%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET721+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 : n026.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 02:47:57 PM UTC 2026
% Result : Theorem 16.08s 3.28s
% Output : CNFRefutation 16.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 79 ( 13 unt; 0 def)
% Number of atoms : 378 ( 49 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 502 ( 203 ~; 205 |; 71 &)
% ( 8 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 8 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-5 aty)
% Number of variables : 289 ( 0 sgn 263 !; 26 ?; 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/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(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] :
( ( injective(compose_function(X1,X0,X2,X3,X4),X2,X4)
& maps(X1,X3,X4)
& maps(X0,X2,X3) )
=> injective(X0,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thII12) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( ( injective(compose_function(X1,X0,X2,X3,X4),X2,X4)
& maps(X1,X3,X4)
& maps(X0,X2,X3) )
=> injective(X0,X2,X3) ),
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,X3,X4] :
( injective(compose_function(X1,X0,X2,X3,X4),X2,X4)
& maps(X1,X3,X4)
& maps(X0,X2,X3)
& ~ injective(X0,X2,X3) ),
inference(ennf_transformation,[],[f30]) ).
fof(f34,plain,
? [X0,X1,X2,X3,X4] :
( injective(compose_function(X1,X0,X2,X3,X4),X2,X4)
& maps(X1,X3,X4)
& maps(X0,X2,X3)
& ~ injective(X0,X2,X3) ),
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] :
( 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(f38,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,[],[f37]) ).
fof(f39,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(f40,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,[],[f39]) ).
fof(f41,plain,
( injective(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)
& maps(sK1,sK3,sK4)
& maps(sK0,sK2,sK3)
& ~ injective(sK0,sK2,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f34]) ).
fof(f42,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,sK5(X0,X2,X3))
& member(sK5(X0,X2,X3),X2) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X4,sK5(X0,X2,X3))],[f36]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ( ~ injective(X0,X1,X2)
| ! [X3,X4,X5] :
( ~ member(X5,X2)
| ~ member(X4,X1)
| ~ member(X3,X1)
| ~ apply(X0,X4,X5)
| ~ apply(X0,X3,X5)
| X3 = X4 ) )
& ( ? [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,[],[f38]) ).
fof(f44,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,[],[f43]) ).
fof(f45,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(sK8(X0,X1,X2),X2)
& member(sK7(X0,X1,X2),X1)
& member(sK6(X0,X1,X2),X1)
& apply(X0,sK7(X0,X1,X2),sK8(X0,X1,X2))
& apply(X0,sK6(X0,X1,X2),sK8(X0,X1,X2))
& sK6(X0,X1,X2) != sK7(X0,X1,X2) )
| injective(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8]),skolemize(X3,sK6(X0,X1,X2)),skolemize(X4,sK7(X0,X1,X2)),skolemize(X5,sK8(X0,X1,X2))],[f44]) ).
fof(f46,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,[],[f40]) ).
fof(f47,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,[],[f46]) ).
fof(f48,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,sK9(X0,X1,X3,X5,X6),X6)
& apply(X1,X5,sK9(X0,X1,X3,X5,X6))
& member(sK9(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,[sK9]),skolemize(X8,sK9(X0,X1,X3,X5,X6))],[f47]) ).
fof(f49,plain,
injective(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),
inference(cnf_transformation,[],[f41]) ).
fof(f50,plain,
maps(sK1,sK3,sK4),
inference(cnf_transformation,[],[f41]) ).
fof(f52,plain,
~ injective(sK0,sK2,sK3),
inference(cnf_transformation,[],[f41]) ).
fof(f54,plain,
! [X2,X3,X0,X1] :
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| apply(X0,X3,sK5(X0,X2,X3)) ),
inference(cnf_transformation,[],[f42]) ).
fof(f55,plain,
! [X2,X3,X0,X1] :
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| member(sK5(X0,X2,X3),X2) ),
inference(cnf_transformation,[],[f42]) ).
fof(f56,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,[],[f45]) ).
fof(f57,plain,
! [X2,X0,X1] :
( member(sK8(X0,X1,X2),X2)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f45]) ).
fof(f58,plain,
! [X2,X0,X1] :
( member(sK7(X0,X1,X2),X1)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f45]) ).
fof(f59,plain,
! [X2,X0,X1] :
( member(sK6(X0,X1,X2),X1)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f45]) ).
fof(f60,plain,
! [X2,X0,X1] :
( apply(X0,sK7(X0,X1,X2),sK8(X0,X1,X2))
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f45]) ).
fof(f61,plain,
! [X2,X0,X1] :
( apply(X0,sK6(X0,X1,X2),sK8(X0,X1,X2))
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f45]) ).
fof(f62,plain,
! [X2,X0,X1] :
( sK6(X0,X1,X2) != sK7(X0,X1,X2)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f45]) ).
fof(f66,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,[],[f48]) ).
tcf(c_49,negated_conjecture,
~ injective(sK0,sK2,sK3),
inference(cnf_transformation,[],[f52]) ).
tcf(c_51,negated_conjecture,
maps(sK1,sK3,sK4),
inference(cnf_transformation,[],[f50]) ).
tcf(c_52,negated_conjecture,
injective(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),
inference(cnf_transformation,[],[f49]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK5(X0,X2,X3),X2)
| ~ member(X3,X1)
| ~ maps(X0,X1,X2) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,X3,sK5(X0,X2,X3))
| ~ member(X3,X1)
| ~ maps(X0,X1,X2) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( injective(X0,X1,X2)
| ( sK6(X0,X1,X2) != sK7(X0,X1,X2) ) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( injective(X0,X1,X2)
| apply(X0,sK6(X0,X1,X2),sK8(X0,X1,X2)) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( injective(X0,X1,X2)
| apply(X0,sK7(X0,X1,X2),sK8(X0,X1,X2)) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( injective(X0,X1,X2)
| member(sK6(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f59]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( injective(X0,X1,X2)
| member(sK7(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] :
( injective(X0,X1,X2)
| member(sK8(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_62,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,[],[f56]) ).
tcf(c_63,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,[],[f66]) ).
tcf(c_355,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X1,X3,sK5(X1,X2,X3))
| ~ member(X3,X0)
| ( X2 != sK4 )
| ( X1 != sK1 )
| ( X0 != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_54]) ).
tcf(c_356,plain,
! [X0: $i] :
( apply(sK1,X0,sK5(sK1,sK4,X0))
| ~ member(X0,sK3) ),
inference(unflattening,[status(thm)],[c_355]) ).
tcf(c_364,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK5(X1,X2,X3),X2)
| ~ member(X3,X0)
| ( X2 != sK4 )
| ( X1 != sK1 )
| ( X0 != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_53]) ).
tcf(c_365,plain,
! [X0: $i] :
( member(sK5(sK1,sK4,X0),sK4)
| ~ member(X0,sK3) ),
inference(unflattening,[status(thm)],[c_364]) ).
tcf(c_547,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(sK8(X0,X1,X2),X2)
| ( X2 != sK3 )
| ( X1 != sK2 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_61]) ).
tcf(c_548,plain,
member(sK8(sK0,sK2,sK3),sK3),
inference(unflattening,[status(thm)],[c_547]) ).
tcf(c_552,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(sK7(X0,X1,X2),X1)
| ( X2 != sK3 )
| ( X1 != sK2 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_60]) ).
tcf(c_553,plain,
member(sK7(sK0,sK2,sK3),sK2),
inference(unflattening,[status(thm)],[c_552]) ).
tcf(c_557,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(sK6(X0,X1,X2),X1)
| ( X2 != sK3 )
| ( X1 != sK2 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_59]) ).
tcf(c_558,plain,
member(sK6(sK0,sK2,sK3),sK2),
inference(unflattening,[status(thm)],[c_557]) ).
tcf(c_562,plain,
! [X0: $i,X1: $i,X2: $i] :
( apply(X0,sK7(X0,X1,X2),sK8(X0,X1,X2))
| ( X2 != sK3 )
| ( X1 != sK2 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_58]) ).
tcf(c_563,plain,
apply(sK0,sK7(sK0,sK2,sK3),sK8(sK0,sK2,sK3)),
inference(unflattening,[status(thm)],[c_562]) ).
tcf(c_567,plain,
! [X0: $i,X1: $i,X2: $i] :
( apply(X0,sK6(X0,X1,X2),sK8(X0,X1,X2))
| ( X2 != sK3 )
| ( X1 != sK2 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_57]) ).
tcf(c_568,plain,
apply(sK0,sK6(sK0,sK2,sK3),sK8(sK0,sK2,sK3)),
inference(unflattening,[status(thm)],[c_567]) ).
tcf(c_572,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 != sK3 )
| ( X1 != sK2 )
| ( X0 != sK0 )
| ( sK6(X0,X1,X2) != sK7(X0,X1,X2) ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_56]) ).
tcf(c_573,plain,
sK6(sK0,sK2,sK3) != sK7(sK0,sK2,sK3),
inference(unflattening,[status(thm)],[c_572]) ).
tcf(c_1721,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( apply(compose_function(X0,X2,X5,sK3,X4),X3,X1)
| ~ member(X3,X5)
| ~ member(X1,X4)
| ~ member(sK8(sK0,sK2,sK3),sK3)
| ~ apply(X2,X3,sK8(sK0,sK2,sK3))
| ~ apply(X0,sK8(sK0,sK2,sK3),X1) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_1723,plain,
( apply(sK1,sK8(sK0,sK2,sK3),sK5(sK1,sK4,sK8(sK0,sK2,sK3)))
| ~ member(sK8(sK0,sK2,sK3),sK3) ),
inference(instantiation,[status(thm)],[c_356]) ).
tcf(c_1724,plain,
( member(sK5(sK1,sK4,sK8(sK0,sK2,sK3)),sK4)
| ~ member(sK8(sK0,sK2,sK3),sK3) ),
inference(instantiation,[status(thm)],[c_365]) ).
tcf(c_1943,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK6(sK0,sK2,sK3) = sK7(sK0,sK2,sK3) )
| ~ member(X1,X3)
| ~ injective(X0,X2,X3)
| ~ member(sK7(sK0,sK2,sK3),X2)
| ~ member(sK6(sK0,sK2,sK3),X2)
| ~ apply(X0,sK7(sK0,sK2,sK3),X1)
| ~ apply(X0,sK6(sK0,sK2,sK3),X1) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_3864,plain,
! [X0: $i,X1: $i] :
( ( sK6(sK0,sK2,sK3) = sK7(sK0,sK2,sK3) )
| ~ injective(X0,X1,sK4)
| ~ member(sK7(sK0,sK2,sK3),X1)
| ~ member(sK6(sK0,sK2,sK3),X1)
| ~ member(sK5(sK1,sK4,sK8(sK0,sK2,sK3)),sK4)
| ~ apply(X0,sK7(sK0,sK2,sK3),sK5(sK1,sK4,sK8(sK0,sK2,sK3)))
| ~ apply(X0,sK6(sK0,sK2,sK3),sK5(sK1,sK4,sK8(sK0,sK2,sK3))) ),
inference(instantiation,[status(thm)],[c_1943]) ).
tcf(c_5435,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(compose_function(X0,X1,X3,sK3,sK4),X2,sK5(sK1,sK4,sK8(sK0,sK2,sK3)))
| ~ member(X2,X3)
| ~ member(sK8(sK0,sK2,sK3),sK3)
| ~ apply(X1,X2,sK8(sK0,sK2,sK3))
| ~ member(sK5(sK1,sK4,sK8(sK0,sK2,sK3)),sK4)
| ~ apply(X0,sK8(sK0,sK2,sK3),sK5(sK1,sK4,sK8(sK0,sK2,sK3))) ),
inference(instantiation,[status(thm)],[c_1721]) ).
tcf(c_8644,plain,
! [X0: $i,X1: $i,X2: $i] :
( apply(compose_function(sK1,X0,X2,sK3,sK4),X1,sK5(sK1,sK4,sK8(sK0,sK2,sK3)))
| ~ member(X1,X2)
| ~ member(sK8(sK0,sK2,sK3),sK3)
| ~ apply(X0,X1,sK8(sK0,sK2,sK3))
| ~ member(sK5(sK1,sK4,sK8(sK0,sK2,sK3)),sK4)
| ~ apply(sK1,sK8(sK0,sK2,sK3),sK5(sK1,sK4,sK8(sK0,sK2,sK3))) ),
inference(instantiation,[status(thm)],[c_5435]) ).
tcf(c_20491,plain,
! [X0: $i] :
( apply(compose_function(sK1,X0,sK2,sK3,sK4),sK7(sK0,sK2,sK3),sK5(sK1,sK4,sK8(sK0,sK2,sK3)))
| ~ member(sK8(sK0,sK2,sK3),sK3)
| ~ member(sK7(sK0,sK2,sK3),sK2)
| ~ member(sK5(sK1,sK4,sK8(sK0,sK2,sK3)),sK4)
| ~ apply(X0,sK7(sK0,sK2,sK3),sK8(sK0,sK2,sK3))
| ~ apply(sK1,sK8(sK0,sK2,sK3),sK5(sK1,sK4,sK8(sK0,sK2,sK3))) ),
inference(instantiation,[status(thm)],[c_8644]) ).
tcf(c_20493,plain,
! [X0: $i] :
( apply(compose_function(sK1,X0,sK2,sK3,sK4),sK6(sK0,sK2,sK3),sK5(sK1,sK4,sK8(sK0,sK2,sK3)))
| ~ member(sK8(sK0,sK2,sK3),sK3)
| ~ member(sK6(sK0,sK2,sK3),sK2)
| ~ member(sK5(sK1,sK4,sK8(sK0,sK2,sK3)),sK4)
| ~ apply(X0,sK6(sK0,sK2,sK3),sK8(sK0,sK2,sK3))
| ~ apply(sK1,sK8(sK0,sK2,sK3),sK5(sK1,sK4,sK8(sK0,sK2,sK3))) ),
inference(instantiation,[status(thm)],[c_8644]) ).
tcf(c_24508,plain,
( apply(compose_function(sK1,sK0,sK2,sK3,sK4),sK7(sK0,sK2,sK3),sK5(sK1,sK4,sK8(sK0,sK2,sK3)))
| ~ member(sK8(sK0,sK2,sK3),sK3)
| ~ member(sK7(sK0,sK2,sK3),sK2)
| ~ member(sK5(sK1,sK4,sK8(sK0,sK2,sK3)),sK4)
| ~ apply(sK0,sK7(sK0,sK2,sK3),sK8(sK0,sK2,sK3))
| ~ apply(sK1,sK8(sK0,sK2,sK3),sK5(sK1,sK4,sK8(sK0,sK2,sK3))) ),
inference(instantiation,[status(thm)],[c_20491]) ).
tcf(c_24509,plain,
( apply(compose_function(sK1,sK0,sK2,sK3,sK4),sK6(sK0,sK2,sK3),sK5(sK1,sK4,sK8(sK0,sK2,sK3)))
| ~ member(sK8(sK0,sK2,sK3),sK3)
| ~ member(sK6(sK0,sK2,sK3),sK2)
| ~ member(sK5(sK1,sK4,sK8(sK0,sK2,sK3)),sK4)
| ~ apply(sK0,sK6(sK0,sK2,sK3),sK8(sK0,sK2,sK3))
| ~ apply(sK1,sK8(sK0,sK2,sK3),sK5(sK1,sK4,sK8(sK0,sK2,sK3))) ),
inference(instantiation,[status(thm)],[c_20493]) ).
tcf(c_29838,plain,
! [X0: $i] :
( ( sK6(sK0,sK2,sK3) = sK7(sK0,sK2,sK3) )
| ~ member(sK7(sK0,sK2,sK3),X0)
| ~ member(sK6(sK0,sK2,sK3),X0)
| ~ member(sK5(sK1,sK4,sK8(sK0,sK2,sK3)),sK4)
| ~ injective(compose_function(sK1,sK0,sK2,sK3,sK4),X0,sK4)
| ~ apply(compose_function(sK1,sK0,sK2,sK3,sK4),sK7(sK0,sK2,sK3),sK5(sK1,sK4,sK8(sK0,sK2,sK3)))
| ~ apply(compose_function(sK1,sK0,sK2,sK3,sK4),sK6(sK0,sK2,sK3),sK5(sK1,sK4,sK8(sK0,sK2,sK3))) ),
inference(instantiation,[status(thm)],[c_3864]) ).
tcf(c_29839,plain,
( ( sK6(sK0,sK2,sK3) = sK7(sK0,sK2,sK3) )
| ~ member(sK7(sK0,sK2,sK3),sK2)
| ~ member(sK6(sK0,sK2,sK3),sK2)
| ~ member(sK5(sK1,sK4,sK8(sK0,sK2,sK3)),sK4)
| ~ injective(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)
| ~ apply(compose_function(sK1,sK0,sK2,sK3,sK4),sK7(sK0,sK2,sK3),sK5(sK1,sK4,sK8(sK0,sK2,sK3)))
| ~ apply(compose_function(sK1,sK0,sK2,sK3,sK4),sK6(sK0,sK2,sK3),sK5(sK1,sK4,sK8(sK0,sK2,sK3))) ),
inference(instantiation,[status(thm)],[c_29838]) ).
tcf(c_29840,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_29839,c_24509,c_24508,c_1723,c_1724,c_573,c_568,c_563,c_558,c_553,c_548,c_52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET721+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n026.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 11:48:25 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 16.08/3.28 % SZS status Started for theBenchmark.p
% 16.08/3.28 % SZS status Theorem for theBenchmark.p
% 16.08/3.28
% 16.08/3.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 16.08/3.28
% 16.08/3.28 % ------ iProver source info
% 16.08/3.28
% 16.08/3.28 % git: date: 2026-07-19 20:42:38 +0200
% 16.08/3.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 16.08/3.28 % git: non_committed_changes: false
% 16.08/3.28
% 16.08/3.28 % ------ Parsing...
% 16.08/3.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 16.08/3.28
% 16.08/3.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e %
% 16.08/3.28
% 16.08/3.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 16.08/3.28
% 16.08/3.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 16.08/3.28 % ------ Proving...
% 16.08/3.28 % ------ Problem Properties
% 16.08/3.28
% 16.08/3.28 %
% 16.08/3.28 % clauses 19
% 16.08/3.28 % conjectures 2
% 16.08/3.28 % EPR 4
% 16.08/3.28 % Horn 14
% 16.08/3.28 % unary 2
% 16.08/3.28 % binary 10
% 16.08/3.28 % lits 59
% 16.08/3.28 % lits eq 4
% 16.08/3.28 % fd_pure 0
% 16.08/3.28 % fd_pseudo 0
% 16.08/3.28 % fd_cond 0
% 16.08/3.28 % fd_pseudo_cond 3
% 16.08/3.28 % AC symbols 0
% 16.08/3.28
% 16.08/3.28 % ------ Schedule dynamic 5 is on
% 16.08/3.28
% 16.08/3.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 16.08/3.28
% 16.08/3.28
% 16.08/3.28 % ------
% 16.08/3.28 % Current options:
% 16.08/3.28 % ------
% 16.08/3.28
% 16.08/3.28
% 16.08/3.28 %
% 16.08/3.28
% 16.08/3.28 % ------ Proving...
% 16.08/3.28 %
% 16.08/3.28
% 16.08/3.28 % SZS status Theorem for theBenchmark.p
% 16.08/3.28
% 16.08/3.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 16.08/3.29
% 16.08/3.29
%------------------------------------------------------------------------------