%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET755+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 : n009.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 3.58s 1.17s
% Output : CNFRefutation 3.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 41 ( 7 unt; 0 def)
% Number of atoms : 127 ( 4 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 141 ( 55 ~; 49 |; 31 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 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 : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 96 ( 0 sgn 81 !; 15 ?; 24 :)
% 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(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,X4] :
( ( subset(X3,X4)
& subset(X4,X2)
& subset(X3,X2)
& maps(X0,X1,X2) )
=> subset(inverse_image2(X0,X3),inverse_image2(X0,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIIa05) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( ( subset(X3,X4)
& subset(X4,X2)
& subset(X3,X2)
& maps(X0,X1,X2) )
=> subset(inverse_image2(X0,X3),inverse_image2(X0,X4)) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f33,plain,
? [X0,X1,X2,X3,X4] :
( subset(X3,X4)
& subset(X4,X2)
& subset(X3,X2)
& maps(X0,X1,X2)
& ~ subset(inverse_image2(X0,X3),inverse_image2(X0,X4)) ),
inference(ennf_transformation,[],[f30]) ).
fof(f34,plain,
? [X0,X1,X2,X3,X4] :
( subset(X3,X4)
& subset(X4,X2)
& subset(X3,X2)
& maps(X0,X1,X2)
& ~ subset(inverse_image2(X0,X3),inverse_image2(X0,X4)) ),
inference(flattening,[],[f33]) ).
fof(f35,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f38,plain,
( subset(sK3,sK4)
& subset(sK4,sK2)
& subset(sK3,sK2)
& maps(sK0,sK1,sK2)
& ~ subset(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)) ),
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(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(sK5(X0,X1),X0)
& ~ member(sK5(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f40]) ).
fof(f43,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(f44,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,[],[f43]) ).
fof(f45,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))],[f44]) ).
fof(f46,plain,
subset(sK3,sK4),
inference(cnf_transformation,[],[f38]) ).
fof(f50,plain,
~ subset(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),
inference(cnf_transformation,[],[f38]) ).
fof(f51,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f52,plain,
! [X0,X1] :
( member(sK5(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f53,plain,
! [X0,X1] :
( ~ member(sK5(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f57,plain,
! [X2,X0,X1] :
( ~ member(X2,inverse_image2(X0,X1))
| apply(X0,X2,sK7(X0,X1,X2)) ),
inference(cnf_transformation,[],[f45]) ).
fof(f58,plain,
! [X2,X0,X1] :
( ~ member(X2,inverse_image2(X0,X1))
| member(sK7(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f45]) ).
fof(f59,plain,
! [X2,X3,X0,X1] :
( ~ apply(X0,X2,X3)
| ~ member(X3,X1)
| member(X2,inverse_image2(X0,X1)) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_49,negated_conjecture,
~ subset(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),
inference(cnf_transformation,[],[f50]) ).
tcf(c_53,negated_conjecture,
subset(sK3,sK4),
inference(cnf_transformation,[],[f46]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK5(X0,X1),X1) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK5(X0,X1),X0) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_60,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,[],[f59]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(sK7(X1,X2,X0),X2)
| ~ member(X0,inverse_image2(X1,X2)) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] :
( apply(X1,X0,sK7(X1,X2,X0))
| ~ member(X0,inverse_image2(X1,X2)) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_287,plain,
! [X0: $i,X1: $i] :
( member(sK5(X0,X1),X0)
| ( inverse_image2(sK0,sK4) != X1 )
| ( inverse_image2(sK0,sK3) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_55]) ).
tcf(c_288,plain,
member(sK5(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,sK3)),
inference(unflattening,[status(thm)],[c_287]) ).
tcf(c_292,plain,
! [X0: $i,X1: $i] :
( ~ member(sK5(X0,X1),X1)
| ( inverse_image2(sK0,sK4) != X1 )
| ( inverse_image2(sK0,sK3) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_54]) ).
tcf(c_293,plain,
~ member(sK5(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,sK4)),
inference(unflattening,[status(thm)],[c_292]) ).
tcf(c_1012,plain,
( apply(sK0,sK5(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),sK7(sK0,sK3,sK5(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))))
| ~ member(sK5(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,sK3)) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_1013,plain,
( member(sK7(sK0,sK3,sK5(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))),sK3)
| ~ member(sK5(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,sK3)) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_1211,plain,
! [X0: $i] :
( member(sK7(sK0,sK3,sK5(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))),X0)
| ~ subset(sK3,X0)
| ~ member(sK7(sK0,sK3,sK5(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))),sK3) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_1640,plain,
( member(sK7(sK0,sK3,sK5(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))),sK4)
| ~ subset(sK3,sK4)
| ~ member(sK7(sK0,sK3,sK5(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))),sK3) ),
inference(instantiation,[status(thm)],[c_1211]) ).
tcf(c_2497,plain,
! [X0: $i,X1: $i] :
( member(X1,inverse_image2(X0,sK4))
| ~ member(sK7(sK0,sK3,sK5(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))),sK4)
| ~ apply(X0,X1,sK7(sK0,sK3,sK5(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)))) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_4062,plain,
( member(sK5(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,sK4))
| ~ member(sK7(sK0,sK3,sK5(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))),sK4)
| ~ apply(sK0,sK5(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),sK7(sK0,sK3,sK5(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)))) ),
inference(instantiation,[status(thm)],[c_2497]) ).
tcf(c_4063,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_4062,c_1640,c_1012,c_1013,c_293,c_288,c_53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET755+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n009.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 11:52:16 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.41 % Detected problem language: tptp
% 0.10/0.42 % Proving...
% 3.58/1.17 % SZS status Started for theBenchmark.p
% 3.58/1.17 % SZS status Theorem for theBenchmark.p
% 3.58/1.17
% 3.58/1.17 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.58/1.17
% 3.58/1.17 % ------ iProver source info
% 3.58/1.17
% 3.58/1.17 % git: date: 2026-07-19 20:42:38 +0200
% 3.58/1.17 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.58/1.17 % git: non_committed_changes: false
% 3.58/1.17
% 3.58/1.17 % ------ Parsing...
% 3.58/1.17 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.58/1.17
% 3.58/1.17 % ------ 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 %
% 3.58/1.17
% 3.58/1.17 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.58/1.17
% 3.58/1.17 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.58/1.17 % ------ Proving...
% 3.58/1.17 % ------ Problem Properties
% 3.58/1.17
% 3.58/1.17 %
% 3.58/1.17 % clauses 13
% 3.58/1.17 % conjectures 4
% 3.58/1.17 % EPR 5
% 3.58/1.17 % Horn 12
% 3.58/1.17 % unary 4
% 3.58/1.17 % binary 6
% 3.58/1.17 % lits 28
% 3.58/1.17 % lits eq 1
% 3.58/1.17 % fd_pure 0
% 3.58/1.17 % fd_pseudo 0
% 3.58/1.17 % fd_cond 0
% 3.58/1.17 % fd_pseudo_cond 1
% 3.58/1.17 % AC symbols 0
% 3.58/1.17
% 3.58/1.17 % ------ Schedule dynamic 5 is on
% 3.58/1.17
% 3.58/1.17 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.58/1.17
% 3.58/1.17
% 3.58/1.17 % ------
% 3.58/1.17 % Current options:
% 3.58/1.17 % ------
% 3.58/1.17
% 3.58/1.17
% 3.58/1.17 %
% 3.58/1.17
% 3.58/1.17 % ------ Proving...
% 3.58/1.17 %
% 3.58/1.17
% 3.58/1.17 % SZS status Theorem for theBenchmark.p
% 3.58/1.17
% 3.58/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.58/1.17
%------------------------------------------------------------------------------