%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET713+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 1.45s 1.78s
% Output : CNFRefutation 1.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 6
% Syntax : Number of formulae : 180 ( 29 unt; 0 def)
% Number of atoms : 633 ( 109 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 796 ( 343 ~; 358 |; 68 &)
% ( 11 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 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 : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 438 ( 0 sgn 415 !; 23 ?; 207 :)
% 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) )
=> one_to_one(inverse_function(X0,X1,X2),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thII04) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2] :
( ( one_to_one(X0,X1,X2)
& maps(X0,X1,X2) )
=> one_to_one(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] :
( 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(f33,plain,
? [X0,X1,X2] :
( one_to_one(X0,X1,X2)
& maps(X0,X1,X2)
& ~ one_to_one(inverse_function(X0,X1,X2),X2,X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f34,plain,
? [X0,X1,X2] :
( one_to_one(X0,X1,X2)
& maps(X0,X1,X2)
& ~ one_to_one(inverse_function(X0,X1,X2),X2,X1) ),
inference(flattening,[],[f33]) ).
fof(f35,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,[],[f32]) ).
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(flattening,[],[f35]) ).
fof(f37,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(f38,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,[],[f37]) ).
fof(f39,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,[],[f17]) ).
fof(f40,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,[],[f39]) ).
fof(f41,plain,
! [X0,X1,X2] :
( surjective(X0,X1,X2)
<=> ! [X3] :
( ~ member(X3,X2)
| ? [X4] :
( apply(X0,X4,X3)
& member(X4,X1) ) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f42,plain,
( one_to_one(sK0,sK1,sK2)
& maps(sK0,sK1,sK2)
& ~ one_to_one(inverse_function(sK0,sK1,sK2),sK2,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f34]) ).
fof(f43,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))],[f36]) ).
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) )
& ( ~ apply(inverse_function(X0,X1,X2),X4,X3)
| apply(X0,X3,X4) ) ) ),
inference(nnf_transformation,[],[f38]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ( ~ one_to_one(X0,X1,X2)
| ( surjective(X0,X1,X2)
& injective(X0,X1,X2) ) )
& ( ~ surjective(X0,X1,X2)
| ~ injective(X0,X1,X2)
| one_to_one(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f19]) ).
fof(f46,plain,
! [X0,X1,X2] :
( ( ~ one_to_one(X0,X1,X2)
| ( surjective(X0,X1,X2)
& injective(X0,X1,X2) ) )
& ( ~ surjective(X0,X1,X2)
| ~ injective(X0,X1,X2)
| one_to_one(X0,X1,X2) ) ),
inference(flattening,[],[f45]) ).
fof(f47,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 ) )
& ( ? [X3,X4,X5] :
( member(X5,X2)
& member(X4,X1)
& member(X3,X1)
& apply(X0,X4,X5)
& apply(X0,X3,X5)
& X3 != X4 )
| injective(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f40]) ).
fof(f48,plain,
! [X0,X1,X2] :
( ( ~ injective(X0,X1,X2)
| ! [X6,X7,X8] :
( ~ member(X8,X2)
| ~ member(X7,X1)
| ~ member(X6,X1)
| ~ apply(X0,X7,X8)
| ~ apply(X0,X6,X8)
| X6 = X7 ) )
& ( ? [X3,X4,X5] :
( member(X5,X2)
& member(X4,X1)
& member(X3,X1)
& apply(X0,X4,X5)
& apply(X0,X3,X5)
& X3 != X4 )
| injective(X0,X1,X2) ) ),
inference(rectify,[],[f47]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ( ~ injective(X0,X1,X2)
| ! [X6,X7,X8] :
( ~ member(X8,X2)
| ~ member(X7,X1)
| ~ member(X6,X1)
| ~ apply(X0,X7,X8)
| ~ apply(X0,X6,X8)
| X6 = X7 ) )
& ( ( member(sK6(X0,X1,X2),X2)
& member(sK5(X0,X1,X2),X1)
& member(sK4(X0,X1,X2),X1)
& apply(X0,sK5(X0,X1,X2),sK6(X0,X1,X2))
& apply(X0,sK4(X0,X1,X2),sK6(X0,X1,X2))
& sK4(X0,X1,X2) != sK5(X0,X1,X2) )
| injective(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))],[f48]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ( ~ surjective(X0,X1,X2)
| ! [X3] :
( ~ member(X3,X2)
| ? [X4] :
( apply(X0,X4,X3)
& member(X4,X1) ) ) )
& ( ? [X3] :
( member(X3,X2)
& ! [X4] :
( ~ apply(X0,X4,X3)
| ~ member(X4,X1) ) )
| surjective(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f41]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ( ~ surjective(X0,X1,X2)
| ! [X5] :
( ~ member(X5,X2)
| ? [X6] :
( apply(X0,X6,X5)
& member(X6,X1) ) ) )
& ( ? [X3] :
( member(X3,X2)
& ! [X4] :
( ~ apply(X0,X4,X3)
| ~ member(X4,X1) ) )
| surjective(X0,X1,X2) ) ),
inference(rectify,[],[f50]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ( ~ surjective(X0,X1,X2)
| ! [X5] :
( ~ member(X5,X2)
| ( apply(X0,sK8(X0,X1,X5),X5)
& member(sK8(X0,X1,X5),X1) ) ) )
& ( ( member(sK7(X0,X1,X2),X2)
& ! [X4] :
( ~ apply(X0,X4,sK7(X0,X1,X2))
| ~ member(X4,X1) ) )
| surjective(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X3,sK7(X0,X1,X2)),skolemize(X6,sK8(X0,X1,X5))],[f51]) ).
fof(f53,plain,
one_to_one(sK0,sK1,sK2),
inference(cnf_transformation,[],[f42]) ).
fof(f54,plain,
maps(sK0,sK1,sK2),
inference(cnf_transformation,[],[f42]) ).
fof(f55,plain,
~ one_to_one(inverse_function(sK0,sK1,sK2),sK2,sK1),
inference(cnf_transformation,[],[f42]) ).
fof(f56,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,[],[f43]) ).
fof(f57,plain,
! [X2,X3,X0,X1] :
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| apply(X0,X3,sK3(X0,X2,X3)) ),
inference(cnf_transformation,[],[f43]) ).
fof(f58,plain,
! [X2,X3,X0,X1] :
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| member(sK3(X0,X2,X3),X2) ),
inference(cnf_transformation,[],[f43]) ).
fof(f59,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,[],[f44]) ).
fof(f60,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,[],[f44]) ).
fof(f61,plain,
! [X2,X0,X1] :
( ~ one_to_one(X0,X1,X2)
| surjective(X0,X1,X2) ),
inference(cnf_transformation,[],[f46]) ).
fof(f62,plain,
! [X2,X0,X1] :
( ~ one_to_one(X0,X1,X2)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f46]) ).
fof(f63,plain,
! [X2,X0,X1] :
( ~ surjective(X0,X1,X2)
| ~ injective(X0,X1,X2)
| one_to_one(X0,X1,X2) ),
inference(cnf_transformation,[],[f46]) ).
fof(f64,plain,
! [X2,X0,X1,X8,X6,X7] :
( ~ injective(X0,X1,X2)
| ~ member(X8,X2)
| ~ member(X7,X1)
| ~ member(X6,X1)
| ~ apply(X0,X7,X8)
| ~ apply(X0,X6,X8)
| X6 = X7 ),
inference(cnf_transformation,[],[f49]) ).
fof(f65,plain,
! [X2,X0,X1] :
( member(sK6(X0,X1,X2),X2)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f49]) ).
fof(f66,plain,
! [X2,X0,X1] :
( member(sK5(X0,X1,X2),X1)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f49]) ).
fof(f67,plain,
! [X2,X0,X1] :
( member(sK4(X0,X1,X2),X1)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f49]) ).
fof(f68,plain,
! [X2,X0,X1] :
( apply(X0,sK5(X0,X1,X2),sK6(X0,X1,X2))
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f49]) ).
fof(f69,plain,
! [X2,X0,X1] :
( apply(X0,sK4(X0,X1,X2),sK6(X0,X1,X2))
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f49]) ).
fof(f70,plain,
! [X2,X0,X1] :
( sK4(X0,X1,X2) != sK5(X0,X1,X2)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f49]) ).
fof(f71,plain,
! [X2,X0,X1,X5] :
( ~ surjective(X0,X1,X2)
| ~ member(X5,X2)
| apply(X0,sK8(X0,X1,X5),X5) ),
inference(cnf_transformation,[],[f52]) ).
fof(f72,plain,
! [X2,X0,X1,X5] :
( ~ surjective(X0,X1,X2)
| ~ member(X5,X2)
| member(sK8(X0,X1,X5),X1) ),
inference(cnf_transformation,[],[f52]) ).
fof(f73,plain,
! [X2,X0,X1] :
( member(sK7(X0,X1,X2),X2)
| surjective(X0,X1,X2) ),
inference(cnf_transformation,[],[f52]) ).
fof(f74,plain,
! [X2,X0,X1,X4] :
( ~ apply(X0,X4,sK7(X0,X1,X2))
| ~ member(X4,X1)
| surjective(X0,X1,X2) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_49,negated_conjecture,
~ one_to_one(inverse_function(sK0,sK1,sK2),sK2,sK1),
inference(cnf_transformation,[],[f55]) ).
tcf(c_50,negated_conjecture,
maps(sK0,sK1,sK2),
inference(cnf_transformation,[],[f54]) ).
tcf(c_51,negated_conjecture,
one_to_one(sK0,sK1,sK2),
inference(cnf_transformation,[],[f53]) ).
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,[],[f58]) ).
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,[],[f57]) ).
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,[],[f56]) ).
tcf(c_55,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,[],[f60]) ).
tcf(c_56,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,[],[f59]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( one_to_one(X0,X1,X2)
| ~ surjective(X0,X1,X2)
| ~ injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( injective(X0,X1,X2)
| ~ one_to_one(X0,X1,X2) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( surjective(X0,X1,X2)
| ~ one_to_one(X0,X1,X2) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( injective(X0,X1,X2)
| ( sK4(X0,X1,X2) != sK5(X0,X1,X2) ) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] :
( injective(X0,X1,X2)
| apply(X0,sK4(X0,X1,X2),sK6(X0,X1,X2)) ),
inference(cnf_transformation,[],[f69]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] :
( injective(X0,X1,X2)
| apply(X0,sK5(X0,X1,X2),sK6(X0,X1,X2)) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( injective(X0,X1,X2)
| member(sK4(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( injective(X0,X1,X2)
| member(sK5(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( injective(X0,X1,X2)
| member(sK6(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_66,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,[],[f64]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( surjective(X0,X2,X3)
| ~ member(X1,X2)
| ~ apply(X0,X1,sK7(X0,X2,X3)) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] :
( surjective(X0,X1,X2)
| member(sK7(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK8(X0,X1,X3),X1)
| ~ member(X3,X2)
| ~ surjective(X0,X1,X2) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,sK8(X0,X1,X3),X3)
| ~ member(X3,X2)
| ~ surjective(X0,X1,X2) ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_345,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ surjective(X0,X2,X1)
| ~ injective(X0,X2,X1)
| ( X2 != sK2 )
| ( X1 != sK1 )
| ( inverse_function(sK0,sK1,sK2) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_57]) ).
tcf(c_346,plain,
( ~ surjective(inverse_function(sK0,sK1,sK2),sK2,sK1)
| ~ injective(inverse_function(sK0,sK1,sK2),sK2,sK1) ),
inference(unflattening,[status(thm)],[c_345]) ).
tcf(c_353,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_59]) ).
tcf(c_354,plain,
surjective(sK0,sK1,sK2),
inference(unflattening,[status(thm)],[c_353]) ).
tcf(c_358,plain,
! [X0: $i,X1: $i,X2: $i] :
( injective(X0,X1,X2)
| ( X2 != sK2 )
| ( X1 != sK1 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_58]) ).
tcf(c_359,plain,
injective(sK0,sK1,sK2),
inference(unflattening,[status(thm)],[c_358]) ).
tcf(c_369,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_370,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_369]) ).
tcf(c_390,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_391,plain,
! [X0: $i] :
( apply(sK0,X0,sK3(sK0,sK2,X0))
| ~ member(X0,sK1) ),
inference(unflattening,[status(thm)],[c_390]) ).
tcf(c_399,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_400,plain,
! [X0: $i] :
( member(sK3(sK0,sK2,X0),sK2)
| ~ member(X0,sK1) ),
inference(unflattening,[status(thm)],[c_399]) ).
tcf(c_489,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK8(X0,X1,X3),X1)
| ~ member(X3,X2)
| ( X2 != sK2 )
| ( X1 != sK1 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_69,c_354]) ).
tcf(c_490,plain,
! [X0: $i] :
( member(sK8(sK0,sK1,X0),sK1)
| ~ member(X0,sK2) ),
inference(unflattening,[status(thm)],[c_489]) ).
tcf(c_678,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(sK6(X0,X1,X2),X2)
| ~ surjective(inverse_function(sK0,sK1,sK2),sK2,sK1)
| ( X2 != sK1 )
| ( X1 != sK2 )
| ( inverse_function(sK0,sK1,sK2) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_65,c_346]) ).
tcf(c_679,plain,
( member(sK6(inverse_function(sK0,sK1,sK2),sK2,sK1),sK1)
| ~ surjective(inverse_function(sK0,sK1,sK2),sK2,sK1) ),
inference(unflattening,[status(thm)],[c_678]) ).
tcf(c_686,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(sK5(X0,X1,X2),X1)
| ~ surjective(inverse_function(sK0,sK1,sK2),sK2,sK1)
| ( X2 != sK1 )
| ( X1 != sK2 )
| ( inverse_function(sK0,sK1,sK2) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_64,c_346]) ).
tcf(c_687,plain,
( member(sK5(inverse_function(sK0,sK1,sK2),sK2,sK1),sK2)
| ~ surjective(inverse_function(sK0,sK1,sK2),sK2,sK1) ),
inference(unflattening,[status(thm)],[c_686]) ).
tcf(c_694,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(sK4(X0,X1,X2),X1)
| ~ surjective(inverse_function(sK0,sK1,sK2),sK2,sK1)
| ( X2 != sK1 )
| ( X1 != sK2 )
| ( inverse_function(sK0,sK1,sK2) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_63,c_346]) ).
tcf(c_695,plain,
( member(sK4(inverse_function(sK0,sK1,sK2),sK2,sK1),sK2)
| ~ surjective(inverse_function(sK0,sK1,sK2),sK2,sK1) ),
inference(unflattening,[status(thm)],[c_694]) ).
tcf(c_718,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ surjective(inverse_function(sK0,sK1,sK2),sK2,sK1)
| ( X2 != sK1 )
| ( X1 != sK2 )
| ( inverse_function(sK0,sK1,sK2) != X0 )
| ( sK4(X0,X1,X2) != sK5(X0,X1,X2) ) ),
inference(resolution_lifted,[status(thm)],[c_60,c_346]) ).
tcf(c_719,plain,
( ~ surjective(inverse_function(sK0,sK1,sK2),sK2,sK1)
| ( sK4(inverse_function(sK0,sK1,sK2),sK2,sK1) != sK5(inverse_function(sK0,sK1,sK2),sK2,sK1) ) ),
inference(unflattening,[status(thm)],[c_718]) ).
tcf(c_1779,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_391,c_370]) ).
tcf(c_1786,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_1779,c_400,c_1779]) ).
tcf(c_1826,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( injective(inverse_function(X0,X1,X2),X3,X4)
| apply(X0,sK6(inverse_function(X0,X1,X2),X3,X4),sK4(inverse_function(X0,X1,X2),X3,X4))
| ~ member(sK6(inverse_function(X0,X1,X2),X3,X4),X1)
| ~ member(sK4(inverse_function(X0,X1,X2),X3,X4),X2) ),
inference(superposition,[status(thm)],[c_61,c_55]) ).
tcf(c_1880,plain,
! [X0: $i] :
( member(sK8(sK0,sK1,X0),sK1)
| ~ member(X0,sK2) ),
inference(superposition,[status(thm)],[c_354,c_69]) ).
tcf(c_1968,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( surjective(inverse_function(X0,X1,X2),X3,X4)
| ~ member(X5,X3)
| ~ member(X5,X2)
| ~ member(sK7(inverse_function(X0,X1,X2),X3,X4),X1)
| ~ apply(X0,sK7(inverse_function(X0,X1,X2),X3,X4),X5) ),
inference(superposition,[status(thm)],[c_56,c_67]) ).
tcf(c_1981,plain,
! [X0: $i] :
( apply(sK0,sK8(sK0,sK1,X0),X0)
| ~ member(X0,sK2) ),
inference(superposition,[status(thm)],[c_354,c_70]) ).
tcf(c_2036,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK8(sK0,sK1,X0) = X2 )
| ~ member(X0,sK2)
| ~ member(X2,X1)
| ~ member(X0,X3)
| ~ injective(sK0,X1,X3)
| ~ apply(sK0,X2,X0)
| ~ member(sK8(sK0,sK1,X0),X1) ),
inference(superposition,[status(thm)],[c_1981,c_66]) ).
tcf(c_2038,plain,
! [X0: $i] :
( ( sK3(sK0,sK2,sK8(sK0,sK1,X0)) = X0 )
| ~ member(X0,sK2)
| ~ member(sK8(sK0,sK1,X0),sK1) ),
inference(superposition,[status(thm)],[c_1981,c_1786]) ).
tcf(c_2039,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ member(X1,sK2)
| ~ member(X0,sK2)
| ~ member(sK8(sK0,sK1,X0),sK1)
| ~ apply(sK0,sK8(sK0,sK1,X0),X1) ),
inference(superposition,[status(thm)],[c_1981,c_370]) ).
tcf(c_2076,plain,
! [X0: $i] :
( ( sK3(sK0,sK2,sK8(sK0,sK1,X0)) = X0 )
| ~ member(X0,sK2) ),
inference(global_subsumption_just,[status(thm)],[c_2038,c_490,c_2038]) ).
tcf(c_2083,plain,
! [X0: $i,X1: $i] :
( injective(X0,sK2,X1)
| ( sK3(sK0,sK2,sK8(sK0,sK1,sK4(X0,sK2,X1))) = sK4(X0,sK2,X1) ) ),
inference(superposition,[status(thm)],[c_63,c_2076]) ).
tcf(c_2087,plain,
! [X0: $i] :
( ( sK3(sK0,sK2,sK8(sK0,sK1,sK3(sK0,sK2,X0))) = sK3(sK0,sK2,X0) )
| ~ member(X0,sK1) ),
inference(superposition,[status(thm)],[c_400,c_2076]) ).
tcf(c_2109,plain,
( ( sK3(sK0,sK2,sK8(sK0,sK1,sK4(inverse_function(sK0,sK1,sK2),sK2,sK1))) = sK4(inverse_function(sK0,sK1,sK2),sK2,sK1) )
| ~ surjective(inverse_function(sK0,sK1,sK2),sK2,sK1) ),
inference(superposition,[status(thm)],[c_2083,c_346]) ).
tcf(c_2127,plain,
! [X0: $i,X1: $i] :
( injective(X0,X1,sK1)
| ( sK3(sK0,sK2,sK8(sK0,sK1,sK3(sK0,sK2,sK6(X0,X1,sK1)))) = sK3(sK0,sK2,sK6(X0,X1,sK1)) ) ),
inference(superposition,[status(thm)],[c_65,c_2087]) ).
tcf(c_2128,plain,
! [X0: $i,X1: $i] :
( surjective(X0,X1,sK1)
| ( sK3(sK0,sK2,sK8(sK0,sK1,sK3(sK0,sK2,sK7(X0,X1,sK1)))) = sK3(sK0,sK2,sK7(X0,X1,sK1)) ) ),
inference(superposition,[status(thm)],[c_68,c_2087]) ).
tcf(c_2149,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ member(X1,sK2)
| ~ member(X0,sK2)
| ~ apply(sK0,sK8(sK0,sK1,X0),X1) ),
inference(global_subsumption_just,[status(thm)],[c_2039,c_490,c_2039]) ).
tcf(c_2207,plain,
( ( sK3(sK0,sK2,sK8(sK0,sK1,sK3(sK0,sK2,sK6(inverse_function(sK0,sK1,sK2),sK2,sK1)))) = sK3(sK0,sK2,sK6(inverse_function(sK0,sK1,sK2),sK2,sK1)) )
| ~ surjective(inverse_function(sK0,sK1,sK2),sK2,sK1) ),
inference(superposition,[status(thm)],[c_2127,c_346]) ).
tcf(c_2277,plain,
( surjective(inverse_function(sK0,sK1,sK2),sK2,sK1)
| member(sK7(inverse_function(sK0,sK1,sK2),sK2,sK1),sK1) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_2598,plain,
( ( sK3(sK0,sK2,sK8(sK0,sK1,sK3(sK0,sK2,sK7(inverse_function(sK0,sK1,sK2),sK2,sK1)))) = sK3(sK0,sK2,sK7(inverse_function(sK0,sK1,sK2),sK2,sK1)) )
| ( sK3(sK0,sK2,sK8(sK0,sK1,sK3(sK0,sK2,sK6(inverse_function(sK0,sK1,sK2),sK2,sK1)))) = sK3(sK0,sK2,sK6(inverse_function(sK0,sK1,sK2),sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_2128,c_2207]) ).
tcf(c_2648,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK8(sK0,sK1,X1) = X0 )
| ~ member(X1,sK2)
| ~ member(X0,sK1)
| ~ member(X1,X2)
| ~ injective(sK0,sK1,X2)
| ~ apply(sK0,X0,X1) ),
inference(superposition,[status(thm)],[c_1880,c_2036]) ).
tcf(c_2691,plain,
! [X0: $i,X1: $i] :
( ( sK8(sK0,sK1,sK3(sK0,sK2,X0)) = X0 )
| ~ member(X0,sK1)
| ~ injective(sK0,sK1,X1)
| ~ member(sK3(sK0,sK2,X0),sK2)
| ~ member(sK3(sK0,sK2,X0),X1) ),
inference(superposition,[status(thm)],[c_391,c_2648]) ).
tcf(c_2755,plain,
! [X0: $i,X1: $i] :
( ( sK8(sK0,sK1,sK3(sK0,sK2,X0)) = X0 )
| ~ member(X0,sK1)
| ~ injective(sK0,sK1,X1)
| ~ member(sK3(sK0,sK2,X0),X1) ),
inference(global_subsumption_just,[status(thm)],[c_2691,c_400,c_2691]) ).
tcf(c_2766,plain,
! [X0: $i] :
( ( sK8(sK0,sK1,sK3(sK0,sK2,X0)) = X0 )
| ~ member(X0,sK1)
| ~ injective(sK0,sK1,sK2) ),
inference(superposition,[status(thm)],[c_400,c_2755]) ).
tcf(c_2767,plain,
! [X0: $i] :
( ( sK8(sK0,sK1,sK3(sK0,sK2,X0)) = X0 )
| ~ member(X0,sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2766,c_359]) ).
tcf(c_2797,plain,
! [X0: $i,X1: $i] :
( injective(X0,X1,sK1)
| ( sK8(sK0,sK1,sK3(sK0,sK2,sK6(X0,X1,sK1))) = sK6(X0,X1,sK1) ) ),
inference(superposition,[status(thm)],[c_65,c_2767]) ).
tcf(c_2874,plain,
( ( sK8(sK0,sK1,sK3(sK0,sK2,sK6(inverse_function(sK0,sK1,sK2),sK2,sK1))) = sK6(inverse_function(sK0,sK1,sK2),sK2,sK1) )
| ~ surjective(inverse_function(sK0,sK1,sK2),sK2,sK1) ),
inference(superposition,[status(thm)],[c_2797,c_346]) ).
tcf(c_3009,plain,
( apply(sK0,sK6(inverse_function(sK0,sK1,sK2),sK2,sK1),sK3(sK0,sK2,sK6(inverse_function(sK0,sK1,sK2),sK2,sK1)))
| ~ member(sK6(inverse_function(sK0,sK1,sK2),sK2,sK1),sK1) ),
inference(instantiation,[status(thm)],[c_391]) ).
tcf(c_3010,plain,
( member(sK3(sK0,sK2,sK6(inverse_function(sK0,sK1,sK2),sK2,sK1)),sK2)
| ~ member(sK6(inverse_function(sK0,sK1,sK2),sK2,sK1),sK1) ),
inference(instantiation,[status(thm)],[c_400]) ).
tcf(c_3157,plain,
! [X0: $i] :
( ( sK4(inverse_function(sK0,sK1,sK2),sK2,sK1) = sK5(inverse_function(sK0,sK1,sK2),sK2,sK1) )
| ~ member(X0,sK1)
| ~ member(sK5(inverse_function(sK0,sK1,sK2),sK2,sK1),sK2)
| ~ member(sK4(inverse_function(sK0,sK1,sK2),sK2,sK1),sK2)
| ~ apply(sK0,X0,sK5(inverse_function(sK0,sK1,sK2),sK2,sK1))
| ~ apply(sK0,X0,sK4(inverse_function(sK0,sK1,sK2),sK2,sK1)) ),
inference(instantiation,[status(thm)],[c_370]) ).
tcf(c_3706,plain,
( member(sK3(sK0,sK2,sK7(inverse_function(sK0,sK1,sK2),sK2,sK1)),sK2)
| ( sK3(sK0,sK2,sK8(sK0,sK1,sK3(sK0,sK2,sK6(inverse_function(sK0,sK1,sK2),sK2,sK1)))) = sK3(sK0,sK2,sK6(inverse_function(sK0,sK1,sK2),sK2,sK1)) )
| ~ member(sK8(sK0,sK1,sK3(sK0,sK2,sK7(inverse_function(sK0,sK1,sK2),sK2,sK1))),sK1) ),
inference(superposition,[status(thm)],[c_2598,c_400]) ).
tcf(c_4200,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( surjective(inverse_function(sK0,X0,X1),X2,X3)
| ~ member(sK7(inverse_function(sK0,X0,X1),X2,X3),sK1)
| ~ member(sK7(inverse_function(sK0,X0,X1),X2,X3),X0)
| ~ member(sK3(sK0,sK2,sK7(inverse_function(sK0,X0,X1),X2,X3)),X2)
| ~ member(sK3(sK0,sK2,sK7(inverse_function(sK0,X0,X1),X2,X3)),X1) ),
inference(superposition,[status(thm)],[c_391,c_1968]) ).
tcf(c_4361,plain,
! [X0: $i,X1: $i,X2: $i] :
( surjective(inverse_function(sK0,X0,sK2),X1,X2)
| ~ member(sK7(inverse_function(sK0,X0,sK2),X1,X2),sK1)
| ~ member(sK7(inverse_function(sK0,X0,sK2),X1,X2),X0)
| ~ member(sK3(sK0,sK2,sK7(inverse_function(sK0,X0,sK2),X1,X2)),X1) ),
inference(superposition,[status(thm)],[c_400,c_4200]) ).
tcf(c_4403,plain,
! [X0: $i,X1: $i] :
( surjective(inverse_function(sK0,X0,sK2),sK2,X1)
| ~ member(sK7(inverse_function(sK0,X0,sK2),sK2,X1),sK1)
| ~ member(sK7(inverse_function(sK0,X0,sK2),sK2,X1),X0) ),
inference(superposition,[status(thm)],[c_400,c_4361]) ).
tcf(c_4415,plain,
( surjective(inverse_function(sK0,sK1,sK2),sK2,sK1)
| ~ member(sK7(inverse_function(sK0,sK1,sK2),sK2,sK1),sK1) ),
inference(instantiation,[status(thm)],[c_4403]) ).
tcf(c_4422,plain,
! [X0: $i] :
( surjective(inverse_function(sK0,X0,sK2),sK2,sK1)
| ~ member(sK7(inverse_function(sK0,X0,sK2),sK2,sK1),X0) ),
inference(superposition,[status(thm)],[c_68,c_4403]) ).
tcf(c_4425,plain,
sK3(sK0,sK2,sK8(sK0,sK1,sK3(sK0,sK2,sK6(inverse_function(sK0,sK1,sK2),sK2,sK1)))) = sK3(sK0,sK2,sK6(inverse_function(sK0,sK1,sK2),sK2,sK1)),
inference(global_subsumption_just,[status(thm)],[c_3706,c_2207,c_2277,c_4415]) ).
tcf(c_4430,plain,
( member(sK3(sK0,sK2,sK6(inverse_function(sK0,sK1,sK2),sK2,sK1)),sK2)
| ~ member(sK8(sK0,sK1,sK3(sK0,sK2,sK6(inverse_function(sK0,sK1,sK2),sK2,sK1))),sK1) ),
inference(superposition,[status(thm)],[c_4425,c_400]) ).
tcf(c_4445,plain,
member(sK3(sK0,sK2,sK6(inverse_function(sK0,sK1,sK2),sK2,sK1)),sK2),
inference(global_subsumption_just,[status(thm)],[c_4430,c_679,c_2277,c_3010,c_4415]) ).
tcf(c_4458,plain,
surjective(inverse_function(sK0,sK1,sK2),sK2,sK1),
inference(superposition,[status(thm)],[c_68,c_4422]) ).
tcf(c_4463,plain,
sK8(sK0,sK1,sK3(sK0,sK2,sK6(inverse_function(sK0,sK1,sK2),sK2,sK1))) = sK6(inverse_function(sK0,sK1,sK2),sK2,sK1),
inference(backward_subsumption_resolution,[status(thm)],[c_2874,c_4458]) ).
tcf(c_4465,plain,
sK3(sK0,sK2,sK8(sK0,sK1,sK4(inverse_function(sK0,sK1,sK2),sK2,sK1))) = sK4(inverse_function(sK0,sK1,sK2),sK2,sK1),
inference(backward_subsumption_resolution,[status(thm)],[c_2109,c_4458]) ).
tcf(c_4466,plain,
~ injective(inverse_function(sK0,sK1,sK2),sK2,sK1),
inference(backward_subsumption_resolution,[status(thm)],[c_346,c_4458]) ).
tcf(c_4529,plain,
! [X0: $i] :
( ( sK3(sK0,sK2,sK6(inverse_function(sK0,sK1,sK2),sK2,sK1)) = X0 )
| ~ member(X0,sK2)
| ~ apply(sK0,sK6(inverse_function(sK0,sK1,sK2),sK2,sK1),X0)
| ~ member(sK3(sK0,sK2,sK6(inverse_function(sK0,sK1,sK2),sK2,sK1)),sK2) ),
inference(superposition,[status(thm)],[c_4463,c_2149]) ).
tcf(c_4531,plain,
( member(sK6(inverse_function(sK0,sK1,sK2),sK2,sK1),sK1)
| ~ member(sK3(sK0,sK2,sK6(inverse_function(sK0,sK1,sK2),sK2,sK1)),sK2) ),
inference(superposition,[status(thm)],[c_4463,c_1880]) ).
tcf(c_4544,plain,
member(sK6(inverse_function(sK0,sK1,sK2),sK2,sK1),sK1),
inference(forward_subsumption_resolution,[status(thm)],[c_4531,c_4445]) ).
tcf(c_4546,plain,
! [X0: $i] :
( ( sK3(sK0,sK2,sK6(inverse_function(sK0,sK1,sK2),sK2,sK1)) = X0 )
| ~ member(X0,sK2)
| ~ apply(sK0,sK6(inverse_function(sK0,sK1,sK2),sK2,sK1),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4529,c_4445]) ).
tcf(c_4637,plain,
( apply(sK0,sK8(sK0,sK1,sK4(inverse_function(sK0,sK1,sK2),sK2,sK1)),sK4(inverse_function(sK0,sK1,sK2),sK2,sK1))
| ~ member(sK8(sK0,sK1,sK4(inverse_function(sK0,sK1,sK2),sK2,sK1)),sK1) ),
inference(superposition,[status(thm)],[c_4465,c_391]) ).
tcf(c_4638,plain,
( member(sK4(inverse_function(sK0,sK1,sK2),sK2,sK1),sK2)
| ~ member(sK8(sK0,sK1,sK4(inverse_function(sK0,sK1,sK2),sK2,sK1)),sK1) ),
inference(superposition,[status(thm)],[c_4465,c_400]) ).
tcf(c_4653,plain,
member(sK4(inverse_function(sK0,sK1,sK2),sK2,sK1),sK2),
inference(global_subsumption_just,[status(thm)],[c_4638,c_695,c_2277,c_4415]) ).
tcf(c_5587,plain,
( injective(inverse_function(sK0,sK1,sK2),sK2,sK1)
| ( sK3(sK0,sK2,sK6(inverse_function(sK0,sK1,sK2),sK2,sK1)) = sK4(inverse_function(sK0,sK1,sK2),sK2,sK1) )
| ~ member(sK6(inverse_function(sK0,sK1,sK2),sK2,sK1),sK1)
| ~ member(sK4(inverse_function(sK0,sK1,sK2),sK2,sK1),sK2) ),
inference(superposition,[status(thm)],[c_1826,c_4546]) ).
tcf(c_5590,plain,
sK3(sK0,sK2,sK6(inverse_function(sK0,sK1,sK2),sK2,sK1)) = sK4(inverse_function(sK0,sK1,sK2),sK2,sK1),
inference(forward_subsumption_resolution,[status(thm)],[c_5587,c_4466,c_4544,c_4653]) ).
tcf(c_5593,plain,
sK8(sK0,sK1,sK4(inverse_function(sK0,sK1,sK2),sK2,sK1)) = sK6(inverse_function(sK0,sK1,sK2),sK2,sK1),
inference(demodulation,[status(thm)],[c_4463,c_5590]) ).
tcf(c_5595,plain,
( apply(sK0,sK6(inverse_function(sK0,sK1,sK2),sK2,sK1),sK4(inverse_function(sK0,sK1,sK2),sK2,sK1))
| ~ member(sK6(inverse_function(sK0,sK1,sK2),sK2,sK1),sK1) ),
inference(demodulation,[status(thm)],[c_4637,c_5593]) ).
tcf(c_5597,plain,
apply(sK0,sK6(inverse_function(sK0,sK1,sK2),sK2,sK1),sK4(inverse_function(sK0,sK1,sK2),sK2,sK1)),
inference(forward_subsumption_resolution,[status(thm)],[c_5595,c_4544]) ).
tcf(c_5807,plain,
( ( sK4(inverse_function(sK0,sK1,sK2),sK2,sK1) = sK5(inverse_function(sK0,sK1,sK2),sK2,sK1) )
| ~ member(sK6(inverse_function(sK0,sK1,sK2),sK2,sK1),sK1)
| ~ member(sK5(inverse_function(sK0,sK1,sK2),sK2,sK1),sK2)
| ~ member(sK4(inverse_function(sK0,sK1,sK2),sK2,sK1),sK2)
| ~ apply(sK0,sK6(inverse_function(sK0,sK1,sK2),sK2,sK1),sK5(inverse_function(sK0,sK1,sK2),sK2,sK1))
| ~ apply(sK0,sK6(inverse_function(sK0,sK1,sK2),sK2,sK1),sK4(inverse_function(sK0,sK1,sK2),sK2,sK1)) ),
inference(instantiation,[status(thm)],[c_3157]) ).
tcf(c_12023,plain,
~ injective(inverse_function(sK0,sK1,sK2),sK2,sK1),
inference(global_subsumption_just,[status(thm)],[c_346,c_346,c_4458]) ).
tcf(c_12037,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_391,c_370]) ).
tcf(c_12043,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_12037,c_400,c_1779]) ).
tcf(c_12230,plain,
! [X0: $i] :
( apply(sK0,sK8(sK0,sK1,X0),X0)
| ~ member(X0,sK2) ),
inference(superposition,[status(thm)],[c_354,c_70]) ).
tcf(c_12242,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( injective(inverse_function(X0,X1,X2),X3,X4)
| apply(X0,sK6(inverse_function(X0,X1,X2),X3,X4),sK5(inverse_function(X0,X1,X2),X3,X4))
| ~ member(sK6(inverse_function(X0,X1,X2),X3,X4),X1)
| ~ member(sK5(inverse_function(X0,X1,X2),X3,X4),X2) ),
inference(superposition,[status(thm)],[c_62,c_55]) ).
tcf(c_12261,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( injective(inverse_function(sK0,X0,X1),X2,X3)
| ( sK5(inverse_function(sK0,X0,X1),X2,X3) = X4 )
| ~ member(X4,sK2)
| ~ member(sK6(inverse_function(sK0,X0,X1),X2,X3),sK1)
| ~ member(sK5(inverse_function(sK0,X0,X1),X2,X3),sK2)
| ~ member(sK6(inverse_function(sK0,X0,X1),X2,X3),X0)
| ~ member(sK5(inverse_function(sK0,X0,X1),X2,X3),X1)
| ~ apply(sK0,sK6(inverse_function(sK0,X0,X1),X2,X3),X4) ),
inference(superposition,[status(thm)],[c_12242,c_370]) ).
tcf(c_12340,plain,
! [X0: $i] :
( ( sK3(sK0,sK2,sK8(sK0,sK1,X0)) = X0 )
| ~ member(X0,sK2)
| ~ member(sK8(sK0,sK1,X0),sK1) ),
inference(superposition,[status(thm)],[c_12230,c_12043]) ).
tcf(c_12426,plain,
! [X0: $i] :
( ( sK3(sK0,sK2,sK8(sK0,sK1,X0)) = X0 )
| ~ member(X0,sK2) ),
inference(global_subsumption_just,[status(thm)],[c_12340,c_2076]) ).
tcf(c_12433,plain,
! [X0: $i,X1: $i] :
( injective(X0,sK2,X1)
| ( sK3(sK0,sK2,sK8(sK0,sK1,sK5(X0,sK2,X1))) = sK5(X0,sK2,X1) ) ),
inference(superposition,[status(thm)],[c_64,c_12426]) ).
tcf(c_12436,plain,
! [X0: $i] :
( ( sK3(sK0,sK2,sK8(sK0,sK1,sK3(sK0,sK2,X0))) = sK3(sK0,sK2,X0) )
| ~ member(X0,sK1) ),
inference(superposition,[status(thm)],[c_400,c_12426]) ).
tcf(c_12465,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X1 )
| ~ member(X1,sK1)
| ~ member(X1,X3)
| ~ member(X0,X3)
| ~ injective(sK0,X3,X2)
| ~ member(sK3(sK0,sK2,X1),X2)
| ~ apply(sK0,X0,sK3(sK0,sK2,X1)) ),
inference(superposition,[status(thm)],[c_391,c_66]) ).
tcf(c_12709,plain,
! [X0: $i,X1: $i] :
( injective(X0,X1,sK1)
| ( sK3(sK0,sK2,sK8(sK0,sK1,sK3(sK0,sK2,sK6(X0,X1,sK1)))) = sK3(sK0,sK2,sK6(X0,X1,sK1)) ) ),
inference(superposition,[status(thm)],[c_65,c_12436]) ).
tcf(c_12737,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK8(sK0,sK1,sK3(sK0,sK2,X0)) = X0 )
| ~ member(X0,sK1)
| ~ member(X0,X1)
| ~ injective(sK0,X1,X2)
| ~ member(sK3(sK0,sK2,X0),sK2)
| ~ member(sK3(sK0,sK2,X0),X2)
| ~ member(sK8(sK0,sK1,sK3(sK0,sK2,X0)),X1) ),
inference(superposition,[status(thm)],[c_12230,c_12465]) ).
tcf(c_12780,plain,
sK3(sK0,sK2,sK8(sK0,sK1,sK3(sK0,sK2,sK6(inverse_function(sK0,sK1,sK2),sK2,sK1)))) = sK3(sK0,sK2,sK6(inverse_function(sK0,sK1,sK2),sK2,sK1)),
inference(superposition,[status(thm)],[c_12709,c_12023]) ).
tcf(c_12781,plain,
( apply(sK0,sK8(sK0,sK1,sK3(sK0,sK2,sK6(inverse_function(sK0,sK1,sK2),sK2,sK1))),sK3(sK0,sK2,sK6(inverse_function(sK0,sK1,sK2),sK2,sK1)))
| ~ member(sK8(sK0,sK1,sK3(sK0,sK2,sK6(inverse_function(sK0,sK1,sK2),sK2,sK1))),sK1) ),
inference(superposition,[status(thm)],[c_12780,c_391]) ).
tcf(c_12782,plain,
( member(sK3(sK0,sK2,sK6(inverse_function(sK0,sK1,sK2),sK2,sK1)),sK2)
| ~ member(sK8(sK0,sK1,sK3(sK0,sK2,sK6(inverse_function(sK0,sK1,sK2),sK2,sK1))),sK1) ),
inference(superposition,[status(thm)],[c_12780,c_400]) ).
tcf(c_12825,plain,
sK3(sK0,sK2,sK8(sK0,sK1,sK5(inverse_function(sK0,sK1,sK2),sK2,sK1))) = sK5(inverse_function(sK0,sK1,sK2),sK2,sK1),
inference(superposition,[status(thm)],[c_12433,c_12023]) ).
tcf(c_12899,plain,
( member(sK5(inverse_function(sK0,sK1,sK2),sK2,sK1),sK2)
| ~ member(sK8(sK0,sK1,sK5(inverse_function(sK0,sK1,sK2),sK2,sK1)),sK1) ),
inference(superposition,[status(thm)],[c_12825,c_400]) ).
tcf(c_12921,plain,
member(sK5(inverse_function(sK0,sK1,sK2),sK2,sK1),sK2),
inference(global_subsumption_just,[status(thm)],[c_12899,c_687,c_4458]) ).
tcf(c_12924,plain,
member(sK3(sK0,sK2,sK6(inverse_function(sK0,sK1,sK2),sK2,sK1)),sK2),
inference(global_subsumption_just,[status(thm)],[c_12782,c_4445]) ).
tcf(c_12927,plain,
! [X0: $i] :
( ( sK8(sK0,sK1,sK3(sK0,sK2,X0)) = X0 )
| ~ member(X0,sK1) ),
inference(global_subsumption_just,[status(thm)],[c_12737,c_2767]) ).
tcf(c_12935,plain,
! [X0: $i,X1: $i] :
( injective(X0,X1,sK1)
| ( sK8(sK0,sK1,sK3(sK0,sK2,sK6(X0,X1,sK1))) = sK6(X0,X1,sK1) ) ),
inference(superposition,[status(thm)],[c_65,c_12927]) ).
tcf(c_13122,plain,
sK8(sK0,sK1,sK3(sK0,sK2,sK6(inverse_function(sK0,sK1,sK2),sK2,sK1))) = sK6(inverse_function(sK0,sK1,sK2),sK2,sK1),
inference(superposition,[status(thm)],[c_12935,c_12023]) ).
tcf(c_13123,plain,
( apply(sK0,sK6(inverse_function(sK0,sK1,sK2),sK2,sK1),sK3(sK0,sK2,sK6(inverse_function(sK0,sK1,sK2),sK2,sK1)))
| ~ member(sK6(inverse_function(sK0,sK1,sK2),sK2,sK1),sK1) ),
inference(demodulation,[status(thm)],[c_12781,c_13122]) ).
tcf(c_13143,plain,
apply(sK0,sK6(inverse_function(sK0,sK1,sK2),sK2,sK1),sK3(sK0,sK2,sK6(inverse_function(sK0,sK1,sK2),sK2,sK1))),
inference(global_subsumption_just,[status(thm)],[c_13123,c_679,c_3009,c_4458]) ).
tcf(c_13150,plain,
( injective(inverse_function(sK0,sK1,sK2),sK2,sK1)
| ( sK3(sK0,sK2,sK6(inverse_function(sK0,sK1,sK2),sK2,sK1)) = sK5(inverse_function(sK0,sK1,sK2),sK2,sK1) )
| ~ member(sK6(inverse_function(sK0,sK1,sK2),sK2,sK1),sK1)
| ~ member(sK5(inverse_function(sK0,sK1,sK2),sK2,sK1),sK2)
| ~ member(sK3(sK0,sK2,sK6(inverse_function(sK0,sK1,sK2),sK2,sK1)),sK2) ),
inference(superposition,[status(thm)],[c_13143,c_12261]) ).
tcf(c_13165,plain,
( ( sK3(sK0,sK2,sK6(inverse_function(sK0,sK1,sK2),sK2,sK1)) = sK5(inverse_function(sK0,sK1,sK2),sK2,sK1) )
| ~ member(sK6(inverse_function(sK0,sK1,sK2),sK2,sK1),sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13150,c_12023,c_12921,c_12924]) ).
tcf(c_13185,plain,
sK3(sK0,sK2,sK6(inverse_function(sK0,sK1,sK2),sK2,sK1)) = sK5(inverse_function(sK0,sK1,sK2),sK2,sK1),
inference(global_subsumption_just,[status(thm)],[c_13165,c_679,c_4458,c_13165]) ).
tcf(c_13188,plain,
apply(sK0,sK6(inverse_function(sK0,sK1,sK2),sK2,sK1),sK5(inverse_function(sK0,sK1,sK2),sK2,sK1)),
inference(demodulation,[status(thm)],[c_13143,c_13185]) ).
tcf(c_13192,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_13188,c_5807,c_5597,c_4458,c_719,c_695,c_687,c_679]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET713+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n020.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 11:45:33 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
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 1.45/1.78 % SZS status Started for theBenchmark.p
% 1.45/1.78 % SZS status Theorem for theBenchmark.p
% 1.45/1.78
% 1.45/1.78 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.45/1.78
% 1.45/1.78 % ------ iProver source info
% 1.45/1.78
% 1.45/1.78 % git: date: 2026-07-19 20:42:38 +0200
% 1.45/1.78 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.45/1.78 % git: non_committed_changes: false
% 1.45/1.78
% 1.45/1.78 % ------ Parsing...
% 1.45/1.78 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.45/1.78
% 1.45/1.78 % ------ 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: 3 0s sf_e pe_s pe_e %
% 1.45/1.78
% 1.45/1.78 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.45/1.78
% 1.45/1.78 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.45/1.78 % ------ Proving...
% 1.45/1.78 % ------ Problem Properties
% 1.45/1.78
% 1.45/1.78 %
% 1.45/1.78 % clauses 20
% 1.45/1.78 % conjectures 0
% 1.45/1.78 % EPR 4
% 1.45/1.78 % Horn 14
% 1.45/1.78 % unary 2
% 1.45/1.78 % binary 11
% 1.45/1.78 % lits 54
% 1.45/1.78 % lits eq 5
% 1.45/1.78 % fd_pure 0
% 1.45/1.78 % fd_pseudo 0
% 1.45/1.78 % fd_cond 0
% 1.45/1.78 % fd_pseudo_cond 2
% 1.45/1.78 % AC symbols 0
% 1.45/1.78
% 1.45/1.78 % ------ Schedule dynamic 5 is on
% 1.45/1.78
% 1.45/1.78 % ------ no conjectures: strip conj schedule
% 1.45/1.78
% 1.45/1.78 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 1.45/1.78
% 1.45/1.78
% 1.45/1.78 % ------
% 1.45/1.78 % Current options:
% 1.45/1.78 % ------
% 1.45/1.78
% 1.45/1.78
% 1.45/1.78 %
% 1.45/1.78
% 1.45/1.78 % ------ Proving...
% 1.45/1.78 %
% 1.45/1.78
% 1.45/1.78 % SZS status Theorem for theBenchmark.p
% 1.45/1.78
% 1.45/1.78 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.45/1.78
% 1.45/1.78
%------------------------------------------------------------------------------