%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET715+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 : n020.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 4.36s 1.30s
% Output : CNFRefutation 4.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 88 ( 12 unt; 0 def)
% Number of atoms : 347 ( 37 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 441 ( 182 ~; 171 |; 56 &)
% ( 11 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-5 aty)
% Number of variables : 300 ( 0 sgn 280 !; 20 ?; 90 :)
% 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(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/sandbox2/benchmark/Axioms/SET006+1.ax',compose_function) ).
fof(f16,axiom,
! [X0,X1] :
( identity(X0,X1)
<=> ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',identity) ).
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) )
=> identity(compose_function(X0,inverse_function(X0,X1,X2),X2,X1,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thII06) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2] :
( ( one_to_one(X0,X1,X2)
& maps(X0,X1,X2) )
=> identity(compose_function(X0,inverse_function(X0,X1,X2),X2,X1,X2),X2) ),
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(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] :
( member(X2,X1)
=> apply(X0,X2,X2) )
=> identity(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f16]) ).
fof(f36,plain,
! [X0,X1,X2] :
( maps(X0,X1,X2)
=> ( ! [X5,X6,X7] :
( ( member(X7,X2)
& member(X6,X2)
& member(X5,X1) )
=> ( ( apply(X0,X5,X7)
& apply(X0,X5,X6) )
=> X6 = X7 ) )
& ! [X3] :
( member(X3,X1)
=> ? [X4] :
( apply(X0,X3,X4)
& member(X4,X2) ) ) ) ),
inference(unused_predicate_definition_removal,[],[f31]) ).
fof(f37,plain,
? [X0,X1,X2] :
( one_to_one(X0,X1,X2)
& maps(X0,X1,X2)
& ~ identity(compose_function(X0,inverse_function(X0,X1,X2),X2,X1,X2),X2) ),
inference(ennf_transformation,[],[f30]) ).
fof(f38,plain,
? [X0,X1,X2] :
( one_to_one(X0,X1,X2)
& maps(X0,X1,X2)
& ~ identity(compose_function(X0,inverse_function(X0,X1,X2),X2,X1,X2),X2) ),
inference(flattening,[],[f37]) ).
fof(f39,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,[],[f36]) ).
fof(f40,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,[],[f39]) ).
fof(f41,plain,
! [X0,X1] :
( ? [X2] :
( member(X2,X1)
& ~ apply(X0,X2,X2) )
| identity(X0,X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f42,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(f43,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,[],[f42]) ).
fof(f44,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(f45,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,[],[f44]) ).
fof(f46,plain,
! [X0,X1,X2] :
( ~ one_to_one(X0,X1,X2)
| ( surjective(X0,X1,X2)
& injective(X0,X1,X2) ) ),
inference(ennf_transformation,[],[f32]) ).
fof(f49,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(f50,plain,
( one_to_one(sK0,sK1,sK2)
& maps(sK0,sK1,sK2)
& ~ identity(compose_function(sK0,inverse_function(sK0,sK1,sK2),sK2,sK1,sK2),sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f38]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ~ maps(X0,X1,X2)
| ( ! [X5,X6,X7] :
( ~ member(X7,X2)
| ~ member(X6,X2)
| ~ member(X5,X1)
| ~ apply(X0,X5,X7)
| ~ apply(X0,X5,X6)
| X6 = X7 )
& ! [X3] :
( ~ member(X3,X1)
| ( apply(X0,X3,sK3(X0,X2,X3))
& member(sK3(X0,X2,X3),X2) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X4,sK3(X0,X2,X3))],[f40]) ).
fof(f52,plain,
! [X0,X1] :
( ( member(sK4(X0,X1),X1)
& ~ apply(X0,sK4(X0,X1),sK4(X0,X1)) )
| identity(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X2,sK4(X0,X1))],[f41]) ).
fof(f53,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,[],[f43]) ).
fof(f54,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,[],[f53]) ).
fof(f55,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,sK5(X0,X1,X3,X5,X6),X6)
& apply(X1,X5,sK5(X0,X1,X3,X5,X6))
& member(sK5(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,[sK5]),skolemize(X8,sK5(X0,X1,X3,X5,X6))],[f54]) ).
fof(f56,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,[],[f45]) ).
fof(f57,plain,
! [X0,X1,X2] :
( ~ surjective(X0,X1,X2)
| ! [X3] :
( ~ member(X3,X2)
| ( apply(X0,sK6(X0,X1,X3),X3)
& member(sK6(X0,X1,X3),X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X4,sK6(X0,X1,X3))],[f49]) ).
fof(f58,plain,
one_to_one(sK0,sK1,sK2),
inference(cnf_transformation,[],[f50]) ).
fof(f59,plain,
maps(sK0,sK1,sK2),
inference(cnf_transformation,[],[f50]) ).
fof(f60,plain,
~ identity(compose_function(sK0,inverse_function(sK0,sK1,sK2),sK2,sK1,sK2),sK2),
inference(cnf_transformation,[],[f50]) ).
fof(f61,plain,
! [X2,X0,X1,X6,X7,X5] :
( ~ maps(X0,X1,X2)
| ~ member(X7,X2)
| ~ member(X6,X2)
| ~ member(X5,X1)
| ~ apply(X0,X5,X7)
| ~ apply(X0,X5,X6)
| X6 = X7 ),
inference(cnf_transformation,[],[f51]) ).
fof(f62,plain,
! [X2,X3,X0,X1] :
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| apply(X0,X3,sK3(X0,X2,X3)) ),
inference(cnf_transformation,[],[f51]) ).
fof(f63,plain,
! [X2,X3,X0,X1] :
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| member(sK3(X0,X2,X3),X2) ),
inference(cnf_transformation,[],[f51]) ).
fof(f64,plain,
! [X0,X1] :
( member(sK4(X0,X1),X1)
| identity(X0,X1) ),
inference(cnf_transformation,[],[f52]) ).
fof(f65,plain,
! [X0,X1] :
( ~ apply(X0,sK4(X0,X1),sK4(X0,X1))
| identity(X0,X1) ),
inference(cnf_transformation,[],[f52]) ).
fof(f69,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ member(X6,X4)
| ~ member(X5,X2)
| ~ apply(X0,X7,X6)
| ~ apply(X1,X5,X7)
| ~ member(X7,X3)
| apply(compose_function(X0,X1,X2,X3,X4),X5,X6) ),
inference(cnf_transformation,[],[f55]) ).
fof(f70,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,[],[f56]) ).
fof(f72,plain,
! [X2,X0,X1] :
( ~ one_to_one(X0,X1,X2)
| surjective(X0,X1,X2) ),
inference(cnf_transformation,[],[f46]) ).
fof(f75,plain,
! [X2,X3,X0,X1] :
( ~ surjective(X0,X1,X2)
| ~ member(X3,X2)
| apply(X0,sK6(X0,X1,X3),X3) ),
inference(cnf_transformation,[],[f57]) ).
fof(f76,plain,
! [X2,X3,X0,X1] :
( ~ surjective(X0,X1,X2)
| ~ member(X3,X2)
| member(sK6(X0,X1,X3),X1) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_49,negated_conjecture,
~ identity(compose_function(sK0,inverse_function(sK0,sK1,sK2),sK2,sK1,sK2),sK2),
inference(cnf_transformation,[],[f60]) ).
tcf(c_50,negated_conjecture,
maps(sK0,sK1,sK2),
inference(cnf_transformation,[],[f59]) ).
tcf(c_51,negated_conjecture,
one_to_one(sK0,sK1,sK2),
inference(cnf_transformation,[],[f58]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK3(X0,X2,X3),X2)
| ~ member(X3,X1)
| ~ maps(X0,X1,X2) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,X3,sK3(X0,X2,X3))
| ~ member(X3,X1)
| ~ maps(X0,X1,X2) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( X4 = X5 )
| ~ member(X5,X2)
| ~ member(X4,X2)
| ~ member(X3,X1)
| ~ apply(X0,X3,X5)
| ~ apply(X0,X3,X4)
| ~ maps(X0,X1,X2) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( identity(X0,X1)
| ~ apply(X0,sK4(X0,X1),sK4(X0,X1)) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( identity(X0,X1)
| member(sK4(X0,X1),X1) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( apply(compose_function(X0,X3,X7,X6,X5),X4,X2)
| ~ member(X4,X7)
| ~ member(X2,X5)
| ~ member(X1,X6)
| ~ apply(X3,X4,X1)
| ~ apply(X0,X1,X2) ),
inference(cnf_transformation,[],[f69]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apply(inverse_function(X0,X3,X4),X2,X1)
| ~ member(X2,X4)
| ~ member(X1,X3)
| ~ apply(X0,X1,X2) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( surjective(X0,X1,X2)
| ~ one_to_one(X0,X1,X2) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK6(X0,X1,X3),X1)
| ~ member(X3,X2)
| ~ surjective(X0,X1,X2) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,sK6(X0,X1,X3),X3)
| ~ member(X3,X2)
| ~ surjective(X0,X1,X2) ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_338,plain,
! [X0: $i,X1: $i] :
( member(sK4(X0,X1),X1)
| ( X1 != sK2 )
| ( compose_function(sK0,inverse_function(sK0,sK1,sK2),sK2,sK1,sK2) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_56]) ).
tcf(c_339,plain,
member(sK4(compose_function(sK0,inverse_function(sK0,sK1,sK2),sK2,sK1,sK2),sK2),sK2),
inference(unflattening,[status(thm)],[c_338]) ).
tcf(c_343,plain,
! [X0: $i,X1: $i] :
( ~ apply(X0,sK4(X0,X1),sK4(X0,X1))
| ( X1 != sK2 )
| ( compose_function(sK0,inverse_function(sK0,sK1,sK2),sK2,sK1,sK2) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_55]) ).
tcf(c_344,plain,
~ apply(compose_function(sK0,inverse_function(sK0,sK1,sK2),sK2,sK1,sK2),sK4(compose_function(sK0,inverse_function(sK0,sK1,sK2),sK2,sK1,sK2),sK2),sK4(compose_function(sK0,inverse_function(sK0,sK1,sK2),sK2,sK1,sK2),sK2)),
inference(unflattening,[status(thm)],[c_343]) ).
tcf(c_350,plain,
! [X0: $i,X1: $i,X2: $i] :
( surjective(X0,X1,X2)
| ( X2 != sK2 )
| ( X1 != sK1 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_64]) ).
tcf(c_351,plain,
surjective(sK0,sK1,sK2),
inference(unflattening,[status(thm)],[c_350]) ).
tcf(c_362,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,sK6(X0,X1,X3),X3)
| ~ member(X3,X2)
| ( X2 != sK2 )
| ( X1 != sK1 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_67,c_351]) ).
tcf(c_363,plain,
! [X0: $i] :
( apply(sK0,sK6(sK0,sK1,X0),X0)
| ~ member(X0,sK2) ),
inference(unflattening,[status(thm)],[c_362]) ).
tcf(c_371,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK6(X0,X1,X3),X1)
| ~ member(X3,X2)
| ( X2 != sK2 )
| ( X1 != sK1 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_66,c_351]) ).
tcf(c_372,plain,
! [X0: $i] :
( member(sK6(sK0,sK1,X0),sK1)
| ~ member(X0,sK2) ),
inference(unflattening,[status(thm)],[c_371]) ).
tcf(c_411,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( X4 = X5 )
| ~ member(X5,X2)
| ~ member(X4,X2)
| ~ member(X3,X1)
| ~ apply(X0,X3,X5)
| ~ apply(X0,X3,X4)
| ( X2 != sK2 )
| ( X1 != sK1 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_54]) ).
tcf(c_412,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ member(X2,sK2)
| ~ member(X1,sK2)
| ~ member(X0,sK1)
| ~ apply(sK0,X0,X2)
| ~ apply(sK0,X0,X1) ),
inference(unflattening,[status(thm)],[c_411]) ).
tcf(c_431,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,X3,sK3(X0,X2,X3))
| ~ member(X3,X1)
| ( X2 != sK2 )
| ( X1 != sK1 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_53]) ).
tcf(c_432,plain,
! [X0: $i] :
( apply(sK0,X0,sK3(sK0,sK2,X0))
| ~ member(X0,sK1) ),
inference(unflattening,[status(thm)],[c_431]) ).
tcf(c_440,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK3(X0,X2,X3),X2)
| ~ member(X3,X1)
| ( X2 != sK2 )
| ( X1 != sK1 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_52]) ).
tcf(c_441,plain,
! [X0: $i] :
( member(sK3(sK0,sK2,X0),sK2)
| ~ member(X0,sK1) ),
inference(unflattening,[status(thm)],[c_440]) ).
tcf(c_1012,plain,
! [X0: $i,X1: $i] :
( ( sK3(sK0,sK2,X0) = X1 )
| ~ member(X1,sK2)
| ~ member(X0,sK1)
| ~ apply(sK0,X0,X1)
| ~ member(sK3(sK0,sK2,X0),sK2) ),
inference(superposition,[status(thm)],[c_432,c_412]) ).
tcf(c_1070,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( apply(compose_function(sK0,X0,X5,X3,X4),X1,X2)
| ~ member(X2,sK2)
| ~ member(X2,X4)
| ~ member(X1,X5)
| ~ member(sK6(sK0,sK1,X2),X3)
| ~ apply(X0,X1,sK6(sK0,sK1,X2)) ),
inference(superposition,[status(thm)],[c_363,c_57]) ).
tcf(c_1137,plain,
! [X0: $i,X1: $i] :
( ( sK3(sK0,sK2,X0) = X1 )
| ~ member(X1,sK2)
| ~ member(X0,sK1)
| ~ apply(sK0,X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_1012,c_441,c_1012]) ).
tcf(c_1148,plain,
! [X0: $i] :
( ( sK3(sK0,sK2,sK6(sK0,sK1,X0)) = X0 )
| ~ member(X0,sK2)
| ~ member(sK6(sK0,sK1,X0),sK1) ),
inference(superposition,[status(thm)],[c_363,c_1137]) ).
tcf(c_1154,plain,
! [X0: $i] :
( ( sK3(sK0,sK2,sK6(sK0,sK1,X0)) = X0 )
| ~ member(X0,sK2) ),
inference(global_subsumption_just,[status(thm)],[c_1148,c_372,c_1148]) ).
tcf(c_1161,plain,
sK3(sK0,sK2,sK6(sK0,sK1,sK4(compose_function(sK0,inverse_function(sK0,sK1,sK2),sK2,sK1,sK2),sK2))) = sK4(compose_function(sK0,inverse_function(sK0,sK1,sK2),sK2,sK1,sK2),sK2),
inference(superposition,[status(thm)],[c_339,c_1154]) ).
tcf(c_1211,plain,
( apply(sK0,sK6(sK0,sK1,sK4(compose_function(sK0,inverse_function(sK0,sK1,sK2),sK2,sK1,sK2),sK2)),sK4(compose_function(sK0,inverse_function(sK0,sK1,sK2),sK2,sK1,sK2),sK2))
| ~ member(sK6(sK0,sK1,sK4(compose_function(sK0,inverse_function(sK0,sK1,sK2),sK2,sK1,sK2),sK2)),sK1) ),
inference(superposition,[status(thm)],[c_1161,c_432]) ).
tcf(c_1323,plain,
( member(sK6(sK0,sK1,sK4(compose_function(sK0,inverse_function(sK0,sK1,sK2),sK2,sK1,sK2),sK2)),sK1)
| ~ member(sK4(compose_function(sK0,inverse_function(sK0,sK1,sK2),sK2,sK1,sK2),sK2),sK2) ),
inference(instantiation,[status(thm)],[c_372]) ).
tcf(c_1384,plain,
( ~ member(sK4(compose_function(sK0,inverse_function(sK0,sK1,sK2),sK2,sK1,sK2),sK2),sK2)
| ~ member(sK6(sK0,sK1,sK4(compose_function(sK0,inverse_function(sK0,sK1,sK2),sK2,sK1,sK2),sK2)),sK1)
| ~ apply(inverse_function(sK0,sK1,sK2),sK4(compose_function(sK0,inverse_function(sK0,sK1,sK2),sK2,sK1,sK2),sK2),sK6(sK0,sK1,sK4(compose_function(sK0,inverse_function(sK0,sK1,sK2),sK2,sK1,sK2),sK2))) ),
inference(superposition,[status(thm)],[c_1070,c_344]) ).
tcf(c_1413,plain,
( ~ member(sK6(sK0,sK1,sK4(compose_function(sK0,inverse_function(sK0,sK1,sK2),sK2,sK1,sK2),sK2)),sK1)
| ~ apply(inverse_function(sK0,sK1,sK2),sK4(compose_function(sK0,inverse_function(sK0,sK1,sK2),sK2,sK1,sK2),sK2),sK6(sK0,sK1,sK4(compose_function(sK0,inverse_function(sK0,sK1,sK2),sK2,sK1,sK2),sK2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1384,c_339]) ).
tcf(c_2283,plain,
~ apply(inverse_function(sK0,sK1,sK2),sK4(compose_function(sK0,inverse_function(sK0,sK1,sK2),sK2,sK1,sK2),sK2),sK6(sK0,sK1,sK4(compose_function(sK0,inverse_function(sK0,sK1,sK2),sK2,sK1,sK2),sK2))),
inference(global_subsumption_just,[status(thm)],[c_1413,c_339,c_1323,c_1413]) ).
tcf(c_2285,plain,
( ~ member(sK4(compose_function(sK0,inverse_function(sK0,sK1,sK2),sK2,sK1,sK2),sK2),sK2)
| ~ member(sK6(sK0,sK1,sK4(compose_function(sK0,inverse_function(sK0,sK1,sK2),sK2,sK1,sK2),sK2)),sK1)
| ~ apply(sK0,sK6(sK0,sK1,sK4(compose_function(sK0,inverse_function(sK0,sK1,sK2),sK2,sK1,sK2),sK2)),sK4(compose_function(sK0,inverse_function(sK0,sK1,sK2),sK2,sK1,sK2),sK2)) ),
inference(superposition,[status(thm)],[c_62,c_2283]) ).
tcf(c_2286,plain,
( ~ member(sK6(sK0,sK1,sK4(compose_function(sK0,inverse_function(sK0,sK1,sK2),sK2,sK1,sK2),sK2)),sK1)
| ~ apply(sK0,sK6(sK0,sK1,sK4(compose_function(sK0,inverse_function(sK0,sK1,sK2),sK2,sK1,sK2),sK2)),sK4(compose_function(sK0,inverse_function(sK0,sK1,sK2),sK2,sK1,sK2),sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2285,c_339]) ).
tcf(c_2289,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2286,c_1323,c_1211,c_339]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET715+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n020.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 11:45:48 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 4.36/1.30 % SZS status Started for theBenchmark.p
% 4.36/1.30 % SZS status Theorem for theBenchmark.p
% 4.36/1.30
% 4.36/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.36/1.30
% 4.36/1.30 % ------ iProver source info
% 4.36/1.30
% 4.36/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 4.36/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.36/1.30 % git: non_committed_changes: false
% 4.36/1.30
% 4.36/1.30 % ------ Parsing...
% 4.36/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.36/1.30
% 4.36/1.30 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e %
% 4.36/1.30
% 4.36/1.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.36/1.30
% 4.36/1.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.36/1.30 % ------ Proving...
% 4.36/1.30 % ------ Problem Properties
% 4.36/1.30
% 4.36/1.30 %
% 4.36/1.30 % clauses 14
% 4.36/1.30 % conjectures 0
% 4.36/1.30 % EPR 2
% 4.36/1.30 % Horn 14
% 4.36/1.30 % unary 2
% 4.36/1.30 % binary 4
% 4.36/1.30 % lits 48
% 4.36/1.30 % lits eq 2
% 4.36/1.30 % fd_pure 0
% 4.36/1.30 % fd_pseudo 0
% 4.36/1.30 % fd_cond 0
% 4.36/1.30 % fd_pseudo_cond 2
% 4.36/1.30 % AC symbols 0
% 4.36/1.30
% 4.36/1.30 % ------ Schedule dynamic 5 is on
% 4.36/1.30
% 4.36/1.30 % ------ no conjectures: strip conj schedule
% 4.36/1.30
% 4.36/1.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 4.36/1.30
% 4.36/1.30
% 4.36/1.30 % ------
% 4.36/1.30 % Current options:
% 4.36/1.30 % ------
% 4.36/1.30
% 4.36/1.30
% 4.36/1.30 %
% 4.36/1.30
% 4.36/1.30 % ------ Proving...
% 4.36/1.30 %
% 4.36/1.30
% 4.36/1.30 % SZS status Theorem for theBenchmark.p
% 4.36/1.30
% 4.36/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.36/1.30
% 4.36/1.30
%------------------------------------------------------------------------------