%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET712+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:47:56 PM UTC 2026
% Result : Theorem 8.87s 4.06s
% Output : CNFRefutation 8.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 100 ( 7 unt; 1 def)
% Number of atoms : 487 ( 42 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 540 ( 213 ~; 224 |; 73 &)
% ( 12 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 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 : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 326 ( 0 sgn 300 !; 26 ?; 94 :)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [X0,X1,X2] :
( maps(X0,X1,X2)
<=> ( ! [X3,X5,X6] :
( ( member(X6,X2)
& member(X5,X2)
& member(X3,X1) )
=> ( ( apply(X0,X3,X6)
& apply(X0,X3,X5) )
=> X5 = X6 ) )
& ! [X3] :
( member(X3,X1)
=> ? [X4] :
( apply(X0,X3,X4)
& member(X4,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',maps) ).
fof(f17,axiom,
! [X0,X1,X2] :
( injective(X0,X1,X2)
<=> ! [X3,X4,X5] :
( ( member(X5,X2)
& member(X4,X1)
& member(X3,X1) )
=> ( ( apply(X0,X4,X5)
& apply(X0,X3,X5) )
=> X3 = X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',injective) ).
fof(f18,axiom,
! [X0,X1,X2] :
( surjective(X0,X1,X2)
<=> ! [X3] :
( member(X3,X2)
=> ? [X4] :
( apply(X0,X4,X3)
& member(X4,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',surjective) ).
fof(f19,axiom,
! [X0,X1,X2] :
( one_to_one(X0,X1,X2)
<=> ( surjective(X0,X1,X2)
& injective(X0,X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',one_to_one) ).
fof(f21,axiom,
! [X0,X1,X2,X3,X4] :
( ( member(X4,X2)
& member(X3,X1) )
=> ( apply(X0,X3,X4)
<=> apply(inverse_function(X0,X1,X2),X4,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',inverse_function) ).
fof(f29,conjecture,
! [X0,X1,X2] :
( ( one_to_one(X0,X1,X2)
& maps(X0,X1,X2) )
=> maps(inverse_function(X0,X1,X2),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thII03) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2] :
( ( one_to_one(X0,X1,X2)
& maps(X0,X1,X2) )
=> maps(inverse_function(X0,X1,X2),X2,X1) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f31,plain,
! [X0,X1,X2] :
( maps(X0,X1,X2)
<=> ( ! [X5,X6,X7] :
( ( member(X7,X2)
& member(X6,X2)
& member(X5,X1) )
=> ( ( apply(X0,X5,X7)
& apply(X0,X5,X6) )
=> X6 = X7 ) )
& ! [X3] :
( member(X3,X1)
=> ? [X4] :
( apply(X0,X3,X4)
& member(X4,X2) ) ) ) ),
inference(rectify,[],[f12]) ).
fof(f32,plain,
! [X0,X1,X2] :
( one_to_one(X0,X1,X2)
=> ( surjective(X0,X1,X2)
& injective(X0,X1,X2) ) ),
inference(unused_predicate_definition_removal,[],[f19]) ).
fof(f33,plain,
! [X0,X1,X2] :
( injective(X0,X1,X2)
=> ! [X3,X4,X5] :
( ( member(X5,X2)
& member(X4,X1)
& member(X3,X1) )
=> ( ( apply(X0,X4,X5)
& apply(X0,X3,X5) )
=> X3 = X4 ) ) ),
inference(unused_predicate_definition_removal,[],[f17]) ).
fof(f34,plain,
! [X0,X1,X2] :
( surjective(X0,X1,X2)
=> ! [X3] :
( member(X3,X2)
=> ? [X4] :
( apply(X0,X4,X3)
& member(X4,X1) ) ) ),
inference(unused_predicate_definition_removal,[],[f18]) ).
fof(f35,plain,
? [X0,X1,X2] :
( one_to_one(X0,X1,X2)
& maps(X0,X1,X2)
& ~ maps(inverse_function(X0,X1,X2),X2,X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f36,plain,
? [X0,X1,X2] :
( one_to_one(X0,X1,X2)
& maps(X0,X1,X2)
& ~ maps(inverse_function(X0,X1,X2),X2,X1) ),
inference(flattening,[],[f35]) ).
fof(f37,plain,
! [X0,X1,X2] :
( maps(X0,X1,X2)
<=> ( ! [X5,X6,X7] :
( ~ member(X7,X2)
| ~ member(X6,X2)
| ~ member(X5,X1)
| ~ apply(X0,X5,X7)
| ~ apply(X0,X5,X6)
| X6 = X7 )
& ! [X3] :
( ~ member(X3,X1)
| ? [X4] :
( apply(X0,X3,X4)
& member(X4,X2) ) ) ) ),
inference(ennf_transformation,[],[f31]) ).
fof(f38,plain,
! [X0,X1,X2] :
( maps(X0,X1,X2)
<=> ( ! [X5,X6,X7] :
( ~ member(X7,X2)
| ~ member(X6,X2)
| ~ member(X5,X1)
| ~ apply(X0,X5,X7)
| ~ apply(X0,X5,X6)
| X6 = X7 )
& ! [X3] :
( ~ member(X3,X1)
| ? [X4] :
( apply(X0,X3,X4)
& member(X4,X2) ) ) ) ),
inference(flattening,[],[f37]) ).
fof(f39,plain,
! [X0,X1,X2,X3,X4] :
( ~ member(X4,X2)
| ~ member(X3,X1)
| ( apply(X0,X3,X4)
<=> apply(inverse_function(X0,X1,X2),X4,X3) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f40,plain,
! [X0,X1,X2,X3,X4] :
( ~ member(X4,X2)
| ~ member(X3,X1)
| ( apply(X0,X3,X4)
<=> apply(inverse_function(X0,X1,X2),X4,X3) ) ),
inference(flattening,[],[f39]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ~ one_to_one(X0,X1,X2)
| ( surjective(X0,X1,X2)
& injective(X0,X1,X2) ) ),
inference(ennf_transformation,[],[f32]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ~ injective(X0,X1,X2)
| ! [X3,X4,X5] :
( ~ member(X5,X2)
| ~ member(X4,X1)
| ~ member(X3,X1)
| ~ apply(X0,X4,X5)
| ~ apply(X0,X3,X5)
| X3 = X4 ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ~ injective(X0,X1,X2)
| ! [X3,X4,X5] :
( ~ member(X5,X2)
| ~ member(X4,X1)
| ~ member(X3,X1)
| ~ apply(X0,X4,X5)
| ~ apply(X0,X3,X5)
| X3 = X4 ) ),
inference(flattening,[],[f42]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ~ surjective(X0,X1,X2)
| ! [X3] :
( ~ member(X3,X2)
| ? [X4] :
( apply(X0,X4,X3)
& member(X4,X1) ) ) ),
inference(ennf_transformation,[],[f34]) ).
fof(f47,plain,
( one_to_one(sK1,sK2,sK3)
& maps(sK1,sK2,sK3)
& ~ maps(inverse_function(sK1,sK2,sK3),sK3,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f36]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ( ~ maps(X0,X1,X2)
| ( sP0(X0,X1,X2)
& ! [X3] :
( ~ member(X3,X1)
| ? [X4] :
( apply(X0,X3,X4)
& member(X4,X2) ) ) ) )
& ( ~ sP0(X0,X1,X2)
| ? [X3] :
( member(X3,X1)
& ! [X4] :
( ~ apply(X0,X3,X4)
| ~ member(X4,X2) ) )
| maps(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f46]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ( ~ maps(X0,X1,X2)
| ( sP0(X0,X1,X2)
& ! [X3] :
( ~ member(X3,X1)
| ? [X4] :
( apply(X0,X3,X4)
& member(X4,X2) ) ) ) )
& ( ~ sP0(X0,X1,X2)
| ? [X3] :
( member(X3,X1)
& ! [X4] :
( ~ apply(X0,X3,X4)
| ~ member(X4,X2) ) )
| maps(X0,X1,X2) ) ),
inference(flattening,[],[f51]) ).
fof(f53,plain,
! [X0,X1,X2] :
( ( ~ maps(X0,X1,X2)
| ( sP0(X0,X1,X2)
& ! [X5] :
( ~ member(X5,X1)
| ? [X6] :
( apply(X0,X5,X6)
& member(X6,X2) ) ) ) )
& ( ~ sP0(X0,X1,X2)
| ? [X3] :
( member(X3,X1)
& ! [X4] :
( ~ apply(X0,X3,X4)
| ~ member(X4,X2) ) )
| maps(X0,X1,X2) ) ),
inference(rectify,[],[f52]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ( ~ maps(X0,X1,X2)
| ( sP0(X0,X1,X2)
& ! [X5] :
( ~ member(X5,X1)
| ( apply(X0,X5,sK8(X0,X2,X5))
& member(sK8(X0,X2,X5),X2) ) ) ) )
& ( ~ sP0(X0,X1,X2)
| ( member(sK7(X0,X1,X2),X1)
& ! [X4] :
( ~ apply(X0,sK7(X0,X1,X2),X4)
| ~ member(X4,X2) ) )
| maps(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X3,sK7(X0,X1,X2)),skolemize(X6,sK8(X0,X2,X5))],[f53]) ).
fof(f55,plain,
! [X0,X1,X2,X3,X4] :
( ~ member(X4,X2)
| ~ member(X3,X1)
| ( ( ~ apply(X0,X3,X4)
| apply(inverse_function(X0,X1,X2),X4,X3) )
& ( ~ apply(inverse_function(X0,X1,X2),X4,X3)
| apply(X0,X3,X4) ) ) ),
inference(nnf_transformation,[],[f40]) ).
fof(f56,plain,
! [X0,X1,X2] :
( ~ surjective(X0,X1,X2)
| ! [X3] :
( ~ member(X3,X2)
| ( apply(X0,sK9(X0,X1,X3),X3)
& member(sK9(X0,X1,X3),X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X4,sK9(X0,X1,X3))],[f44]) ).
fof(f57,plain,
one_to_one(sK1,sK2,sK3),
inference(cnf_transformation,[],[f47]) ).
fof(f59,plain,
~ maps(inverse_function(sK1,sK2,sK3),sK3,sK2),
inference(cnf_transformation,[],[f47]) ).
fof(f70,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1,X2)
| member(sK7(X0,X1,X2),X1)
| maps(X0,X1,X2) ),
inference(cnf_transformation,[],[f54]) ).
fof(f71,plain,
! [X2,X0,X1,X4] :
( ~ sP0(X0,X1,X2)
| ~ apply(X0,sK7(X0,X1,X2),X4)
| ~ member(X4,X2)
| maps(X0,X1,X2) ),
inference(cnf_transformation,[],[f54]) ).
fof(f72,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(X4,X2)
| ~ member(X3,X1)
| ~ apply(X0,X3,X4)
| apply(inverse_function(X0,X1,X2),X4,X3) ),
inference(cnf_transformation,[],[f55]) ).
fof(f73,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(X4,X2)
| ~ member(X3,X1)
| ~ apply(inverse_function(X0,X1,X2),X4,X3)
| apply(X0,X3,X4) ),
inference(cnf_transformation,[],[f55]) ).
fof(f74,plain,
! [X2,X0,X1] :
( ~ one_to_one(X0,X1,X2)
| surjective(X0,X1,X2) ),
inference(cnf_transformation,[],[f41]) ).
fof(f75,plain,
! [X2,X0,X1] :
( ~ one_to_one(X0,X1,X2)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f41]) ).
fof(f76,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ injective(X0,X1,X2)
| ~ member(X5,X2)
| ~ member(X4,X1)
| ~ member(X3,X1)
| ~ apply(X0,X4,X5)
| ~ apply(X0,X3,X5)
| X3 = X4 ),
inference(cnf_transformation,[],[f43]) ).
fof(f77,plain,
! [X2,X3,X0,X1] :
( ~ surjective(X0,X1,X2)
| ~ member(X3,X2)
| apply(X0,sK9(X0,X1,X3),X3) ),
inference(cnf_transformation,[],[f56]) ).
fof(f78,plain,
! [X2,X3,X0,X1] :
( ~ surjective(X0,X1,X2)
| ~ member(X3,X2)
| member(sK9(X0,X1,X3),X1) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_49,negated_conjecture,
~ maps(inverse_function(sK1,sK2,sK3),sK3,sK2),
inference(cnf_transformation,[],[f59]) ).
tcf(c_51,negated_conjecture,
one_to_one(sK1,sK2,sK3),
inference(cnf_transformation,[],[f57]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( maps(X0,X1,X2)
| ~ member(X3,X2)
| ~ sP0(X0,X1,X2)
| ~ apply(X0,sK7(X0,X1,X2),X3) ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( maps(X0,X1,X2)
| member(sK7(X0,X1,X2),X1)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apply(X0,X4,X3)
| ~ member(X4,X1)
| ~ member(X3,X2)
| ~ apply(inverse_function(X0,X1,X2),X3,X4) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apply(inverse_function(X0,X4,X3),X2,X1)
| ~ member(X2,X3)
| ~ member(X1,X4)
| ~ apply(X0,X1,X2) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i] :
( injective(X0,X1,X2)
| ~ one_to_one(X0,X1,X2) ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] :
( surjective(X0,X1,X2)
| ~ one_to_one(X0,X1,X2) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( X1 = X3 )
| ~ member(X3,X4)
| ~ member(X2,X5)
| ~ member(X1,X4)
| ~ injective(X0,X4,X5)
| ~ apply(X0,X3,X2)
| ~ apply(X0,X1,X2) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK9(X0,X1,X3),X1)
| ~ member(X3,X2)
| ~ surjective(X0,X1,X2) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,sK9(X0,X1,X3),X3)
| ~ member(X3,X2)
| ~ surjective(X0,X1,X2) ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_338,plain,
! [X0: $i,X1: $i,X2: $i] :
( surjective(X0,X1,X2)
| ( X2 != sK3 )
| ( X1 != sK2 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_67]) ).
tcf(c_339,plain,
surjective(sK1,sK2,sK3),
inference(unflattening,[status(thm)],[c_338]) ).
tcf(c_343,plain,
! [X0: $i,X1: $i,X2: $i] :
( injective(X0,X1,X2)
| ( X2 != sK3 )
| ( X1 != sK2 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_66]) ).
tcf(c_344,plain,
injective(sK1,sK2,sK3),
inference(unflattening,[status(thm)],[c_343]) ).
tcf(c_350,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,sK9(X0,X1,X3),X3)
| ~ member(X3,X2)
| ( X2 != sK3 )
| ( X1 != sK2 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_70,c_339]) ).
tcf(c_351,plain,
! [X0: $i] :
( apply(sK1,sK9(sK1,sK2,X0),X0)
| ~ member(X0,sK3) ),
inference(unflattening,[status(thm)],[c_350]) ).
tcf(c_359,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK9(X0,X1,X3),X1)
| ~ member(X3,X2)
| ( X2 != sK3 )
| ( X1 != sK2 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_69,c_339]) ).
tcf(c_360,plain,
! [X0: $i] :
( member(sK9(sK1,sK2,X0),sK2)
| ~ member(X0,sK3) ),
inference(unflattening,[status(thm)],[c_359]) ).
tcf(c_372,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( X3 = X5 )
| ~ member(X5,X1)
| ~ member(X4,X2)
| ~ member(X3,X1)
| ~ apply(X0,X5,X4)
| ~ apply(X0,X3,X4)
| ( X2 != sK3 )
| ( X1 != sK2 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_68,c_344]) ).
tcf(c_373,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ~ member(X2,sK2)
| ~ member(X1,sK3)
| ~ member(X0,sK2)
| ~ apply(sK1,X2,X1)
| ~ apply(sK1,X0,X1) ),
inference(unflattening,[status(thm)],[c_372]) ).
tcf(c_476,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(sK7(X0,X2,X1),X2)
| ~ sP0(X0,X2,X1)
| ( X2 != sK3 )
| ( X1 != sK2 )
| ( inverse_function(sK1,sK2,sK3) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_60]) ).
tcf(c_477,plain,
( member(sK7(inverse_function(sK1,sK2,sK3),sK3,sK2),sK3)
| ~ sP0(inverse_function(sK1,sK2,sK3),sK3,sK2) ),
inference(unflattening,[status(thm)],[c_476]) ).
tcf(c_2432,plain,
! [X0: $i] :
( maps(inverse_function(sK1,sK2,sK3),sK3,sK2)
| ~ member(X0,sK2)
| ~ sP0(inverse_function(sK1,sK2,sK3),sK3,sK2)
| ~ apply(inverse_function(sK1,sK2,sK3),sK7(inverse_function(sK1,sK2,sK3),sK3,sK2),X0) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_2633,plain,
( apply(sK1,sK9(sK1,sK2,sK7(inverse_function(sK1,sK2,sK3),sK3,sK2)),sK7(inverse_function(sK1,sK2,sK3),sK3,sK2))
| ~ member(sK7(inverse_function(sK1,sK2,sK3),sK3,sK2),sK3) ),
inference(instantiation,[status(thm)],[c_351]) ).
tcf(c_2634,plain,
( member(sK9(sK1,sK2,sK7(inverse_function(sK1,sK2,sK3),sK3,sK2)),sK2)
| ~ member(sK7(inverse_function(sK1,sK2,sK3),sK3,sK2),sK3) ),
inference(instantiation,[status(thm)],[c_360]) ).
tcf(c_2910,plain,
! [X0: $i] :
( ( sK5(inverse_function(sK1,sK2,sK3),sK3,sK2) = sK6(inverse_function(sK1,sK2,sK3),sK3,sK2) )
| ~ member(X0,sK3)
| ~ member(sK6(inverse_function(sK1,sK2,sK3),sK3,sK2),sK2)
| ~ member(sK5(inverse_function(sK1,sK2,sK3),sK3,sK2),sK2)
| ~ apply(sK1,sK6(inverse_function(sK1,sK2,sK3),sK3,sK2),X0)
| ~ apply(sK1,sK5(inverse_function(sK1,sK2,sK3),sK3,sK2),X0) ),
inference(instantiation,[status(thm)],[c_373]) ).
tcf(c_3170,plain,
! [X0: $i,X1: $i,X2: $i] :
( apply(X0,X2,sK4(inverse_function(sK1,sK2,sK3),sK3,sK2))
| ~ member(X2,X1)
| ~ member(sK4(inverse_function(sK1,sK2,sK3),sK3,sK2),sK3)
| ~ apply(inverse_function(X0,X1,sK3),sK4(inverse_function(sK1,sK2,sK3),sK3,sK2),X2) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_3792,plain,
! [X0: $i,X1: $i,X2: $i] :
( apply(inverse_function(X0,sK2,X2),X1,sK9(sK1,sK2,sK7(inverse_function(sK1,sK2,sK3),sK3,sK2)))
| ~ member(X1,X2)
| ~ member(sK9(sK1,sK2,sK7(inverse_function(sK1,sK2,sK3),sK3,sK2)),sK2)
| ~ apply(X0,sK9(sK1,sK2,sK7(inverse_function(sK1,sK2,sK3),sK3,sK2)),X1) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_3794,plain,
( maps(inverse_function(sK1,sK2,sK3),sK3,sK2)
| ~ sP0(inverse_function(sK1,sK2,sK3),sK3,sK2)
| ~ member(sK9(sK1,sK2,sK7(inverse_function(sK1,sK2,sK3),sK3,sK2)),sK2)
| ~ apply(inverse_function(sK1,sK2,sK3),sK7(inverse_function(sK1,sK2,sK3),sK3,sK2),sK9(sK1,sK2,sK7(inverse_function(sK1,sK2,sK3),sK3,sK2))) ),
inference(instantiation,[status(thm)],[c_2432]) ).
tcf(c_4030,plain,
( ( sK5(inverse_function(sK1,sK2,sK3),sK3,sK2) = sK6(inverse_function(sK1,sK2,sK3),sK3,sK2) )
| ~ member(sK4(inverse_function(sK1,sK2,sK3),sK3,sK2),sK3)
| ~ member(sK6(inverse_function(sK1,sK2,sK3),sK3,sK2),sK2)
| ~ member(sK5(inverse_function(sK1,sK2,sK3),sK3,sK2),sK2)
| ~ apply(sK1,sK6(inverse_function(sK1,sK2,sK3),sK3,sK2),sK4(inverse_function(sK1,sK2,sK3),sK3,sK2))
| ~ apply(sK1,sK5(inverse_function(sK1,sK2,sK3),sK3,sK2),sK4(inverse_function(sK1,sK2,sK3),sK3,sK2)) ),
inference(instantiation,[status(thm)],[c_2910]) ).
tcf(c_5483,plain,
! [X0: $i] :
( apply(X0,sK6(inverse_function(sK1,sK2,sK3),sK3,sK2),sK4(inverse_function(sK1,sK2,sK3),sK3,sK2))
| ~ member(sK4(inverse_function(sK1,sK2,sK3),sK3,sK2),sK3)
| ~ member(sK6(inverse_function(sK1,sK2,sK3),sK3,sK2),sK2)
| ~ apply(inverse_function(X0,sK2,sK3),sK4(inverse_function(sK1,sK2,sK3),sK3,sK2),sK6(inverse_function(sK1,sK2,sK3),sK3,sK2)) ),
inference(instantiation,[status(thm)],[c_3170]) ).
tcf(c_5485,plain,
! [X0: $i] :
( apply(X0,sK5(inverse_function(sK1,sK2,sK3),sK3,sK2),sK4(inverse_function(sK1,sK2,sK3),sK3,sK2))
| ~ member(sK4(inverse_function(sK1,sK2,sK3),sK3,sK2),sK3)
| ~ member(sK5(inverse_function(sK1,sK2,sK3),sK3,sK2),sK2)
| ~ apply(inverse_function(X0,sK2,sK3),sK4(inverse_function(sK1,sK2,sK3),sK3,sK2),sK5(inverse_function(sK1,sK2,sK3),sK3,sK2)) ),
inference(instantiation,[status(thm)],[c_3170]) ).
tcf(c_8822,plain,
! [X0: $i] :
( apply(inverse_function(X0,sK2,sK3),sK7(inverse_function(sK1,sK2,sK3),sK3,sK2),sK9(sK1,sK2,sK7(inverse_function(sK1,sK2,sK3),sK3,sK2)))
| ~ member(sK7(inverse_function(sK1,sK2,sK3),sK3,sK2),sK3)
| ~ member(sK9(sK1,sK2,sK7(inverse_function(sK1,sK2,sK3),sK3,sK2)),sK2)
| ~ apply(X0,sK9(sK1,sK2,sK7(inverse_function(sK1,sK2,sK3),sK3,sK2)),sK7(inverse_function(sK1,sK2,sK3),sK3,sK2)) ),
inference(instantiation,[status(thm)],[c_3792]) ).
tcf(c_18548,plain,
( apply(inverse_function(sK1,sK2,sK3),sK7(inverse_function(sK1,sK2,sK3),sK3,sK2),sK9(sK1,sK2,sK7(inverse_function(sK1,sK2,sK3),sK3,sK2)))
| ~ member(sK7(inverse_function(sK1,sK2,sK3),sK3,sK2),sK3)
| ~ member(sK9(sK1,sK2,sK7(inverse_function(sK1,sK2,sK3),sK3,sK2)),sK2)
| ~ apply(sK1,sK9(sK1,sK2,sK7(inverse_function(sK1,sK2,sK3),sK3,sK2)),sK7(inverse_function(sK1,sK2,sK3),sK3,sK2)) ),
inference(instantiation,[status(thm)],[c_8822]) ).
tcf(c_23742,plain,
( apply(sK1,sK6(inverse_function(sK1,sK2,sK3),sK3,sK2),sK4(inverse_function(sK1,sK2,sK3),sK3,sK2))
| ~ member(sK4(inverse_function(sK1,sK2,sK3),sK3,sK2),sK3)
| ~ member(sK6(inverse_function(sK1,sK2,sK3),sK3,sK2),sK2)
| ~ apply(inverse_function(sK1,sK2,sK3),sK4(inverse_function(sK1,sK2,sK3),sK3,sK2),sK6(inverse_function(sK1,sK2,sK3),sK3,sK2)) ),
inference(instantiation,[status(thm)],[c_5483]) ).
tcf(c_23745,plain,
( apply(sK1,sK5(inverse_function(sK1,sK2,sK3),sK3,sK2),sK4(inverse_function(sK1,sK2,sK3),sK3,sK2))
| ~ member(sK4(inverse_function(sK1,sK2,sK3),sK3,sK2),sK3)
| ~ member(sK5(inverse_function(sK1,sK2,sK3),sK3,sK2),sK2)
| ~ apply(inverse_function(sK1,sK2,sK3),sK4(inverse_function(sK1,sK2,sK3),sK3,sK2),sK5(inverse_function(sK1,sK2,sK3),sK3,sK2)) ),
inference(instantiation,[status(thm)],[c_5485]) ).
fof(f45,definition,
! [X0,X1,X2] :
( sP0(X0,X1,X2)
<=> ! [X5,X6,X7] :
( ~ member(X7,X2)
| ~ member(X6,X2)
| ~ member(X5,X1)
| ~ apply(X0,X5,X7)
| ~ apply(X0,X5,X6)
| X6 = X7 ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f46,plain,
! [X0,X1,X2] :
( maps(X0,X1,X2)
<=> ( sP0(X0,X1,X2)
& ! [X3] :
( ~ member(X3,X1)
| ? [X4] :
( apply(X0,X3,X4)
& member(X4,X2) ) ) ) ),
inference(definition_folding,[],[f38,f45]) ).
fof(f48,plain,
! [X0,X1,X2] :
( ( ~ sP0(X0,X1,X2)
| ! [X5,X6,X7] :
( ~ member(X7,X2)
| ~ member(X6,X2)
| ~ member(X5,X1)
| ~ apply(X0,X5,X7)
| ~ apply(X0,X5,X6)
| X6 = X7 ) )
& ( ? [X5,X6,X7] :
( member(X7,X2)
& member(X6,X2)
& member(X5,X1)
& apply(X0,X5,X7)
& apply(X0,X5,X6)
& X6 != X7 )
| sP0(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f45]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ( ~ sP0(X0,X1,X2)
| ! [X6,X7,X8] :
( ~ member(X8,X2)
| ~ member(X7,X2)
| ~ member(X6,X1)
| ~ apply(X0,X6,X8)
| ~ apply(X0,X6,X7)
| X7 = X8 ) )
& ( ? [X3,X4,X5] :
( member(X5,X2)
& member(X4,X2)
& member(X3,X1)
& apply(X0,X3,X5)
& apply(X0,X3,X4)
& X4 != X5 )
| sP0(X0,X1,X2) ) ),
inference(rectify,[],[f48]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ( ~ sP0(X0,X1,X2)
| ! [X6,X7,X8] :
( ~ member(X8,X2)
| ~ member(X7,X2)
| ~ member(X6,X1)
| ~ apply(X0,X6,X8)
| ~ apply(X0,X6,X7)
| X7 = X8 ) )
& ( ( member(sK6(X0,X1,X2),X2)
& member(sK5(X0,X1,X2),X2)
& member(sK4(X0,X1,X2),X1)
& apply(X0,sK4(X0,X1,X2),sK6(X0,X1,X2))
& apply(X0,sK4(X0,X1,X2),sK5(X0,X1,X2))
& sK5(X0,X1,X2) != sK6(X0,X1,X2) )
| sP0(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X3,sK4(X0,X1,X2)),skolemize(X4,sK5(X0,X1,X2)),skolemize(X5,sK6(X0,X1,X2))],[f49]) ).
fof(f61,plain,
! [X2,X0,X1] :
( member(sK6(X0,X1,X2),X2)
| sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f50]) ).
fof(f62,plain,
! [X2,X0,X1] :
( member(sK5(X0,X1,X2),X2)
| sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f50]) ).
fof(f63,plain,
! [X2,X0,X1] :
( member(sK4(X0,X1,X2),X1)
| sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f50]) ).
fof(f64,plain,
! [X2,X0,X1] :
( apply(X0,sK4(X0,X1,X2),sK6(X0,X1,X2))
| sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f50]) ).
fof(f65,plain,
! [X2,X0,X1] :
( apply(X0,sK4(X0,X1,X2),sK5(X0,X1,X2))
| sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f50]) ).
fof(f66,plain,
! [X2,X0,X1] :
( sK5(X0,X1,X2) != sK6(X0,X1,X2)
| sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X0,X1,X2)
| ( sK5(X0,X1,X2) != sK6(X0,X1,X2) ) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X0,X1,X2)
| apply(X0,sK4(X0,X1,X2),sK5(X0,X1,X2)) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X0,X1,X2)
| apply(X0,sK4(X0,X1,X2),sK6(X0,X1,X2)) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X0,X1,X2)
| member(sK4(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X0,X1,X2)
| member(sK5(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X0,X1,X2)
| member(sK6(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_2445,plain,
( sP0(inverse_function(sK1,sK2,sK3),sK3,sK2)
| apply(inverse_function(sK1,sK2,sK3),sK4(inverse_function(sK1,sK2,sK3),sK3,sK2),sK6(inverse_function(sK1,sK2,sK3),sK3,sK2)) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_2446,plain,
( sP0(inverse_function(sK1,sK2,sK3),sK3,sK2)
| apply(inverse_function(sK1,sK2,sK3),sK4(inverse_function(sK1,sK2,sK3),sK3,sK2),sK5(inverse_function(sK1,sK2,sK3),sK3,sK2)) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_2447,plain,
( sP0(inverse_function(sK1,sK2,sK3),sK3,sK2)
| ( sK5(inverse_function(sK1,sK2,sK3),sK3,sK2) != sK6(inverse_function(sK1,sK2,sK3),sK3,sK2) ) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_2448,plain,
( sP0(inverse_function(sK1,sK2,sK3),sK3,sK2)
| member(sK6(inverse_function(sK1,sK2,sK3),sK3,sK2),sK2) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_2449,plain,
( sP0(inverse_function(sK1,sK2,sK3),sK3,sK2)
| member(sK5(inverse_function(sK1,sK2,sK3),sK3,sK2),sK2) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_2450,plain,
( sP0(inverse_function(sK1,sK2,sK3),sK3,sK2)
| member(sK4(inverse_function(sK1,sK2,sK3),sK3,sK2),sK3) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_24054,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_23745,c_23742,c_18548,c_4030,c_3794,c_2633,c_2634,c_2445,c_2446,c_2447,c_2448,c_2449,c_2450,c_477,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET712+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.18/0.45 % Computer : n019.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Thu Sep 24 11:44:49 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.23/0.51 Running first-order theorem proving
% 0.23/0.51 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
% 0.23/0.53
% 0.23/0.53 % ======== iProver multi-core TPTP/SMT =========
% 0.23/0.53
% 0.23/0.53 % Detected problem language: tptp
% 0.23/0.55 % Proving...
% 8.87/4.06 % SZS status Started for theBenchmark.p
% 8.87/4.06 % SZS status Theorem for theBenchmark.p
% 8.87/4.06
% 8.87/4.06 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.87/4.06
% 8.87/4.06 % ------ iProver source info
% 8.87/4.06
% 8.87/4.06 % git: date: 2026-07-19 20:42:38 +0200
% 8.87/4.06 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.87/4.06 % git: non_committed_changes: false
% 8.87/4.06
% 8.87/4.06 % ------ Parsing...
% 8.87/4.06 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 8.87/4.06
% 8.87/4.06 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 8.87/4.06
% 8.87/4.06 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 8.87/4.06
% 8.87/4.06 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 8.87/4.06 % ------ Proving...
% 8.87/4.06 % ------ Problem Properties
% 8.87/4.06
% 8.87/4.06 %
% 8.87/4.06 % clauses 19
% 8.87/4.06 % conjectures 2
% 8.87/4.06 % EPR 4
% 8.87/4.06 % Horn 13
% 8.87/4.06 % unary 2
% 8.87/4.06 % binary 9
% 8.87/4.06 % lits 54
% 8.87/4.06 % lits eq 3
% 8.87/4.06 % fd_pure 0
% 8.87/4.06 % fd_pseudo 0
% 8.87/4.06 % fd_cond 0
% 8.87/4.06 % fd_pseudo_cond 2
% 8.87/4.06 % AC symbols 0
% 8.87/4.06
% 8.87/4.06 % ------ Schedule dynamic 5 is on
% 8.87/4.06
% 8.87/4.06 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 8.87/4.06
% 8.87/4.06
% 8.87/4.06 % ------
% 8.87/4.06 % Current options:
% 8.87/4.06 % ------
% 8.87/4.06
% 8.87/4.06
% 8.87/4.06 %
% 8.87/4.06
% 8.87/4.06 % ------ Proving...
% 8.87/4.06 %
% 8.87/4.06
% 8.87/4.06 % SZS status Theorem for theBenchmark.p
% 8.87/4.06
% 8.87/4.06 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.87/4.06
% 8.87/4.06
%------------------------------------------------------------------------------