%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET775+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 : n007.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 3.87s 1.20s
% Output : CNFRefutation 1.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 149 ( 5 unt; 1 def)
% Number of atoms : 806 ( 0 equ)
% Maximal formula atoms : 13 ( 5 avg)
% Number of connectives : 758 ( 266 ~; 352 |; 102 &)
% ( 8 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 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 : 9 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 229 ( 0 sgn 193 !; 36 ?; 61 :)
% 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(f16,axiom,
! [X0,X1] :
( pre_order(X0,X1)
<=> ( ! [X2,X3,X4] :
( ( member(X4,X1)
& member(X3,X1)
& member(X2,X1) )
=> ( ( apply(X0,X3,X4)
& apply(X0,X2,X3) )
=> apply(X0,X2,X4) ) )
& ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+2.ax',pre_order) ).
fof(f17,conjecture,
! [X0,X1,X2] :
( ( ! [X3,X4] :
( ( member(X4,X0)
& member(X3,X0) )
=> ( apply(X2,X3,X4)
<=> ( apply(X1,X4,X3)
& apply(X1,X3,X4) ) ) )
& pre_order(X1,X0) )
=> equivalence(X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIII11) ).
fof(f18,negated_conjecture,
~ ! [X0,X1,X2] :
( ( ! [X3,X4] :
( ( member(X4,X0)
& member(X3,X0) )
=> ( apply(X2,X3,X4)
<=> ( apply(X1,X4,X3)
& apply(X1,X3,X4) ) ) )
& pre_order(X1,X0) )
=> equivalence(X2,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] :
( pre_order(X0,X1)
<=> ( ! [X3,X4,X5] :
( ( member(X5,X1)
& member(X4,X1)
& member(X3,X1) )
=> ( ( apply(X0,X4,X5)
& apply(X0,X3,X4) )
=> apply(X0,X3,X5) ) )
& ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) ) ) ),
inference(rectify,[],[f16]) ).
fof(f21,plain,
! [X0,X1] :
( pre_order(X0,X1)
=> ( ! [X3,X4,X5] :
( ( member(X5,X1)
& member(X4,X1)
& member(X3,X1) )
=> ( ( apply(X0,X4,X5)
& apply(X0,X3,X4) )
=> apply(X0,X3,X5) ) )
& ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) ) ) ),
inference(unused_predicate_definition_removal,[],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( ( ! [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) ) )
=> equivalence(X1,X0) ),
inference(unused_predicate_definition_removal,[],[f19]) ).
fof(f23,plain,
? [X0,X1,X2] :
( ! [X3,X4] :
( ~ member(X4,X0)
| ~ member(X3,X0)
| ( apply(X2,X3,X4)
<=> ( apply(X1,X4,X3)
& apply(X1,X3,X4) ) ) )
& pre_order(X1,X0)
& ~ equivalence(X2,X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f24,plain,
? [X0,X1,X2] :
( ! [X3,X4] :
( ~ member(X4,X0)
| ~ member(X3,X0)
| ( apply(X2,X3,X4)
<=> ( apply(X1,X4,X3)
& apply(X1,X3,X4) ) ) )
& pre_order(X1,X0)
& ~ equivalence(X2,X0) ),
inference(flattening,[],[f23]) ).
fof(f25,plain,
! [X0,X1] :
( ? [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) )
| equivalence(X1,X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f26,plain,
! [X0,X1] :
( ? [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) )
| equivalence(X1,X0) ),
inference(flattening,[],[f25]) ).
fof(f27,plain,
! [X0,X1] :
( ~ pre_order(X0,X1)
| ( ! [X3,X4,X5] :
( ~ member(X5,X1)
| ~ member(X4,X1)
| ~ member(X3,X1)
| ~ apply(X0,X4,X5)
| ~ apply(X0,X3,X4)
| apply(X0,X3,X5) )
& ! [X2] :
( ~ member(X2,X1)
| apply(X0,X2,X2) ) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f28,plain,
! [X0,X1] :
( ~ pre_order(X0,X1)
| ( ! [X3,X4,X5] :
( ~ member(X5,X1)
| ~ member(X4,X1)
| ~ member(X3,X1)
| ~ apply(X0,X4,X5)
| ~ apply(X0,X3,X4)
| apply(X0,X3,X5) )
& ! [X2] :
( ~ member(X2,X1)
| apply(X0,X2,X2) ) ) ),
inference(flattening,[],[f27]) ).
fof(f31,plain,
? [X0,X1,X2] :
( ! [X3,X4] :
( ~ member(X4,X0)
| ~ member(X3,X0)
| ( ( ~ apply(X2,X3,X4)
| ( apply(X1,X4,X3)
& apply(X1,X3,X4) ) )
& ( ~ apply(X1,X4,X3)
| ~ apply(X1,X3,X4)
| apply(X2,X3,X4) ) ) )
& pre_order(X1,X0)
& ~ equivalence(X2,X0) ),
inference(nnf_transformation,[],[f24]) ).
fof(f32,plain,
? [X0,X1,X2] :
( ! [X3,X4] :
( ~ member(X4,X0)
| ~ member(X3,X0)
| ( ( ~ apply(X2,X3,X4)
| ( apply(X1,X4,X3)
& apply(X1,X3,X4) ) )
& ( ~ apply(X1,X4,X3)
| ~ apply(X1,X3,X4)
| apply(X2,X3,X4) ) ) )
& pre_order(X1,X0)
& ~ equivalence(X2,X0) ),
inference(flattening,[],[f31]) ).
fof(f33,plain,
( ! [X3,X4] :
( ~ member(X4,sK1)
| ~ member(X3,sK1)
| ( ( ~ apply(sK3,X3,X4)
| ( apply(sK2,X4,X3)
& apply(sK2,X3,X4) ) )
& ( ~ apply(sK2,X4,X3)
| ~ apply(sK2,X3,X4)
| apply(sK3,X3,X4) ) ) )
& pre_order(sK2,sK1)
& ~ equivalence(sK3,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f32]) ).
fof(f37,plain,
! [X0,X1] :
( sP0(X1,X0)
| ( member(sK9(X0,X1),X0)
& member(sK8(X0,X1),X0)
& apply(X1,sK8(X0,X1),sK9(X0,X1))
& ~ apply(X1,sK9(X0,X1),sK8(X0,X1)) )
| ( member(sK7(X0,X1),X0)
& ~ apply(X1,sK7(X0,X1),sK7(X0,X1)) )
| equivalence(X1,X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9]),skolemize(X2,sK7(X0,X1)),skolemize(X3,sK8(X0,X1)),skolemize(X4,sK9(X0,X1))],[f30]) ).
fof(f38,plain,
! [X3,X4] :
( ~ member(X4,sK1)
| ~ member(X3,sK1)
| ~ apply(sK3,X3,X4)
| apply(sK2,X4,X3) ),
inference(cnf_transformation,[],[f33]) ).
fof(f39,plain,
! [X3,X4] :
( ~ member(X4,sK1)
| ~ member(X3,sK1)
| ~ apply(sK3,X3,X4)
| apply(sK2,X3,X4) ),
inference(cnf_transformation,[],[f33]) ).
fof(f40,plain,
! [X3,X4] :
( ~ member(X4,sK1)
| ~ member(X3,sK1)
| ~ apply(sK2,X4,X3)
| ~ apply(sK2,X3,X4)
| apply(sK3,X3,X4) ),
inference(cnf_transformation,[],[f33]) ).
fof(f41,plain,
pre_order(sK2,sK1),
inference(cnf_transformation,[],[f33]) ).
fof(f42,plain,
~ equivalence(sK3,sK1),
inference(cnf_transformation,[],[f33]) ).
fof(f49,plain,
! [X0,X1] :
( sP0(X1,X0)
| member(sK9(X0,X1),X0)
| member(sK7(X0,X1),X0)
| equivalence(X1,X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f50,plain,
! [X0,X1] :
( sP0(X1,X0)
| member(sK8(X0,X1),X0)
| member(sK7(X0,X1),X0)
| equivalence(X1,X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f51,plain,
! [X0,X1] :
( sP0(X1,X0)
| apply(X1,sK8(X0,X1),sK9(X0,X1))
| member(sK7(X0,X1),X0)
| equivalence(X1,X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f52,plain,
! [X0,X1] :
( sP0(X1,X0)
| ~ apply(X1,sK9(X0,X1),sK8(X0,X1))
| member(sK7(X0,X1),X0)
| equivalence(X1,X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f53,plain,
! [X0,X1] :
( sP0(X1,X0)
| member(sK9(X0,X1),X0)
| ~ apply(X1,sK7(X0,X1),sK7(X0,X1))
| equivalence(X1,X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f54,plain,
! [X0,X1] :
( sP0(X1,X0)
| member(sK8(X0,X1),X0)
| ~ apply(X1,sK7(X0,X1),sK7(X0,X1))
| equivalence(X1,X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f55,plain,
! [X0,X1] :
( sP0(X1,X0)
| apply(X1,sK8(X0,X1),sK9(X0,X1))
| ~ apply(X1,sK7(X0,X1),sK7(X0,X1))
| equivalence(X1,X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f56,plain,
! [X0,X1] :
( sP0(X1,X0)
| ~ apply(X1,sK9(X0,X1),sK8(X0,X1))
| ~ apply(X1,sK7(X0,X1),sK7(X0,X1))
| equivalence(X1,X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f57,plain,
! [X3,X0,X1,X4,X5] :
( ~ pre_order(X0,X1)
| ~ member(X5,X1)
| ~ member(X4,X1)
| ~ member(X3,X1)
| ~ apply(X0,X4,X5)
| ~ apply(X0,X3,X4)
| apply(X0,X3,X5) ),
inference(cnf_transformation,[],[f28]) ).
fof(f58,plain,
! [X2,X0,X1] :
( ~ pre_order(X0,X1)
| ~ member(X2,X1)
| apply(X0,X2,X2) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_49,negated_conjecture,
~ equivalence(sK3,sK1),
inference(cnf_transformation,[],[f42]) ).
tcf(c_50,negated_conjecture,
pre_order(sK2,sK1),
inference(cnf_transformation,[],[f41]) ).
tcf(c_51,negated_conjecture,
! [X0: $i,X1: $i] :
( apply(sK3,X0,X1)
| ~ member(X1,sK1)
| ~ member(X0,sK1)
| ~ apply(sK2,X1,X0)
| ~ apply(sK2,X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_52,negated_conjecture,
! [X0: $i,X1: $i] :
( apply(sK2,X0,X1)
| ~ member(X1,sK1)
| ~ member(X0,sK1)
| ~ apply(sK3,X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_53,negated_conjecture,
! [X0: $i,X1: $i] :
( apply(sK2,X1,X0)
| ~ member(X1,sK1)
| ~ member(X0,sK1)
| ~ apply(sK3,X0,X1) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( sP0(X0,X1)
| equivalence(X0,X1)
| ~ apply(X0,sK9(X1,X0),sK8(X1,X0))
| ~ apply(X0,sK7(X1,X0),sK7(X1,X0)) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( sP0(X0,X1)
| equivalence(X0,X1)
| apply(X0,sK8(X1,X0),sK9(X1,X0))
| ~ apply(X0,sK7(X1,X0),sK7(X1,X0)) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( sP0(X0,X1)
| equivalence(X0,X1)
| member(sK8(X1,X0),X1)
| ~ apply(X0,sK7(X1,X0),sK7(X1,X0)) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( sP0(X0,X1)
| equivalence(X0,X1)
| member(sK9(X1,X0),X1)
| ~ apply(X0,sK7(X1,X0),sK7(X1,X0)) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( sP0(X0,X1)
| equivalence(X0,X1)
| member(sK7(X1,X0),X1)
| ~ apply(X0,sK9(X1,X0),sK8(X1,X0)) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( sP0(X0,X1)
| equivalence(X0,X1)
| member(sK7(X1,X0),X1)
| apply(X0,sK8(X1,X0),sK9(X1,X0)) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( sP0(X1,X0)
| equivalence(X1,X0)
| member(sK8(X0,X1),X0)
| member(sK7(X0,X1),X0) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( sP0(X1,X0)
| equivalence(X1,X0)
| member(sK9(X0,X1),X0)
| member(sK7(X0,X1),X0) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] :
( apply(X0,X2,X2)
| ~ member(X2,X1)
| ~ pre_order(X0,X1) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apply(X0,X1,X3)
| ~ member(X3,X4)
| ~ member(X2,X4)
| ~ member(X1,X4)
| ~ pre_order(X0,X4)
| ~ apply(X0,X2,X3)
| ~ apply(X0,X1,X2) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_225,plain,
! [X0: $i] :
( apply(sK2,X0,X0)
| ~ member(X0,sK1) ),
inference(resolution,[status(thm)],[c_50,c_68]) ).
tcf(c_233,plain,
! [X0: $i,X1: $i,X2: $i] :
( apply(sK2,X0,X2)
| ~ member(X2,sK1)
| ~ member(X1,sK1)
| ~ member(X0,sK1)
| ~ apply(sK2,X1,X2)
| ~ apply(sK2,X0,X1) ),
inference(resolution,[status(thm)],[c_50,c_69]) ).
tcf(c_260,plain,
( sP0(sK3,sK1)
| member(sK7(sK1,sK3),sK1)
| apply(sK3,sK8(sK1,sK3),sK9(sK1,sK3)) ),
inference(resolution,[status(thm)],[c_49,c_65]) ).
tcf(c_270,plain,
( sP0(sK3,sK1)
| member(sK7(sK1,sK3),sK1)
| ~ apply(sK3,sK9(sK1,sK3),sK8(sK1,sK3)) ),
inference(resolution,[status(thm)],[c_49,c_64]) ).
tcf(c_280,plain,
( sP0(sK3,sK1)
| member(sK9(sK1,sK3),sK1)
| ~ apply(sK3,sK7(sK1,sK3),sK7(sK1,sK3)) ),
inference(resolution,[status(thm)],[c_49,c_63]) ).
tcf(c_290,plain,
( sP0(sK3,sK1)
| member(sK8(sK1,sK3),sK1)
| ~ apply(sK3,sK7(sK1,sK3),sK7(sK1,sK3)) ),
inference(resolution,[status(thm)],[c_49,c_62]) ).
tcf(c_300,plain,
( sP0(sK3,sK1)
| apply(sK3,sK8(sK1,sK3),sK9(sK1,sK3))
| ~ apply(sK3,sK7(sK1,sK3),sK7(sK1,sK3)) ),
inference(resolution,[status(thm)],[c_49,c_61]) ).
tcf(c_310,plain,
( sP0(sK3,sK1)
| ~ apply(sK3,sK9(sK1,sK3),sK8(sK1,sK3))
| ~ apply(sK3,sK7(sK1,sK3),sK7(sK1,sK3)) ),
inference(resolution,[status(thm)],[c_49,c_60]) ).
tcf(c_320,plain,
( sP0(sK3,sK1)
| member(sK9(sK1,sK3),sK1)
| member(sK7(sK1,sK3),sK1) ),
inference(resolution,[status(thm)],[c_49,c_67]) ).
tcf(c_330,plain,
( sP0(sK3,sK1)
| member(sK8(sK1,sK3),sK1)
| member(sK7(sK1,sK3),sK1) ),
inference(resolution,[status(thm)],[c_49,c_66]) ).
tcf(c_989,plain,
( apply(sK2,sK7(sK1,sK3),sK7(sK1,sK3))
| ~ member(sK7(sK1,sK3),sK1) ),
inference(instantiation,[status(thm)],[c_225]) ).
tcf(c_990,plain,
! [X0: $i] :
( apply(sK3,sK7(sK1,sK3),X0)
| ~ member(X0,sK1)
| ~ member(sK7(sK1,sK3),sK1)
| ~ apply(sK2,X0,sK7(sK1,sK3))
| ~ apply(sK2,sK7(sK1,sK3),X0) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_1111,plain,
( apply(sK3,sK7(sK1,sK3),sK7(sK1,sK3))
| ~ member(sK7(sK1,sK3),sK1)
| ~ apply(sK2,sK7(sK1,sK3),sK7(sK1,sK3)) ),
inference(instantiation,[status(thm)],[c_990]) ).
tcf(c_1115,plain,
! [X0: $i] :
( apply(sK2,X0,sK8(sK1,sK3))
| ~ member(X0,sK1)
| ~ member(sK8(sK1,sK3),sK1)
| ~ apply(sK3,sK8(sK1,sK3),X0) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_1116,plain,
! [X0: $i] :
( apply(sK2,sK8(sK1,sK3),X0)
| ~ member(X0,sK1)
| ~ member(sK8(sK1,sK3),sK1)
| ~ apply(sK3,sK8(sK1,sK3),X0) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_1122,plain,
! [X0: $i] :
( apply(sK3,sK9(sK1,sK3),X0)
| ~ member(X0,sK1)
| ~ member(sK9(sK1,sK3),sK1)
| ~ apply(sK2,X0,sK9(sK1,sK3))
| ~ apply(sK2,sK9(sK1,sK3),X0) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_1178,plain,
( apply(sK3,sK9(sK1,sK3),sK8(sK1,sK3))
| ~ member(sK8(sK1,sK3),sK1)
| ~ member(sK9(sK1,sK3),sK1)
| ~ apply(sK2,sK8(sK1,sK3),sK9(sK1,sK3))
| ~ apply(sK2,sK9(sK1,sK3),sK8(sK1,sK3)) ),
inference(instantiation,[status(thm)],[c_1122]) ).
tcf(c_1179,plain,
! [X0: $i,X1: $i] :
( apply(sK2,sK6(sK3,sK1),X1)
| ~ member(X1,sK1)
| ~ member(X0,sK1)
| ~ apply(sK2,X0,X1)
| ~ member(sK6(sK3,sK1),sK1)
| ~ apply(sK2,sK6(sK3,sK1),X0) ),
inference(instantiation,[status(thm)],[c_233]) ).
tcf(c_1190,plain,
! [X0: $i] :
( apply(sK2,X0,sK5(sK3,sK1))
| ~ member(X0,sK1)
| ~ member(sK5(sK3,sK1),sK1)
| ~ apply(sK3,sK5(sK3,sK1),X0) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_1191,plain,
! [X0: $i] :
( apply(sK2,sK5(sK3,sK1),X0)
| ~ member(X0,sK1)
| ~ member(sK5(sK3,sK1),sK1)
| ~ apply(sK3,sK5(sK3,sK1),X0) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_1195,plain,
! [X0: $i,X1: $i] :
( apply(sK2,sK4(sK3,sK1),X1)
| ~ member(X1,sK1)
| ~ member(X0,sK1)
| ~ apply(sK2,X0,X1)
| ~ member(sK4(sK3,sK1),sK1)
| ~ apply(sK2,sK4(sK3,sK1),X0) ),
inference(instantiation,[status(thm)],[c_233]) ).
tcf(c_1197,plain,
! [X0: $i] :
( apply(sK3,sK4(sK3,sK1),X0)
| ~ member(X0,sK1)
| ~ member(sK4(sK3,sK1),sK1)
| ~ apply(sK2,X0,sK4(sK3,sK1))
| ~ apply(sK2,sK4(sK3,sK1),X0) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_1198,plain,
! [X0: $i] :
( apply(sK2,X0,sK4(sK3,sK1))
| ~ member(X0,sK1)
| ~ member(sK4(sK3,sK1),sK1)
| ~ apply(sK3,sK4(sK3,sK1),X0) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_1199,plain,
! [X0: $i] :
( apply(sK2,sK4(sK3,sK1),X0)
| ~ member(X0,sK1)
| ~ member(sK4(sK3,sK1),sK1)
| ~ apply(sK3,sK4(sK3,sK1),X0) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_1203,plain,
( apply(sK3,sK4(sK3,sK1),sK6(sK3,sK1))
| ~ member(sK6(sK3,sK1),sK1)
| ~ member(sK4(sK3,sK1),sK1)
| ~ apply(sK2,sK6(sK3,sK1),sK4(sK3,sK1))
| ~ apply(sK2,sK4(sK3,sK1),sK6(sK3,sK1)) ),
inference(instantiation,[status(thm)],[c_1197]) ).
tcf(c_1209,plain,
( apply(sK2,sK9(sK1,sK3),sK8(sK1,sK3))
| ~ member(sK8(sK1,sK3),sK1)
| ~ member(sK9(sK1,sK3),sK1)
| ~ apply(sK3,sK8(sK1,sK3),sK9(sK1,sK3)) ),
inference(instantiation,[status(thm)],[c_1115]) ).
tcf(c_1230,plain,
( apply(sK2,sK8(sK1,sK3),sK9(sK1,sK3))
| ~ member(sK8(sK1,sK3),sK1)
| ~ member(sK9(sK1,sK3),sK1)
| ~ apply(sK3,sK8(sK1,sK3),sK9(sK1,sK3)) ),
inference(instantiation,[status(thm)],[c_1116]) ).
tcf(c_1289,plain,
( apply(sK2,sK4(sK3,sK1),sK5(sK3,sK1))
| ~ member(sK5(sK3,sK1),sK1)
| ~ member(sK4(sK3,sK1),sK1)
| ~ apply(sK3,sK4(sK3,sK1),sK5(sK3,sK1)) ),
inference(instantiation,[status(thm)],[c_1199]) ).
tcf(c_1297,plain,
! [X0: $i] :
( apply(sK2,sK4(sK3,sK1),X0)
| ~ member(X0,sK1)
| ~ member(sK5(sK3,sK1),sK1)
| ~ member(sK4(sK3,sK1),sK1)
| ~ apply(sK2,sK5(sK3,sK1),X0)
| ~ apply(sK2,sK4(sK3,sK1),sK5(sK3,sK1)) ),
inference(instantiation,[status(thm)],[c_1195]) ).
tcf(c_1327,plain,
( apply(sK2,sK6(sK3,sK1),sK5(sK3,sK1))
| ~ member(sK5(sK3,sK1),sK1)
| ~ member(sK6(sK3,sK1),sK1)
| ~ apply(sK3,sK5(sK3,sK1),sK6(sK3,sK1)) ),
inference(instantiation,[status(thm)],[c_1190]) ).
tcf(c_1333,plain,
( apply(sK2,sK5(sK3,sK1),sK4(sK3,sK1))
| ~ member(sK5(sK3,sK1),sK1)
| ~ member(sK4(sK3,sK1),sK1)
| ~ apply(sK3,sK4(sK3,sK1),sK5(sK3,sK1)) ),
inference(instantiation,[status(thm)],[c_1198]) ).
tcf(c_1337,plain,
( apply(sK2,sK4(sK3,sK1),sK6(sK3,sK1))
| ~ member(sK5(sK3,sK1),sK1)
| ~ member(sK6(sK3,sK1),sK1)
| ~ member(sK4(sK3,sK1),sK1)
| ~ apply(sK2,sK5(sK3,sK1),sK6(sK3,sK1))
| ~ apply(sK2,sK4(sK3,sK1),sK5(sK3,sK1)) ),
inference(instantiation,[status(thm)],[c_1297]) ).
tcf(c_1347,plain,
( apply(sK2,sK5(sK3,sK1),sK6(sK3,sK1))
| ~ member(sK5(sK3,sK1),sK1)
| ~ member(sK6(sK3,sK1),sK1)
| ~ apply(sK3,sK5(sK3,sK1),sK6(sK3,sK1)) ),
inference(instantiation,[status(thm)],[c_1191]) ).
tcf(c_1360,plain,
! [X0: $i] :
( apply(sK2,sK6(sK3,sK1),X0)
| ~ member(X0,sK1)
| ~ member(sK5(sK3,sK1),sK1)
| ~ member(sK6(sK3,sK1),sK1)
| ~ apply(sK2,sK5(sK3,sK1),X0)
| ~ apply(sK2,sK6(sK3,sK1),sK5(sK3,sK1)) ),
inference(instantiation,[status(thm)],[c_1179]) ).
tcf(c_1382,plain,
( apply(sK2,sK6(sK3,sK1),sK4(sK3,sK1))
| ~ member(sK5(sK3,sK1),sK1)
| ~ member(sK6(sK3,sK1),sK1)
| ~ member(sK4(sK3,sK1),sK1)
| ~ apply(sK2,sK5(sK3,sK1),sK4(sK3,sK1))
| ~ apply(sK2,sK6(sK3,sK1),sK5(sK3,sK1)) ),
inference(instantiation,[status(thm)],[c_1360]) ).
fof(f29,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(f30,plain,
! [X0,X1] :
( 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) )
| equivalence(X1,X0) ),
inference(definition_folding,[],[f26,f29]) ).
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) ) ),
inference(nnf_transformation,[],[f29]) ).
fof(f35,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ? [X2,X3,X4] :
( member(X4,X1)
& member(X3,X1)
& member(X2,X1)
& apply(X0,X3,X4)
& apply(X0,X2,X3)
& ~ apply(X0,X2,X4) ) ),
inference(rectify,[],[f34]) ).
fof(f36,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ( member(sK6(X0,X1),X1)
& member(sK5(X0,X1),X1)
& member(sK4(X0,X1),X1)
& apply(X0,sK5(X0,X1),sK6(X0,X1))
& apply(X0,sK4(X0,X1),sK5(X0,X1))
& ~ apply(X0,sK4(X0,X1),sK6(X0,X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X2,sK4(X0,X1)),skolemize(X3,sK5(X0,X1)),skolemize(X4,sK6(X0,X1))],[f35]) ).
fof(f43,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| member(sK6(X0,X1),X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f44,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| member(sK5(X0,X1),X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f45,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| member(sK4(X0,X1),X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f46,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| apply(X0,sK5(X0,X1),sK6(X0,X1)) ),
inference(cnf_transformation,[],[f36]) ).
fof(f47,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| apply(X0,sK4(X0,X1),sK5(X0,X1)) ),
inference(cnf_transformation,[],[f36]) ).
fof(f48,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ~ apply(X0,sK4(X0,X1),sK6(X0,X1)) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( ~ sP0(X0,X1)
| ~ apply(X0,sK4(X0,X1),sK6(X0,X1)) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( apply(X0,sK4(X0,X1),sK5(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( apply(X0,sK5(X0,X1),sK6(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( member(sK4(X0,X1),X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( member(sK5(X0,X1),X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( member(sK6(X0,X1),X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_364,plain,
( member(sK8(sK1,sK3),sK1)
| member(sK7(sK1,sK3),sK1)
| member(sK6(sK3,sK1),sK1) ),
inference(resolution,[status(thm)],[c_59,c_330]) ).
tcf(c_374,plain,
( member(sK9(sK1,sK3),sK1)
| member(sK7(sK1,sK3),sK1)
| member(sK6(sK3,sK1),sK1) ),
inference(resolution,[status(thm)],[c_59,c_320]) ).
tcf(c_384,plain,
( member(sK6(sK3,sK1),sK1)
| ~ apply(sK3,sK9(sK1,sK3),sK8(sK1,sK3))
| ~ apply(sK3,sK7(sK1,sK3),sK7(sK1,sK3)) ),
inference(resolution,[status(thm)],[c_59,c_310]) ).
tcf(c_394,plain,
( member(sK6(sK3,sK1),sK1)
| apply(sK3,sK8(sK1,sK3),sK9(sK1,sK3))
| ~ apply(sK3,sK7(sK1,sK3),sK7(sK1,sK3)) ),
inference(resolution,[status(thm)],[c_59,c_300]) ).
tcf(c_404,plain,
( member(sK8(sK1,sK3),sK1)
| member(sK6(sK3,sK1),sK1)
| ~ apply(sK3,sK7(sK1,sK3),sK7(sK1,sK3)) ),
inference(resolution,[status(thm)],[c_59,c_290]) ).
tcf(c_414,plain,
( member(sK9(sK1,sK3),sK1)
| member(sK6(sK3,sK1),sK1)
| ~ apply(sK3,sK7(sK1,sK3),sK7(sK1,sK3)) ),
inference(resolution,[status(thm)],[c_59,c_280]) ).
tcf(c_424,plain,
( member(sK7(sK1,sK3),sK1)
| member(sK6(sK3,sK1),sK1)
| ~ apply(sK3,sK9(sK1,sK3),sK8(sK1,sK3)) ),
inference(resolution,[status(thm)],[c_59,c_270]) ).
tcf(c_434,plain,
( member(sK7(sK1,sK3),sK1)
| member(sK6(sK3,sK1),sK1)
| apply(sK3,sK8(sK1,sK3),sK9(sK1,sK3)) ),
inference(resolution,[status(thm)],[c_59,c_260]) ).
tcf(c_444,plain,
( member(sK8(sK1,sK3),sK1)
| member(sK7(sK1,sK3),sK1)
| member(sK5(sK3,sK1),sK1) ),
inference(resolution,[status(thm)],[c_58,c_330]) ).
tcf(c_454,plain,
( member(sK9(sK1,sK3),sK1)
| member(sK7(sK1,sK3),sK1)
| member(sK5(sK3,sK1),sK1) ),
inference(resolution,[status(thm)],[c_58,c_320]) ).
tcf(c_464,plain,
( member(sK5(sK3,sK1),sK1)
| ~ apply(sK3,sK9(sK1,sK3),sK8(sK1,sK3))
| ~ apply(sK3,sK7(sK1,sK3),sK7(sK1,sK3)) ),
inference(resolution,[status(thm)],[c_58,c_310]) ).
tcf(c_474,plain,
( member(sK5(sK3,sK1),sK1)
| apply(sK3,sK8(sK1,sK3),sK9(sK1,sK3))
| ~ apply(sK3,sK7(sK1,sK3),sK7(sK1,sK3)) ),
inference(resolution,[status(thm)],[c_58,c_300]) ).
tcf(c_484,plain,
( member(sK8(sK1,sK3),sK1)
| member(sK5(sK3,sK1),sK1)
| ~ apply(sK3,sK7(sK1,sK3),sK7(sK1,sK3)) ),
inference(resolution,[status(thm)],[c_58,c_290]) ).
tcf(c_494,plain,
( member(sK9(sK1,sK3),sK1)
| member(sK5(sK3,sK1),sK1)
| ~ apply(sK3,sK7(sK1,sK3),sK7(sK1,sK3)) ),
inference(resolution,[status(thm)],[c_58,c_280]) ).
tcf(c_504,plain,
( member(sK7(sK1,sK3),sK1)
| member(sK5(sK3,sK1),sK1)
| ~ apply(sK3,sK9(sK1,sK3),sK8(sK1,sK3)) ),
inference(resolution,[status(thm)],[c_58,c_270]) ).
tcf(c_514,plain,
( member(sK7(sK1,sK3),sK1)
| member(sK5(sK3,sK1),sK1)
| apply(sK3,sK8(sK1,sK3),sK9(sK1,sK3)) ),
inference(resolution,[status(thm)],[c_58,c_260]) ).
tcf(c_524,plain,
( member(sK8(sK1,sK3),sK1)
| member(sK7(sK1,sK3),sK1)
| member(sK4(sK3,sK1),sK1) ),
inference(resolution,[status(thm)],[c_57,c_330]) ).
tcf(c_534,plain,
( member(sK9(sK1,sK3),sK1)
| member(sK7(sK1,sK3),sK1)
| member(sK4(sK3,sK1),sK1) ),
inference(resolution,[status(thm)],[c_57,c_320]) ).
tcf(c_544,plain,
( member(sK4(sK3,sK1),sK1)
| ~ apply(sK3,sK9(sK1,sK3),sK8(sK1,sK3))
| ~ apply(sK3,sK7(sK1,sK3),sK7(sK1,sK3)) ),
inference(resolution,[status(thm)],[c_57,c_310]) ).
tcf(c_554,plain,
( member(sK4(sK3,sK1),sK1)
| apply(sK3,sK8(sK1,sK3),sK9(sK1,sK3))
| ~ apply(sK3,sK7(sK1,sK3),sK7(sK1,sK3)) ),
inference(resolution,[status(thm)],[c_57,c_300]) ).
tcf(c_564,plain,
( member(sK8(sK1,sK3),sK1)
| member(sK4(sK3,sK1),sK1)
| ~ apply(sK3,sK7(sK1,sK3),sK7(sK1,sK3)) ),
inference(resolution,[status(thm)],[c_57,c_290]) ).
tcf(c_574,plain,
( member(sK9(sK1,sK3),sK1)
| member(sK4(sK3,sK1),sK1)
| ~ apply(sK3,sK7(sK1,sK3),sK7(sK1,sK3)) ),
inference(resolution,[status(thm)],[c_57,c_280]) ).
tcf(c_584,plain,
( member(sK7(sK1,sK3),sK1)
| member(sK4(sK3,sK1),sK1)
| ~ apply(sK3,sK9(sK1,sK3),sK8(sK1,sK3)) ),
inference(resolution,[status(thm)],[c_57,c_270]) ).
tcf(c_594,plain,
( member(sK7(sK1,sK3),sK1)
| member(sK4(sK3,sK1),sK1)
| apply(sK3,sK8(sK1,sK3),sK9(sK1,sK3)) ),
inference(resolution,[status(thm)],[c_57,c_260]) ).
tcf(c_604,plain,
( member(sK8(sK1,sK3),sK1)
| member(sK7(sK1,sK3),sK1)
| apply(sK3,sK5(sK3,sK1),sK6(sK3,sK1)) ),
inference(resolution,[status(thm)],[c_56,c_330]) ).
tcf(c_614,plain,
( member(sK9(sK1,sK3),sK1)
| member(sK7(sK1,sK3),sK1)
| apply(sK3,sK5(sK3,sK1),sK6(sK3,sK1)) ),
inference(resolution,[status(thm)],[c_56,c_320]) ).
tcf(c_624,plain,
( apply(sK3,sK5(sK3,sK1),sK6(sK3,sK1))
| ~ apply(sK3,sK9(sK1,sK3),sK8(sK1,sK3))
| ~ apply(sK3,sK7(sK1,sK3),sK7(sK1,sK3)) ),
inference(resolution,[status(thm)],[c_56,c_310]) ).
tcf(c_634,plain,
( apply(sK3,sK8(sK1,sK3),sK9(sK1,sK3))
| apply(sK3,sK5(sK3,sK1),sK6(sK3,sK1))
| ~ apply(sK3,sK7(sK1,sK3),sK7(sK1,sK3)) ),
inference(resolution,[status(thm)],[c_56,c_300]) ).
tcf(c_644,plain,
( member(sK8(sK1,sK3),sK1)
| apply(sK3,sK5(sK3,sK1),sK6(sK3,sK1))
| ~ apply(sK3,sK7(sK1,sK3),sK7(sK1,sK3)) ),
inference(resolution,[status(thm)],[c_56,c_290]) ).
tcf(c_654,plain,
( member(sK9(sK1,sK3),sK1)
| apply(sK3,sK5(sK3,sK1),sK6(sK3,sK1))
| ~ apply(sK3,sK7(sK1,sK3),sK7(sK1,sK3)) ),
inference(resolution,[status(thm)],[c_56,c_280]) ).
tcf(c_664,plain,
( member(sK7(sK1,sK3),sK1)
| apply(sK3,sK5(sK3,sK1),sK6(sK3,sK1))
| ~ apply(sK3,sK9(sK1,sK3),sK8(sK1,sK3)) ),
inference(resolution,[status(thm)],[c_56,c_270]) ).
tcf(c_674,plain,
( member(sK7(sK1,sK3),sK1)
| apply(sK3,sK8(sK1,sK3),sK9(sK1,sK3))
| apply(sK3,sK5(sK3,sK1),sK6(sK3,sK1)) ),
inference(resolution,[status(thm)],[c_56,c_260]) ).
tcf(c_684,plain,
( member(sK8(sK1,sK3),sK1)
| member(sK7(sK1,sK3),sK1)
| apply(sK3,sK4(sK3,sK1),sK5(sK3,sK1)) ),
inference(resolution,[status(thm)],[c_55,c_330]) ).
tcf(c_694,plain,
( member(sK9(sK1,sK3),sK1)
| member(sK7(sK1,sK3),sK1)
| apply(sK3,sK4(sK3,sK1),sK5(sK3,sK1)) ),
inference(resolution,[status(thm)],[c_55,c_320]) ).
tcf(c_704,plain,
( apply(sK3,sK4(sK3,sK1),sK5(sK3,sK1))
| ~ apply(sK3,sK9(sK1,sK3),sK8(sK1,sK3))
| ~ apply(sK3,sK7(sK1,sK3),sK7(sK1,sK3)) ),
inference(resolution,[status(thm)],[c_55,c_310]) ).
tcf(c_714,plain,
( apply(sK3,sK8(sK1,sK3),sK9(sK1,sK3))
| apply(sK3,sK4(sK3,sK1),sK5(sK3,sK1))
| ~ apply(sK3,sK7(sK1,sK3),sK7(sK1,sK3)) ),
inference(resolution,[status(thm)],[c_55,c_300]) ).
tcf(c_724,plain,
( member(sK8(sK1,sK3),sK1)
| apply(sK3,sK4(sK3,sK1),sK5(sK3,sK1))
| ~ apply(sK3,sK7(sK1,sK3),sK7(sK1,sK3)) ),
inference(resolution,[status(thm)],[c_55,c_290]) ).
tcf(c_734,plain,
( member(sK9(sK1,sK3),sK1)
| apply(sK3,sK4(sK3,sK1),sK5(sK3,sK1))
| ~ apply(sK3,sK7(sK1,sK3),sK7(sK1,sK3)) ),
inference(resolution,[status(thm)],[c_55,c_280]) ).
tcf(c_744,plain,
( member(sK7(sK1,sK3),sK1)
| apply(sK3,sK4(sK3,sK1),sK5(sK3,sK1))
| ~ apply(sK3,sK9(sK1,sK3),sK8(sK1,sK3)) ),
inference(resolution,[status(thm)],[c_55,c_270]) ).
tcf(c_754,plain,
( member(sK7(sK1,sK3),sK1)
| apply(sK3,sK8(sK1,sK3),sK9(sK1,sK3))
| apply(sK3,sK4(sK3,sK1),sK5(sK3,sK1)) ),
inference(resolution,[status(thm)],[c_55,c_260]) ).
tcf(c_764,plain,
( member(sK8(sK1,sK3),sK1)
| member(sK7(sK1,sK3),sK1)
| ~ apply(sK3,sK4(sK3,sK1),sK6(sK3,sK1)) ),
inference(resolution,[status(thm)],[c_54,c_330]) ).
tcf(c_774,plain,
( member(sK9(sK1,sK3),sK1)
| member(sK7(sK1,sK3),sK1)
| ~ apply(sK3,sK4(sK3,sK1),sK6(sK3,sK1)) ),
inference(resolution,[status(thm)],[c_54,c_320]) ).
tcf(c_784,plain,
( ~ apply(sK3,sK9(sK1,sK3),sK8(sK1,sK3))
| ~ apply(sK3,sK7(sK1,sK3),sK7(sK1,sK3))
| ~ apply(sK3,sK4(sK3,sK1),sK6(sK3,sK1)) ),
inference(resolution,[status(thm)],[c_54,c_310]) ).
tcf(c_794,plain,
( apply(sK3,sK8(sK1,sK3),sK9(sK1,sK3))
| ~ apply(sK3,sK7(sK1,sK3),sK7(sK1,sK3))
| ~ apply(sK3,sK4(sK3,sK1),sK6(sK3,sK1)) ),
inference(resolution,[status(thm)],[c_54,c_300]) ).
tcf(c_804,plain,
( member(sK8(sK1,sK3),sK1)
| ~ apply(sK3,sK7(sK1,sK3),sK7(sK1,sK3))
| ~ apply(sK3,sK4(sK3,sK1),sK6(sK3,sK1)) ),
inference(resolution,[status(thm)],[c_54,c_290]) ).
tcf(c_814,plain,
( member(sK9(sK1,sK3),sK1)
| ~ apply(sK3,sK7(sK1,sK3),sK7(sK1,sK3))
| ~ apply(sK3,sK4(sK3,sK1),sK6(sK3,sK1)) ),
inference(resolution,[status(thm)],[c_54,c_280]) ).
tcf(c_824,plain,
( member(sK7(sK1,sK3),sK1)
| ~ apply(sK3,sK9(sK1,sK3),sK8(sK1,sK3))
| ~ apply(sK3,sK4(sK3,sK1),sK6(sK3,sK1)) ),
inference(resolution,[status(thm)],[c_54,c_270]) ).
tcf(c_834,plain,
( member(sK7(sK1,sK3),sK1)
| apply(sK3,sK8(sK1,sK3),sK9(sK1,sK3))
| ~ apply(sK3,sK4(sK3,sK1),sK6(sK3,sK1)) ),
inference(resolution,[status(thm)],[c_54,c_260]) ).
tcf(c_1393,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1382,c_1347,c_1337,c_1333,c_1327,c_1289,c_1230,c_1209,c_1203,c_1178,c_1111,c_989,c_834,c_824,c_814,c_804,c_794,c_784,c_774,c_764,c_754,c_744,c_734,c_724,c_714,c_704,c_694,c_684,c_674,c_664,c_654,c_644,c_634,c_624,c_614,c_604,c_594,c_584,c_574,c_564,c_554,c_544,c_534,c_524,c_514,c_504,c_494,c_484,c_474,c_464,c_454,c_444,c_434,c_424,c_414,c_404,c_394,c_384,c_374,c_364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET775+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 11:53:22 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 3.87/1.20 % SZS status Started for theBenchmark.p
% 3.87/1.20 % SZS status Theorem for theBenchmark.p
% 3.87/1.20
% 3.87/1.20 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.87/1.20
% 3.87/1.20 % ------ iProver source info
% 3.87/1.20
% 3.87/1.20 % git: date: 2026-07-19 20:42:38 +0200
% 3.87/1.20 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.87/1.20 % git: non_committed_changes: false
% 3.87/1.20
% 3.87/1.20 % ------ Parsing...
% 3.87/1.20 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.87/1.20
% 3.87/1.20 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe:2:0s pe_e %
% 3.87/1.20
% 3.87/1.20 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.87/1.20 % ------ Proving...
% 3.87/1.20 % ------ Problem Properties
% 3.87/1.20
% 3.87/1.20 %
% 3.87/1.20 % clauses 53
% 3.87/1.20 % conjectures 3
% 3.87/1.20 % EPR 5
% 3.87/1.20 % Horn 15
% 3.87/1.20 % unary 0
% 3.87/1.20 % binary 1
% 3.87/1.20 % lits 165
% 3.87/1.20 % lits eq 0
% 3.87/1.20 % fd_pure 0
% 3.87/1.20 % fd_pseudo 0
% 3.87/1.20 % fd_cond 0
% 3.87/1.20 % fd_pseudo_cond 0
% 3.87/1.20 % AC symbols 0
% 3.87/1.20
% 3.87/1.20 % ------ Schedule dynamic 5 is on
% 3.87/1.20
% 3.87/1.20 % ------ no equalities: superposition off
% 3.87/1.20
% 3.87/1.20 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.87/1.20
% 3.87/1.20
% 3.87/1.20 % ------
% 3.87/1.20 % Current options:
% 3.87/1.20 % ------
% 3.87/1.20
% 3.87/1.20
% 3.87/1.20 %
% 3.87/1.20
% 3.87/1.20 % ------ Proving...
% 3.87/1.20 %
% 3.87/1.20
% 3.87/1.20 % SZS status Theorem for theBenchmark.p
% 3.87/1.20
% 3.87/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.60/1.20
%------------------------------------------------------------------------------