%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET723+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n008.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 02:47:58 PM UTC 2026
% Result : Theorem 10.41s 2.63s
% Output : CNFRefutation 10.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 5
% Syntax : Number of formulae : 133 ( 22 unt; 0 def)
% Number of atoms : 617 ( 111 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 843 ( 359 ~; 368 |; 87 &)
% ( 9 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 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 : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-5 aty)
% Number of variables : 464 ( 0 sgn 436 !; 28 ?; 212 :)
% 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/sandbox/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/sandbox/benchmark/Axioms/SET006+1.ax',compose_function) ).
fof(f15,axiom,
! [X0,X1,X2,X3] :
( equal_maps(X0,X1,X2,X3)
<=> ! [X4,X5,X6] :
( ( member(X6,X3)
& member(X5,X3)
& member(X4,X2) )
=> ( ( apply(X1,X4,X6)
& apply(X0,X4,X5) )
=> X5 = X6 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax',equal_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/sandbox/benchmark/Axioms/SET006+1.ax',injective) ).
fof(f29,conjecture,
! [X0,X1,X2,X3,X4,X5] :
( ( equal_maps(compose_function(X0,X1,X3,X4,X5),compose_function(X0,X2,X3,X4,X5),X3,X5)
& injective(X0,X4,X5)
& maps(X2,X3,X4)
& maps(X1,X3,X4)
& maps(X0,X4,X5) )
=> equal_maps(X1,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thII14) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5] :
( ( equal_maps(compose_function(X0,X1,X3,X4,X5),compose_function(X0,X2,X3,X4,X5),X3,X5)
& injective(X0,X4,X5)
& maps(X2,X3,X4)
& maps(X1,X3,X4)
& maps(X0,X4,X5) )
=> equal_maps(X1,X2,X3,X4) ),
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] :
( 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(f33,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(f34,plain,
? [X0,X1,X2,X3,X4,X5] :
( equal_maps(compose_function(X0,X1,X3,X4,X5),compose_function(X0,X2,X3,X4,X5),X3,X5)
& injective(X0,X4,X5)
& maps(X2,X3,X4)
& maps(X1,X3,X4)
& maps(X0,X4,X5)
& ~ equal_maps(X1,X2,X3,X4) ),
inference(ennf_transformation,[],[f30]) ).
fof(f35,plain,
? [X0,X1,X2,X3,X4,X5] :
( equal_maps(compose_function(X0,X1,X3,X4,X5),compose_function(X0,X2,X3,X4,X5),X3,X5)
& injective(X0,X4,X5)
& maps(X2,X3,X4)
& maps(X1,X3,X4)
& maps(X0,X4,X5)
& ~ equal_maps(X1,X2,X3,X4) ),
inference(flattening,[],[f34]) ).
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(ennf_transformation,[],[f33]) ).
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(flattening,[],[f36]) ).
fof(f38,plain,
! [X0,X1,X2,X3] :
( equal_maps(X0,X1,X2,X3)
<=> ! [X4,X5,X6] :
( ~ member(X6,X3)
| ~ member(X5,X3)
| ~ member(X4,X2)
| ~ apply(X1,X4,X6)
| ~ apply(X0,X4,X5)
| X5 = X6 ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f39,plain,
! [X0,X1,X2,X3] :
( equal_maps(X0,X1,X2,X3)
<=> ! [X4,X5,X6] :
( ~ member(X6,X3)
| ~ member(X5,X3)
| ~ member(X4,X2)
| ~ apply(X1,X4,X6)
| ~ apply(X0,X4,X5)
| X5 = X6 ) ),
inference(flattening,[],[f38]) ).
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(ennf_transformation,[],[f32]) ).
fof(f41,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,[],[f40]) ).
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,
( equal_maps(compose_function(sK0,sK1,sK3,sK4,sK5),compose_function(sK0,sK2,sK3,sK4,sK5),sK3,sK5)
& injective(sK0,sK4,sK5)
& maps(sK2,sK3,sK4)
& maps(sK1,sK3,sK4)
& maps(sK0,sK4,sK5)
& ~ equal_maps(sK1,sK2,sK3,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5)],[f35]) ).
fof(f45,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,sK6(X0,X2,X3))
& member(sK6(X0,X2,X3),X2) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X4,sK6(X0,X2,X3))],[f37]) ).
fof(f46,plain,
! [X0,X1,X2,X3] :
( ( ~ equal_maps(X0,X1,X2,X3)
| ! [X4,X5,X6] :
( ~ member(X6,X3)
| ~ member(X5,X3)
| ~ member(X4,X2)
| ~ apply(X1,X4,X6)
| ~ apply(X0,X4,X5)
| X5 = X6 ) )
& ( ? [X4,X5,X6] :
( member(X6,X3)
& member(X5,X3)
& member(X4,X2)
& apply(X1,X4,X6)
& apply(X0,X4,X5)
& X5 != X6 )
| equal_maps(X0,X1,X2,X3) ) ),
inference(nnf_transformation,[],[f39]) ).
fof(f47,plain,
! [X0,X1,X2,X3] :
( ( ~ equal_maps(X0,X1,X2,X3)
| ! [X7,X8,X9] :
( ~ member(X9,X3)
| ~ member(X8,X3)
| ~ member(X7,X2)
| ~ apply(X1,X7,X9)
| ~ apply(X0,X7,X8)
| X8 = X9 ) )
& ( ? [X4,X5,X6] :
( member(X6,X3)
& member(X5,X3)
& member(X4,X2)
& apply(X1,X4,X6)
& apply(X0,X4,X5)
& X5 != X6 )
| equal_maps(X0,X1,X2,X3) ) ),
inference(rectify,[],[f46]) ).
fof(f48,plain,
! [X0,X1,X2,X3] :
( ( ~ equal_maps(X0,X1,X2,X3)
| ! [X7,X8,X9] :
( ~ member(X9,X3)
| ~ member(X8,X3)
| ~ member(X7,X2)
| ~ apply(X1,X7,X9)
| ~ apply(X0,X7,X8)
| X8 = X9 ) )
& ( ( member(sK9(X0,X1,X2,X3),X3)
& member(sK8(X0,X1,X2,X3),X3)
& member(sK7(X0,X1,X2,X3),X2)
& apply(X1,sK7(X0,X1,X2,X3),sK9(X0,X1,X2,X3))
& apply(X0,sK7(X0,X1,X2,X3),sK8(X0,X1,X2,X3))
& sK8(X0,X1,X2,X3) != sK9(X0,X1,X2,X3) )
| equal_maps(X0,X1,X2,X3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9]),skolemize(X4,sK7(X0,X1,X2,X3)),skolemize(X5,sK8(X0,X1,X2,X3)),skolemize(X6,sK9(X0,X1,X2,X3))],[f47]) ).
fof(f49,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(f50,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,[],[f49]) ).
fof(f51,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,sK10(X0,X1,X3,X5,X6),X6)
& apply(X1,X5,sK10(X0,X1,X3,X5,X6))
& member(sK10(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,[sK10]),skolemize(X8,sK10(X0,X1,X3,X5,X6))],[f50]) ).
fof(f52,plain,
equal_maps(compose_function(sK0,sK1,sK3,sK4,sK5),compose_function(sK0,sK2,sK3,sK4,sK5),sK3,sK5),
inference(cnf_transformation,[],[f44]) ).
fof(f53,plain,
injective(sK0,sK4,sK5),
inference(cnf_transformation,[],[f44]) ).
fof(f54,plain,
maps(sK2,sK3,sK4),
inference(cnf_transformation,[],[f44]) ).
fof(f55,plain,
maps(sK1,sK3,sK4),
inference(cnf_transformation,[],[f44]) ).
fof(f56,plain,
maps(sK0,sK4,sK5),
inference(cnf_transformation,[],[f44]) ).
fof(f57,plain,
~ equal_maps(sK1,sK2,sK3,sK4),
inference(cnf_transformation,[],[f44]) ).
fof(f58,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,[],[f45]) ).
fof(f59,plain,
! [X2,X3,X0,X1] :
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| apply(X0,X3,sK6(X0,X2,X3)) ),
inference(cnf_transformation,[],[f45]) ).
fof(f60,plain,
! [X2,X3,X0,X1] :
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| member(sK6(X0,X2,X3),X2) ),
inference(cnf_transformation,[],[f45]) ).
fof(f61,plain,
! [X2,X3,X0,X1,X8,X9,X7] :
( ~ equal_maps(X0,X1,X2,X3)
| ~ member(X9,X3)
| ~ member(X8,X3)
| ~ member(X7,X2)
| ~ apply(X1,X7,X9)
| ~ apply(X0,X7,X8)
| X8 = X9 ),
inference(cnf_transformation,[],[f48]) ).
fof(f62,plain,
! [X2,X3,X0,X1] :
( member(sK9(X0,X1,X2,X3),X3)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f48]) ).
fof(f63,plain,
! [X2,X3,X0,X1] :
( member(sK8(X0,X1,X2,X3),X3)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f48]) ).
fof(f64,plain,
! [X2,X3,X0,X1] :
( member(sK7(X0,X1,X2,X3),X2)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f48]) ).
fof(f65,plain,
! [X2,X3,X0,X1] :
( apply(X1,sK7(X0,X1,X2,X3),sK9(X0,X1,X2,X3))
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f48]) ).
fof(f66,plain,
! [X2,X3,X0,X1] :
( apply(X0,sK7(X0,X1,X2,X3),sK8(X0,X1,X2,X3))
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f48]) ).
fof(f67,plain,
! [X2,X3,X0,X1] :
( sK8(X0,X1,X2,X3) != sK9(X0,X1,X2,X3)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f48]) ).
fof(f68,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,[],[f41]) ).
fof(f72,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,[],[f51]) ).
tcf(c_49,negated_conjecture,
~ equal_maps(sK1,sK2,sK3,sK4),
inference(cnf_transformation,[],[f57]) ).
tcf(c_50,negated_conjecture,
maps(sK0,sK4,sK5),
inference(cnf_transformation,[],[f56]) ).
tcf(c_51,negated_conjecture,
maps(sK1,sK3,sK4),
inference(cnf_transformation,[],[f55]) ).
tcf(c_52,negated_conjecture,
maps(sK2,sK3,sK4),
inference(cnf_transformation,[],[f54]) ).
tcf(c_53,negated_conjecture,
injective(sK0,sK4,sK5),
inference(cnf_transformation,[],[f53]) ).
tcf(c_54,negated_conjecture,
equal_maps(compose_function(sK0,sK1,sK3,sK4,sK5),compose_function(sK0,sK2,sK3,sK4,sK5),sK3,sK5),
inference(cnf_transformation,[],[f52]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK6(X0,X2,X3),X2)
| ~ member(X3,X1)
| ~ maps(X0,X1,X2) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,X3,sK6(X0,X2,X3))
| ~ member(X3,X1)
| ~ maps(X0,X1,X2) ),
inference(cnf_transformation,[],[f59]) ).
tcf(c_57,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,[],[f58]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equal_maps(X0,X1,X2,X3)
| ( sK8(X0,X1,X2,X3) != sK9(X0,X1,X2,X3) ) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equal_maps(X0,X1,X2,X3)
| apply(X0,sK7(X0,X1,X2,X3),sK8(X0,X1,X2,X3)) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equal_maps(X1,X0,X2,X3)
| apply(X0,sK7(X1,X0,X2,X3),sK9(X1,X0,X2,X3)) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equal_maps(X0,X1,X2,X3)
| member(sK7(X0,X1,X2,X3),X2) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equal_maps(X0,X1,X2,X3)
| member(sK8(X0,X1,X2,X3),X3) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equal_maps(X0,X1,X2,X3)
| member(sK9(X0,X1,X2,X3),X3) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( X5 = X6 )
| ~ member(X6,X3)
| ~ member(X5,X3)
| ~ member(X4,X2)
| ~ apply(X1,X4,X6)
| ~ apply(X0,X4,X5)
| ~ equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_65,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)
| ~ injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_66,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,[],[f72]) ).
tcf(c_332,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( X3 = X5 )
| ~ member(X5,X0)
| ~ member(X4,X2)
| ~ member(X3,X0)
| ~ apply(X1,X5,X4)
| ~ apply(X1,X3,X4)
| ( X2 != sK5 )
| ( X1 != sK0 )
| ( X0 != sK4 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_65]) ).
tcf(c_333,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ~ member(X2,sK4)
| ~ member(X1,sK5)
| ~ member(X0,sK4)
| ~ apply(sK0,X2,X1)
| ~ apply(sK0,X0,X1) ),
inference(unflattening,[status(thm)],[c_332]) ).
tcf(c_379,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X1,X3,sK6(X1,X2,X3))
| ~ member(X3,X0)
| ( X2 != sK5 )
| ( X1 != sK0 )
| ( X0 != sK4 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_56]) ).
tcf(c_380,plain,
! [X0: $i] :
( apply(sK0,X0,sK6(sK0,sK5,X0))
| ~ member(X0,sK4) ),
inference(unflattening,[status(thm)],[c_379]) ).
tcf(c_388,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK6(X1,X2,X3),X2)
| ~ member(X3,X0)
| ( X2 != sK5 )
| ( X1 != sK0 )
| ( X0 != sK4 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_55]) ).
tcf(c_389,plain,
! [X0: $i] :
( member(sK6(sK0,sK5,X0),sK5)
| ~ member(X0,sK4) ),
inference(unflattening,[status(thm)],[c_388]) ).
tcf(c_397,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 != sK4 )
| ( X1 != sK3 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_57]) ).
tcf(c_398,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ member(X2,sK4)
| ~ member(X1,sK4)
| ~ member(X0,sK3)
| ~ apply(sK1,X0,X2)
| ~ apply(sK1,X0,X1) ),
inference(unflattening,[status(thm)],[c_397]) ).
tcf(c_418,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,X3,sK6(X0,X2,X3))
| ~ member(X3,X1)
| ( X2 != sK4 )
| ( X1 != sK3 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_56]) ).
tcf(c_419,plain,
! [X0: $i] :
( apply(sK1,X0,sK6(sK1,sK4,X0))
| ~ member(X0,sK3) ),
inference(unflattening,[status(thm)],[c_418]) ).
tcf(c_427,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK6(X0,X2,X3),X2)
| ~ member(X3,X1)
| ( X2 != sK4 )
| ( X1 != sK3 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_55]) ).
tcf(c_428,plain,
! [X0: $i] :
( member(sK6(sK1,sK4,X0),sK4)
| ~ member(X0,sK3) ),
inference(unflattening,[status(thm)],[c_427]) ).
tcf(c_436,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 != sK4 )
| ( X1 != sK3 )
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_57]) ).
tcf(c_437,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ member(X2,sK4)
| ~ member(X1,sK4)
| ~ member(X0,sK3)
| ~ apply(sK2,X0,X2)
| ~ apply(sK2,X0,X1) ),
inference(unflattening,[status(thm)],[c_436]) ).
tcf(c_457,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,X3,sK6(X0,X2,X3))
| ~ member(X3,X1)
| ( X2 != sK4 )
| ( X1 != sK3 )
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_56]) ).
tcf(c_458,plain,
! [X0: $i] :
( apply(sK2,X0,sK6(sK2,sK4,X0))
| ~ member(X0,sK3) ),
inference(unflattening,[status(thm)],[c_457]) ).
tcf(c_466,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK6(X0,X2,X3),X2)
| ~ member(X3,X1)
| ( X2 != sK4 )
| ( X1 != sK3 )
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_55]) ).
tcf(c_467,plain,
! [X0: $i] :
( member(sK6(sK2,sK4,X0),sK4)
| ~ member(X0,sK3) ),
inference(unflattening,[status(thm)],[c_466]) ).
tcf(c_638,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK9(X0,X1,X2,X3),X3)
| ( X3 != sK4 )
| ( X2 != sK3 )
| ( X1 != sK2 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_63]) ).
tcf(c_639,plain,
member(sK9(sK1,sK2,sK3,sK4),sK4),
inference(unflattening,[status(thm)],[c_638]) ).
tcf(c_643,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK8(X0,X1,X2,X3),X3)
| ( X3 != sK4 )
| ( X2 != sK3 )
| ( X1 != sK2 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_62]) ).
tcf(c_644,plain,
member(sK8(sK1,sK2,sK3,sK4),sK4),
inference(unflattening,[status(thm)],[c_643]) ).
tcf(c_658,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 != sK4 )
| ( X2 != sK3 )
| ( X1 != sK2 )
| ( X0 != sK1 )
| ( sK8(X0,X1,X2,X3) != sK9(X0,X1,X2,X3) ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_58]) ).
tcf(c_659,plain,
sK8(sK1,sK2,sK3,sK4) != sK9(sK1,sK2,sK3,sK4),
inference(unflattening,[status(thm)],[c_658]) ).
tcf(c_1346,plain,
! [X0: $i,X1: $i] :
( ( sK6(sK1,sK4,X0) = X1 )
| ~ member(X1,sK4)
| ~ member(X0,sK3)
| ~ apply(sK1,X0,X1)
| ~ member(sK6(sK1,sK4,X0),sK4) ),
inference(superposition,[status(thm)],[c_419,c_398]) ).
tcf(c_1381,plain,
! [X0: $i,X1: $i] :
( ( sK6(sK2,sK4,X0) = X1 )
| ~ member(X1,sK4)
| ~ member(X0,sK3)
| ~ apply(sK2,X0,X1)
| ~ member(sK6(sK2,sK4,X0),sK4) ),
inference(superposition,[status(thm)],[c_458,c_437]) ).
tcf(c_1445,plain,
! [X0: $i,X1: $i] :
( ( sK6(sK1,sK4,X0) = X1 )
| ~ member(X1,sK4)
| ~ member(X0,sK3)
| ~ apply(sK1,X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_1346,c_428,c_1346]) ).
tcf(c_1456,plain,
! [X0: $i,X1: $i,X2: $i] :
( equal_maps(sK1,X0,X1,X2)
| ( sK6(sK1,sK4,sK7(sK1,X0,X1,X2)) = sK8(sK1,X0,X1,X2) )
| ~ member(sK7(sK1,X0,X1,X2),sK3)
| ~ member(sK8(sK1,X0,X1,X2),sK4) ),
inference(superposition,[status(thm)],[c_59,c_1445]) ).
tcf(c_1469,plain,
! [X0: $i,X1: $i] :
( ( sK6(sK2,sK4,X0) = X1 )
| ~ member(X1,sK4)
| ~ member(X0,sK3)
| ~ apply(sK2,X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_1381,c_467,c_1381]) ).
tcf(c_1481,plain,
! [X0: $i,X1: $i,X2: $i] :
( equal_maps(X0,sK2,X1,X2)
| ( sK6(sK2,sK4,sK7(X0,sK2,X1,X2)) = sK9(X0,sK2,X1,X2) )
| ~ member(sK7(X0,sK2,X1,X2),sK3)
| ~ member(sK9(X0,sK2,X1,X2),sK4) ),
inference(superposition,[status(thm)],[c_60,c_1469]) ).
tcf(c_1533,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ member(X2,sK5)
| ~ member(X1,sK5)
| ~ member(X0,sK3)
| ~ apply(compose_function(sK0,sK2,sK3,sK4,sK5),X0,X2)
| ~ apply(compose_function(sK0,sK1,sK3,sK4,sK5),X0,X1) ),
inference(superposition,[status(thm)],[c_54,c_64]) ).
tcf(c_1594,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( apply(compose_function(sK0,X2,X5,X4,X1),X3,sK6(sK0,sK5,X0))
| ~ member(X0,sK4)
| ~ member(X3,X5)
| ~ member(X0,X4)
| ~ apply(X2,X3,X0)
| ~ member(sK6(sK0,sK5,X0),X1) ),
inference(superposition,[status(thm)],[c_380,c_66]) ).
tcf(c_1756,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK6(sK0,sK5,X2) = X1 )
| ~ member(X2,sK4)
| ~ member(X1,sK5)
| ~ member(X0,sK3)
| ~ apply(sK1,X0,X2)
| ~ member(sK6(sK0,sK5,X2),sK5)
| ~ apply(compose_function(sK0,sK2,sK3,sK4,sK5),X0,X1) ),
inference(superposition,[status(thm)],[c_1594,c_1533]) ).
tcf(c_1901,plain,
( apply(sK0,sK8(sK1,sK2,sK3,sK4),sK6(sK0,sK5,sK8(sK1,sK2,sK3,sK4)))
| ~ member(sK8(sK1,sK2,sK3,sK4),sK4) ),
inference(instantiation,[status(thm)],[c_380]) ).
tcf(c_1902,plain,
( member(sK6(sK0,sK5,sK8(sK1,sK2,sK3,sK4)),sK5)
| ~ member(sK8(sK1,sK2,sK3,sK4),sK4) ),
inference(instantiation,[status(thm)],[c_389]) ).
tcf(c_1912,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK6(sK0,sK5,X2) = X1 )
| ~ member(X2,sK4)
| ~ member(X1,sK5)
| ~ member(X0,sK3)
| ~ apply(sK1,X0,X2)
| ~ apply(compose_function(sK0,sK2,sK3,sK4,sK5),X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1756,c_389]) ).
tcf(c_1933,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK6(sK0,sK5,X0) = sK6(sK0,sK5,X2) )
| ~ member(X2,sK4)
| ~ member(X1,sK3)
| ~ member(X0,sK4)
| ~ apply(sK2,X1,X0)
| ~ apply(sK1,X1,X2)
| ~ member(sK6(sK0,sK5,X0),sK5) ),
inference(superposition,[status(thm)],[c_1594,c_1912]) ).
tcf(c_2105,plain,
! [X0: $i,X1: $i] :
( equal_maps(sK1,X0,sK3,X1)
| ( sK6(sK1,sK4,sK7(sK1,X0,sK3,X1)) = sK8(sK1,X0,sK3,X1) )
| ~ member(sK8(sK1,X0,sK3,X1),sK4) ),
inference(superposition,[status(thm)],[c_61,c_1456]) ).
tcf(c_2346,plain,
! [X0: $i] :
( ( sK8(sK1,sK2,sK3,sK4) = sK9(sK1,sK2,sK3,sK4) )
| ~ member(X0,sK5)
| ~ member(sK9(sK1,sK2,sK3,sK4),sK4)
| ~ member(sK8(sK1,sK2,sK3,sK4),sK4)
| ~ apply(sK0,sK9(sK1,sK2,sK3,sK4),X0)
| ~ apply(sK0,sK8(sK1,sK2,sK3,sK4),X0) ),
inference(instantiation,[status(thm)],[c_333]) ).
tcf(c_2360,plain,
! [X0: $i] :
( equal_maps(sK1,X0,sK3,sK4)
| ( sK6(sK1,sK4,sK7(sK1,X0,sK3,sK4)) = sK8(sK1,X0,sK3,sK4) ) ),
inference(superposition,[status(thm)],[c_62,c_2105]) ).
tcf(c_2818,plain,
sK6(sK1,sK4,sK7(sK1,sK2,sK3,sK4)) = sK8(sK1,sK2,sK3,sK4),
inference(superposition,[status(thm)],[c_2360,c_49]) ).
tcf(c_3350,plain,
! [X0: $i,X1: $i] :
( equal_maps(X0,sK2,sK3,X1)
| ( sK6(sK2,sK4,sK7(X0,sK2,sK3,X1)) = sK9(X0,sK2,sK3,X1) )
| ~ member(sK9(X0,sK2,sK3,X1),sK4) ),
inference(superposition,[status(thm)],[c_61,c_1481]) ).
tcf(c_3361,plain,
! [X0: $i] :
( equal_maps(X0,sK2,sK3,sK4)
| ( sK6(sK2,sK4,sK7(X0,sK2,sK3,sK4)) = sK9(X0,sK2,sK3,sK4) ) ),
inference(superposition,[status(thm)],[c_63,c_3350]) ).
tcf(c_3370,plain,
sK6(sK2,sK4,sK7(sK1,sK2,sK3,sK4)) = sK9(sK1,sK2,sK3,sK4),
inference(superposition,[status(thm)],[c_3361,c_49]) ).
tcf(c_3394,plain,
( member(sK9(sK1,sK2,sK3,sK4),sK4)
| ~ member(sK7(sK1,sK2,sK3,sK4),sK3) ),
inference(superposition,[status(thm)],[c_3370,c_467]) ).
tcf(c_3486,plain,
member(sK9(sK1,sK2,sK3,sK4),sK4),
inference(global_subsumption_just,[status(thm)],[c_3394,c_639]) ).
tcf(c_3507,plain,
( ( sK8(sK1,sK2,sK3,sK4) = sK9(sK1,sK2,sK3,sK4) )
| ~ member(sK9(sK1,sK2,sK3,sK4),sK4)
| ~ member(sK8(sK1,sK2,sK3,sK4),sK4)
| ~ member(sK6(sK0,sK5,sK8(sK1,sK2,sK3,sK4)),sK5)
| ~ apply(sK0,sK9(sK1,sK2,sK3,sK4),sK6(sK0,sK5,sK8(sK1,sK2,sK3,sK4)))
| ~ apply(sK0,sK8(sK1,sK2,sK3,sK4),sK6(sK0,sK5,sK8(sK1,sK2,sK3,sK4))) ),
inference(instantiation,[status(thm)],[c_2346]) ).
tcf(c_21299,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ member(X2,sK5)
| ~ member(X1,sK5)
| ~ member(X0,sK3)
| ~ apply(compose_function(sK0,sK2,sK3,sK4,sK5),X0,X2)
| ~ apply(compose_function(sK0,sK1,sK3,sK4,sK5),X0,X1) ),
inference(superposition,[status(thm)],[c_54,c_64]) ).
tcf(c_21855,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( apply(compose_function(sK0,X2,X5,X4,X1),X3,sK6(sK0,sK5,X0))
| ~ member(X0,sK4)
| ~ member(X3,X5)
| ~ member(X0,X4)
| ~ apply(X2,X3,X0)
| ~ member(sK6(sK0,sK5,X0),X1) ),
inference(superposition,[status(thm)],[c_380,c_66]) ).
tcf(c_22011,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK6(sK0,sK5,X2) = X1 )
| ~ member(X2,sK4)
| ~ member(X1,sK5)
| ~ member(X0,sK3)
| ~ apply(sK1,X0,X2)
| ~ member(sK6(sK0,sK5,X2),sK5)
| ~ apply(compose_function(sK0,sK2,sK3,sK4,sK5),X0,X1) ),
inference(superposition,[status(thm)],[c_21855,c_21299]) ).
tcf(c_22160,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK6(sK0,sK5,X2) = X1 )
| ~ member(X2,sK4)
| ~ member(X1,sK5)
| ~ member(X0,sK3)
| ~ apply(sK1,X0,X2)
| ~ apply(compose_function(sK0,sK2,sK3,sK4,sK5),X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22011,c_389]) ).
tcf(c_22181,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK6(sK0,sK5,X0) = sK6(sK0,sK5,X2) )
| ~ member(X2,sK4)
| ~ member(X1,sK3)
| ~ member(X0,sK4)
| ~ apply(sK2,X1,X0)
| ~ apply(sK1,X1,X2)
| ~ member(sK6(sK0,sK5,X0),sK5) ),
inference(superposition,[status(thm)],[c_21855,c_22160]) ).
tcf(c_22535,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK6(sK0,sK5,X0) = sK6(sK0,sK5,X2) )
| ~ member(X2,sK4)
| ~ member(X1,sK3)
| ~ member(X0,sK4)
| ~ apply(sK2,X1,X0)
| ~ apply(sK1,X1,X2) ),
inference(global_subsumption_just,[status(thm)],[c_22181,c_389,c_1933]) ).
tcf(c_22536,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK6(sK0,sK5,X2) = sK6(sK0,sK5,X1) )
| ~ member(X2,sK4)
| ~ member(X1,sK4)
| ~ member(X0,sK3)
| ~ apply(sK2,X0,X2)
| ~ apply(sK1,X0,X1) ),
inference(renaming,[status(thm)],[c_22535]) ).
tcf(c_22552,plain,
! [X0: $i,X1: $i] :
( ( sK6(sK0,sK5,sK6(sK1,sK4,X0)) = sK6(sK0,sK5,X1) )
| ~ member(X1,sK4)
| ~ member(X0,sK3)
| ~ apply(sK2,X0,X1)
| ~ member(sK6(sK1,sK4,X0),sK4) ),
inference(superposition,[status(thm)],[c_419,c_22536]) ).
tcf(c_22590,plain,
! [X0: $i,X1: $i] :
( ( sK6(sK0,sK5,sK6(sK1,sK4,X0)) = sK6(sK0,sK5,X1) )
| ~ member(X1,sK4)
| ~ member(X0,sK3)
| ~ apply(sK2,X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_22552,c_428,c_22552]) ).
tcf(c_22603,plain,
! [X0: $i] :
( ( sK6(sK0,sK5,sK6(sK1,sK4,X0)) = sK6(sK0,sK5,sK6(sK2,sK4,X0)) )
| ~ member(X0,sK3)
| ~ member(sK6(sK2,sK4,X0),sK4) ),
inference(superposition,[status(thm)],[c_458,c_22590]) ).
tcf(c_22626,plain,
! [X0: $i] :
( ( sK6(sK0,sK5,sK6(sK1,sK4,X0)) = sK6(sK0,sK5,sK6(sK2,sK4,X0)) )
| ~ member(X0,sK3) ),
inference(global_subsumption_just,[status(thm)],[c_22603,c_467,c_22603]) ).
tcf(c_27898,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK6(sK0,sK5,X0) = sK6(sK0,sK5,X2) )
| ~ member(X2,sK4)
| ~ member(X1,sK3)
| ~ member(X0,sK4)
| ~ apply(sK2,X1,X0)
| ~ apply(sK1,X1,X2) ),
inference(global_subsumption_just,[status(thm)],[c_1933,c_389,c_1933]) ).
tcf(c_27899,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK6(sK0,sK5,X2) = sK6(sK0,sK5,X1) )
| ~ member(X2,sK4)
| ~ member(X1,sK4)
| ~ member(X0,sK3)
| ~ apply(sK2,X0,X2)
| ~ apply(sK1,X0,X1) ),
inference(renaming,[status(thm)],[c_27898]) ).
tcf(c_27914,plain,
! [X0: $i,X1: $i] :
( ( sK6(sK0,sK5,sK6(sK1,sK4,X0)) = sK6(sK0,sK5,X1) )
| ~ member(X1,sK4)
| ~ member(X0,sK3)
| ~ apply(sK2,X0,X1)
| ~ member(sK6(sK1,sK4,X0),sK4) ),
inference(superposition,[status(thm)],[c_419,c_27899]) ).
tcf(c_28300,plain,
! [X0: $i,X1: $i] :
( ( sK6(sK0,sK5,sK6(sK1,sK4,X0)) = sK6(sK0,sK5,X1) )
| ~ member(X1,sK4)
| ~ member(X0,sK3)
| ~ apply(sK2,X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_27914,c_428,c_22552]) ).
tcf(c_28312,plain,
! [X0: $i] :
( ( sK6(sK0,sK5,sK6(sK1,sK4,X0)) = sK6(sK0,sK5,sK6(sK2,sK4,X0)) )
| ~ member(X0,sK3)
| ~ member(sK6(sK2,sK4,X0),sK4) ),
inference(superposition,[status(thm)],[c_458,c_28300]) ).
tcf(c_28621,plain,
! [X0: $i] :
( ( sK6(sK0,sK5,sK6(sK1,sK4,X0)) = sK6(sK0,sK5,sK6(sK2,sK4,X0)) )
| ~ member(X0,sK3) ),
inference(global_subsumption_just,[status(thm)],[c_28312,c_22626]) ).
tcf(c_28627,plain,
! [X0: $i,X1: $i,X2: $i] :
( equal_maps(X0,X1,sK3,X2)
| ( sK6(sK0,sK5,sK6(sK1,sK4,sK7(X0,X1,sK3,X2))) = sK6(sK0,sK5,sK6(sK2,sK4,sK7(X0,X1,sK3,X2))) ) ),
inference(superposition,[status(thm)],[c_61,c_28621]) ).
tcf(c_29237,plain,
sK6(sK0,sK5,sK6(sK1,sK4,sK7(sK1,sK2,sK3,sK4))) = sK6(sK0,sK5,sK6(sK2,sK4,sK7(sK1,sK2,sK3,sK4))),
inference(superposition,[status(thm)],[c_28627,c_49]) ).
tcf(c_29239,plain,
sK6(sK0,sK5,sK8(sK1,sK2,sK3,sK4)) = sK6(sK0,sK5,sK9(sK1,sK2,sK3,sK4)),
inference(light_normalisation,[status(thm)],[c_29237,c_2818,c_3370]) ).
tcf(c_29252,plain,
( apply(sK0,sK9(sK1,sK2,sK3,sK4),sK6(sK0,sK5,sK8(sK1,sK2,sK3,sK4)))
| ~ member(sK9(sK1,sK2,sK3,sK4),sK4) ),
inference(superposition,[status(thm)],[c_29239,c_380]) ).
tcf(c_29288,plain,
apply(sK0,sK9(sK1,sK2,sK3,sK4),sK6(sK0,sK5,sK8(sK1,sK2,sK3,sK4))),
inference(forward_subsumption_resolution,[status(thm)],[c_29252,c_3486]) ).
tcf(c_29495,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_29288,c_3507,c_1901,c_1902,c_659,c_644,c_639]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET723+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n008.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 11:47:09 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 10.41/2.63 % SZS status Started for theBenchmark.p
% 10.41/2.63 % SZS status Theorem for theBenchmark.p
% 10.41/2.63
% 10.41/2.63 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.41/2.63
% 10.41/2.63 % ------ iProver source info
% 10.41/2.63
% 10.41/2.63 % git: date: 2026-07-19 20:42:38 +0200
% 10.41/2.63 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.41/2.63 % git: non_committed_changes: false
% 10.41/2.63
% 10.41/2.63 % ------ Parsing...
% 10.41/2.63 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.41/2.63
% 10.41/2.63 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e %
% 10.41/2.63
% 10.41/2.63 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.41/2.63
% 10.41/2.63 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.41/2.63 % ------ Proving...
% 10.41/2.63 % ------ Problem Properties
% 10.41/2.63
% 10.41/2.63 %
% 10.41/2.63 % clauses 23
% 10.41/2.63 % conjectures 2
% 10.41/2.63 % EPR 6
% 10.41/2.63 % Horn 18
% 10.41/2.63 % unary 2
% 10.41/2.63 % binary 12
% 10.41/2.63 % lits 75
% 10.41/2.63 % lits eq 6
% 10.41/2.63 % fd_pure 0
% 10.41/2.63 % fd_pseudo 0
% 10.41/2.63 % fd_cond 0
% 10.41/2.63 % fd_pseudo_cond 5
% 10.41/2.63 % AC symbols 0
% 10.41/2.63
% 10.41/2.63 % ------ Schedule dynamic 5 is on
% 10.41/2.63
% 10.41/2.63 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.41/2.63
% 10.41/2.63
% 10.41/2.63 % ------
% 10.41/2.63 % Current options:
% 10.41/2.63 % ------
% 10.41/2.63
% 10.41/2.63
% 10.41/2.63 %
% 10.41/2.63
% 10.41/2.63 % ------ Proving...
% 10.41/2.63 %
% 10.41/2.63
% 10.41/2.63 % SZS status Theorem for theBenchmark.p
% 10.41/2.63
% 10.41/2.63 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.41/2.64
% 10.41/2.64
%------------------------------------------------------------------------------