%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET754+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 : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:48:12 PM UTC 2026
% Result : Theorem 1.23s 1.93s
% Output : CNFRefutation 1.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 56 ( 9 unt; 0 def)
% Number of atoms : 215 ( 13 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 256 ( 97 ~; 91 |; 49 &)
% ( 6 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 5 ( 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 : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 168 ( 0 sgn 147 !; 21 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',subset) ).
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(f22,axiom,
! [X0,X1,X2] :
( member(X2,image2(X0,X1))
<=> ? [X3] :
( apply(X0,X3,X2)
& member(X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax',image2) ).
fof(f24,axiom,
! [X0,X1,X2] :
( member(X2,inverse_image2(X0,X1))
<=> ? [X3] :
( apply(X0,X2,X3)
& member(X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax',inverse_image2) ).
fof(f29,conjecture,
! [X0,X1,X2,X3] :
( ( subset(X3,X1)
& maps(X0,X1,X2) )
=> subset(X3,inverse_image2(X0,image2(X0,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIIa04) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( subset(X3,X1)
& maps(X0,X1,X2) )
=> subset(X3,inverse_image2(X0,image2(X0,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] :
( subset(X3,X1)
& maps(X0,X1,X2)
& ~ subset(X3,inverse_image2(X0,image2(X0,X3))) ),
inference(ennf_transformation,[],[f30]) ).
fof(f34,plain,
? [X0,X1,X2,X3] :
( subset(X3,X1)
& maps(X0,X1,X2)
& ~ subset(X3,inverse_image2(X0,image2(X0,X3))) ),
inference(flattening,[],[f33]) ).
fof(f35,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
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,[],[f32]) ).
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,
( subset(sK3,sK1)
& maps(sK0,sK1,sK2)
& ~ subset(sK3,inverse_image2(sK0,image2(sK0,sK3))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f34]) ).
fof(f39,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) )
& ( ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ) ),
inference(nnf_transformation,[],[f35]) ).
fof(f40,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ) ),
inference(rectify,[],[f39]) ).
fof(f41,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ( member(sK4(X0,X1),X0)
& ~ member(sK4(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X2,sK4(X0,X1))],[f40]) ).
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))],[f37]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ( ~ member(X2,image2(X0,X1))
| ? [X3] :
( apply(X0,X3,X2)
& member(X3,X1) ) )
& ( ! [X3] :
( ~ apply(X0,X3,X2)
| ~ member(X3,X1) )
| member(X2,image2(X0,X1)) ) ),
inference(nnf_transformation,[],[f22]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ( ~ member(X2,image2(X0,X1))
| ? [X4] :
( apply(X0,X4,X2)
& member(X4,X1) ) )
& ( ! [X3] :
( ~ apply(X0,X3,X2)
| ~ member(X3,X1) )
| member(X2,image2(X0,X1)) ) ),
inference(rectify,[],[f43]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ( ~ member(X2,image2(X0,X1))
| ( apply(X0,sK6(X0,X1,X2),X2)
& member(sK6(X0,X1,X2),X1) ) )
& ( ! [X3] :
( ~ apply(X0,X3,X2)
| ~ member(X3,X1) )
| member(X2,image2(X0,X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X4,sK6(X0,X1,X2))],[f44]) ).
fof(f46,plain,
! [X0,X1,X2] :
( ( ~ member(X2,inverse_image2(X0,X1))
| ? [X3] :
( apply(X0,X2,X3)
& member(X3,X1) ) )
& ( ! [X3] :
( ~ apply(X0,X2,X3)
| ~ member(X3,X1) )
| member(X2,inverse_image2(X0,X1)) ) ),
inference(nnf_transformation,[],[f24]) ).
fof(f47,plain,
! [X0,X1,X2] :
( ( ~ member(X2,inverse_image2(X0,X1))
| ? [X4] :
( apply(X0,X2,X4)
& member(X4,X1) ) )
& ( ! [X3] :
( ~ apply(X0,X2,X3)
| ~ member(X3,X1) )
| member(X2,inverse_image2(X0,X1)) ) ),
inference(rectify,[],[f46]) ).
fof(f48,plain,
! [X0,X1,X2] :
( ( ~ member(X2,inverse_image2(X0,X1))
| ( apply(X0,X2,sK7(X0,X1,X2))
& member(sK7(X0,X1,X2),X1) ) )
& ( ! [X3] :
( ~ apply(X0,X2,X3)
| ~ member(X3,X1) )
| member(X2,inverse_image2(X0,X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X4,sK7(X0,X1,X2))],[f47]) ).
fof(f49,plain,
subset(sK3,sK1),
inference(cnf_transformation,[],[f38]) ).
fof(f50,plain,
maps(sK0,sK1,sK2),
inference(cnf_transformation,[],[f38]) ).
fof(f51,plain,
~ subset(sK3,inverse_image2(sK0,image2(sK0,sK3))),
inference(cnf_transformation,[],[f38]) ).
fof(f52,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f53,plain,
! [X0,X1] :
( member(sK4(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f54,plain,
! [X0,X1] :
( ~ member(sK4(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f56,plain,
! [X2,X3,X0,X1] :
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| apply(X0,X3,sK5(X0,X2,X3)) ),
inference(cnf_transformation,[],[f42]) ).
fof(f60,plain,
! [X2,X3,X0,X1] :
( ~ apply(X0,X3,X2)
| ~ member(X3,X1)
| member(X2,image2(X0,X1)) ),
inference(cnf_transformation,[],[f45]) ).
fof(f63,plain,
! [X2,X3,X0,X1] :
( ~ apply(X0,X2,X3)
| ~ member(X3,X1)
| member(X2,inverse_image2(X0,X1)) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_49,negated_conjecture,
~ subset(sK3,inverse_image2(sK0,image2(sK0,sK3))),
inference(cnf_transformation,[],[f51]) ).
tcf(c_50,negated_conjecture,
maps(sK0,sK1,sK2),
inference(cnf_transformation,[],[f50]) ).
tcf(c_51,negated_conjecture,
subset(sK3,sK1),
inference(cnf_transformation,[],[f49]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK4(X0,X1),X1) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK4(X0,X1),X0) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_56,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,[],[f56]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X2,image2(X0,X3))
| ~ member(X1,X3)
| ~ apply(X0,X1,X2) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X1,inverse_image2(X0,X3))
| ~ member(X2,X3)
| ~ apply(X0,X1,X2) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_253,plain,
! [X0: $i,X1: $i] :
( member(sK4(X1,X0),X1)
| ( X1 != sK3 )
| ( inverse_image2(sK0,image2(sK0,sK3)) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_53]) ).
tcf(c_254,plain,
member(sK4(sK3,inverse_image2(sK0,image2(sK0,sK3))),sK3),
inference(unflattening,[status(thm)],[c_253]) ).
tcf(c_258,plain,
! [X0: $i,X1: $i] :
( ~ member(sK4(X1,X0),X0)
| ( X1 != sK3 )
| ( inverse_image2(sK0,image2(sK0,sK3)) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_52]) ).
tcf(c_259,plain,
~ member(sK4(sK3,inverse_image2(sK0,image2(sK0,sK3))),inverse_image2(sK0,image2(sK0,sK3))),
inference(unflattening,[status(thm)],[c_258]) ).
tcf(c_305,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,X3,sK5(X0,X2,X3))
| ~ member(X3,X1)
| ( X2 != sK2 )
| ( X1 != sK1 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_56]) ).
tcf(c_306,plain,
! [X0: $i] :
( apply(sK0,X0,sK5(sK0,sK2,X0))
| ~ member(X0,sK1) ),
inference(unflattening,[status(thm)],[c_305]) ).
tcf(c_1050,plain,
! [X0: $i] :
( member(sK4(sK3,inverse_image2(sK0,image2(sK0,sK3))),X0)
| ~ subset(sK3,X0)
| ~ member(sK4(sK3,inverse_image2(sK0,image2(sK0,sK3))),sK3) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_1053,plain,
! [X0: $i,X1: $i] :
( member(X1,image2(X0,sK3))
| ~ member(sK4(sK3,inverse_image2(sK0,image2(sK0,sK3))),sK3)
| ~ apply(X0,sK4(sK3,inverse_image2(sK0,image2(sK0,sK3))),X1) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_1186,plain,
( member(sK4(sK3,inverse_image2(sK0,image2(sK0,sK3))),sK1)
| ~ subset(sK3,sK1)
| ~ member(sK4(sK3,inverse_image2(sK0,image2(sK0,sK3))),sK3) ),
inference(instantiation,[status(thm)],[c_1050]) ).
tcf(c_1365,plain,
( apply(sK0,sK4(sK3,inverse_image2(sK0,image2(sK0,sK3))),sK5(sK0,sK2,sK4(sK3,inverse_image2(sK0,image2(sK0,sK3)))))
| ~ member(sK4(sK3,inverse_image2(sK0,image2(sK0,sK3))),sK1) ),
inference(instantiation,[status(thm)],[c_306]) ).
tcf(c_1855,plain,
( member(sK5(sK0,sK2,sK4(sK3,inverse_image2(sK0,image2(sK0,sK3)))),image2(sK0,sK3))
| ~ member(sK4(sK3,inverse_image2(sK0,image2(sK0,sK3))),sK3)
| ~ apply(sK0,sK4(sK3,inverse_image2(sK0,image2(sK0,sK3))),sK5(sK0,sK2,sK4(sK3,inverse_image2(sK0,image2(sK0,sK3))))) ),
inference(instantiation,[status(thm)],[c_1053]) ).
tcf(c_2743,plain,
! [X0: $i,X1: $i] :
( member(X1,inverse_image2(X0,image2(sK0,sK3)))
| ~ apply(X0,X1,sK5(sK0,sK2,sK4(sK3,inverse_image2(sK0,image2(sK0,sK3)))))
| ~ member(sK5(sK0,sK2,sK4(sK3,inverse_image2(sK0,image2(sK0,sK3)))),image2(sK0,sK3)) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_5862,plain,
( member(sK4(sK3,inverse_image2(sK0,image2(sK0,sK3))),inverse_image2(sK0,image2(sK0,sK3)))
| ~ member(sK5(sK0,sK2,sK4(sK3,inverse_image2(sK0,image2(sK0,sK3)))),image2(sK0,sK3))
| ~ apply(sK0,sK4(sK3,inverse_image2(sK0,image2(sK0,sK3))),sK5(sK0,sK2,sK4(sK3,inverse_image2(sK0,image2(sK0,sK3))))) ),
inference(instantiation,[status(thm)],[c_2743]) ).
tcf(c_5863,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_5862,c_1855,c_1365,c_1186,c_259,c_254,c_51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET754+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.38 % Computer : n019.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Thu Sep 24 11:52:23 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.17/0.44 Running first-order theorem proving
% 0.17/0.44 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
% 0.17/0.46
% 0.17/0.46 % ======== iProver multi-core TPTP/SMT =========
% 0.17/0.46
% 0.17/0.46 % Detected problem language: tptp
% 0.17/0.48 % Proving...
% 1.23/1.93 % SZS status Started for theBenchmark.p
% 1.23/1.93 % SZS status Theorem for theBenchmark.p
% 1.23/1.93
% 1.23/1.93 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.23/1.93
% 1.23/1.93 % ------ iProver source info
% 1.23/1.93
% 1.23/1.93 % git: date: 2026-07-19 20:42:38 +0200
% 1.23/1.93 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.23/1.93 % git: non_committed_changes: false
% 1.23/1.93
% 1.23/1.93 % ------ Parsing...
% 1.23/1.93 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.23/1.93
% 1.23/1.93 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 1.23/1.93
% 1.23/1.93 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.23/1.93
% 1.23/1.93 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.23/1.93 % ------ Proving...
% 1.23/1.93 % ------ Problem Properties
% 1.23/1.93
% 1.23/1.93 %
% 1.23/1.93 % clauses 14
% 1.23/1.93 % conjectures 2
% 1.23/1.93 % EPR 3
% 1.23/1.93 % Horn 13
% 1.23/1.93 % unary 2
% 1.23/1.93 % binary 8
% 1.23/1.93 % lits 33
% 1.23/1.93 % lits eq 1
% 1.23/1.93 % fd_pure 0
% 1.23/1.93 % fd_pseudo 0
% 1.23/1.93 % fd_cond 0
% 1.23/1.93 % fd_pseudo_cond 1
% 1.23/1.93 % AC symbols 0
% 1.23/1.93
% 1.23/1.93 % ------ Schedule dynamic 5 is on
% 1.23/1.93
% 1.23/1.93 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.23/1.93
% 1.23/1.93
% 1.23/1.93 % ------
% 1.23/1.93 % Current options:
% 1.23/1.93 % ------
% 1.23/1.93
% 1.23/1.93
% 1.23/1.93 %
% 1.23/1.93
% 1.23/1.93 % ------ Proving...
% 1.23/1.93 %
% 1.23/1.93
% 1.23/1.93 % SZS status Theorem for theBenchmark.p
% 1.23/1.93
% 1.23/1.93 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.23/1.93
% 1.23/1.93
%------------------------------------------------------------------------------