(sK4,sK10(sK5,X0),sK11(sK5,X0))
| ~ member(sK10(sK5,X0),sK2)
| ~ member(sK11(sK5,X0),sK2) ),
inference(superposition,[status(thm)],[c_68,c_54]) ).
tcf(c_4363,plain,
! [X0: $i] :
( sP0(sK5,X0)
| apply(sK3,sK10(sK5,X0),sK11(sK5,X0))
| ~ member(sK10(sK5,X0),sK2)
| ~ member(sK11(sK5,X0),sK2) ),
inference(superposition,[status(thm)],[c_68,c_53]) ).
tcf(c_5985,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(sK5,X0)
| apply(sK4,sK9(sK5,X0),X1)
| ~ sP0(sK4,X2)
| ~ member(X1,X2)
| ~ member(sK10(sK5,X0),sK2)
| ~ member(sK9(sK5,X0),sK2)
| ~ member(sK10(sK5,X0),X2)
| ~ member(sK9(sK5,X0),X2)
| ~ apply(sK4,sK10(sK5,X0),X1) ),
inference(superposition,[status(thm)],[c_4260,c_72]) ).
tcf(c_5986,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(sK5,X0)
| apply(sK3,sK9(sK5,X0),X1)
| ~ sP0(sK3,X2)
| ~ member(X1,X2)
| ~ member(sK10(sK5,X0),sK2)
| ~ member(sK9(sK5,X0),sK2)
| ~ member(sK10(sK5,X0),X2)
| ~ member(sK9(sK5,X0),X2)
| ~ apply(sK3,sK10(sK5,X0),X1) ),
inference(superposition,[status(thm)],[c_4261,c_72]) ).
tcf(c_10205,plain,
! [X0: $i,X1: $i] :
( sP0(sK5,X0)
| apply(sK4,sK9(sK5,X0),sK11(sK5,X0))
| ~ sP0(sK4,X1)
| ~ member(sK10(sK5,X0),sK2)
| ~ member(sK11(sK5,X0),sK2)
| ~ member(sK9(sK5,X0),sK2)
| ~ member(sK10(sK5,X0),X1)
| ~ member(sK11(sK5,X0),X1)
| ~ member(sK9(sK5,X0),X1) ),
inference(superposition,[status(thm)],[c_4362,c_5985]) ).
tcf(c_10244,plain,
( sP0(sK5,sK2)
| apply(sK4,sK9(sK5,sK2),sK11(sK5,sK2))
| ~ sP0(sK4,sK2)
| ~ member(sK10(sK5,sK2),sK2)
| ~ member(sK11(sK5,sK2),sK2)
| ~ member(sK9(sK5,sK2),sK2) ),
inference(instantiation,[status(thm)],[c_10205]) ).
tcf(c_10388,plain,
! [X0: $i,X1: $i] :
( sP0(sK5,X0)
| apply(sK3,sK9(sK5,X0),sK11(sK5,X0))
| ~ sP0(sK3,X1)
| ~ member(sK10(sK5,X0),sK2)
| ~ member(sK11(sK5,X0),sK2)
| ~ member(sK9(sK5,X0),sK2)
| ~ member(sK10(sK5,X0),X1)
| ~ member(sK11(sK5,X0),X1)
| ~ member(sK9(sK5,X0),X1) ),
inference(superposition,[status(thm)],[c_4363,c_5986]) ).
tcf(c_10427,plain,
( sP0(sK5,sK2)
| apply(sK3,sK9(sK5,sK2),sK11(sK5,sK2))
| ~ sP0(sK3,sK2)
| ~ member(sK10(sK5,sK2),sK2)
| ~ member(sK11(sK5,sK2),sK2)
| ~ member(sK9(sK5,sK2),sK2) ),
inference(instantiation,[status(thm)],[c_10388]) ).
tcf(c_10428,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_10427,c_10244,c_6320,c_5131,c_5040,c_5038,c_4856,c_3975,c_3864,c_3863,c_3858,c_3776,c_3777,c_3778,c_3779,c_755,c_751,c_741,c_731,c_721,c_711,c_701,c_691,c_681,c_671,c_344,c_340]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET773+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n004.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 11:55:05 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.13/0.40
% 0.13/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40
% 0.13/0.40 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 8.35/1.74 % SZS status Started for theBenchmark.p
% 8.35/1.74 % SZS status Theorem for theBenchmark.p
% 8.35/1.74
% 8.35/1.74 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.35/1.74
% 8.35/1.74 % ------ iProver source info
% 8.35/1.74
% 8.35/1.74 % git: date: 2026-07-19 20:42:38 +0200
% 8.35/1.74 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.35/1.74 % git: non_committed_changes: false
% 8.35/1.74
% 8.35/1.74 % ------ Parsing...
% 8.35/1.74 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 8.35/1.74
% 8.35/1.74 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 8.35/1.74
% 8.35/1.74 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 8.35/1.74 % ------ Proving...
% 8.35/1.74 % ------ Problem Properties
% 8.35/1.74
% 8.35/1.74 %
% 8.35/1.74 % clauses 24
% 8.35/1.74 % conjectures 3
% 8.35/1.74 % EPR 10
% 8.35/1.74 % Horn 12
% 8.35/1.74 % unary 3
% 8.35/1.74 % binary 7
% 8.35/1.74 % lits 77
% 8.35/1.74 % lits eq 0
% 8.35/1.74 % fd_pure 0
% 8.35/1.74 % fd_pseudo 0
% 8.35/1.74 % fd_cond 0
% 8.35/1.74 % fd_pseudo_cond 0
% 8.35/1.74 % AC symbols 0
% 8.35/1.74
% 8.35/1.74 % ------ Schedule dynamic 5 is on
% 8.35/1.74
% 8.35/1.74 % ------ no equalities: superposition off
% 8.35/1.74
% 8.35/1.74 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 8.35/1.74
% 8.35/1.74
% 8.35/1.74 % ------
% 8.35/1.74 % Current options:
% 8.35/1.74 % ------
% 8.35/1.74
% 8.35/1.74
% 8.35/1.74 %
% 8.35/1.74
% 8.35/1.74 % ------ Proving...
% 8.35/1.74 %
% 8.35/1.74
% 8.35/1.74 % SZS status Theorem for theBenchmark.p
% 8.35/1.74
% 8.35/1.74 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.35/1.74
% 8.35/1.74
%------------------------------------------------------------------------------