%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET753+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 : n014.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 1.29s 1.29s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 50 ( 5 unt; 0 def)
% Number of atoms : 153 ( 4 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 174 ( 71 ~; 65 |; 31 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 5 ( 2 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 : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 120 ( 0 sgn 105 !; 15 ?; 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(f4,axiom,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
<=> ( member(X0,X2)
& member(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',intersection) ).
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(f29,conjecture,
! [X0,X1,X2,X3,X4] :
( ( subset(X4,X1)
& subset(X3,X1)
& maps(X0,X1,X2) )
=> subset(image2(X0,intersection(X3,X4)),intersection(image2(X0,X3),image2(X0,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIIa03) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( ( subset(X4,X1)
& subset(X3,X1)
& maps(X0,X1,X2) )
=> subset(image2(X0,intersection(X3,X4)),intersection(image2(X0,X3),image2(X0,X4))) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f33,plain,
? [X0,X1,X2,X3,X4] :
( subset(X4,X1)
& subset(X3,X1)
& maps(X0,X1,X2)
& ~ subset(image2(X0,intersection(X3,X4)),intersection(image2(X0,X3),image2(X0,X4))) ),
inference(ennf_transformation,[],[f30]) ).
fof(f34,plain,
? [X0,X1,X2,X3,X4] :
( subset(X4,X1)
& subset(X3,X1)
& maps(X0,X1,X2)
& ~ subset(image2(X0,intersection(X3,X4)),intersection(image2(X0,X3),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(sK4,sK1)
& subset(sK3,sK1)
& maps(sK0,sK1,sK2)
& ~ subset(image2(sK0,intersection(sK3,sK4)),intersection(image2(sK0,sK3),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(f42,plain,
! [X0,X1,X2] :
( ( ~ member(X0,intersection(X1,X2))
| ( member(X0,X2)
& member(X0,X1) ) )
& ( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,intersection(X1,X2)) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ( ~ member(X0,intersection(X1,X2))
| ( member(X0,X2)
& member(X0,X1) ) )
& ( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,intersection(X1,X2)) ) ),
inference(flattening,[],[f42]) ).
fof(f45,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(f46,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,[],[f45]) ).
fof(f47,plain,
! [X0,X1,X2] :
( ( ~ member(X2,image2(X0,X1))
| ( apply(X0,sK7(X0,X1,X2),X2)
& member(sK7(X0,X1,X2),X1) ) )
& ( ! [X3] :
( ~ apply(X0,X3,X2)
| ~ member(X3,X1) )
| member(X2,image2(X0,X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X4,sK7(X0,X1,X2))],[f46]) ).
fof(f51,plain,
~ subset(image2(sK0,intersection(sK3,sK4)),intersection(image2(sK0,sK3),image2(sK0,sK4))),
inference(cnf_transformation,[],[f38]) ).
fof(f53,plain,
! [X0,X1] :
( member(sK5(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f54,plain,
! [X0,X1] :
( ~ member(sK5(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f55,plain,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[],[f43]) ).
fof(f56,plain,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
fof(f57,plain,
! [X2,X0,X1] :
( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f43]) ).
fof(f61,plain,
! [X2,X0,X1] :
( ~ member(X2,image2(X0,X1))
| apply(X0,sK7(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f47]) ).
fof(f62,plain,
! [X2,X0,X1] :
( ~ member(X2,image2(X0,X1))
| member(sK7(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f63,plain,
! [X2,X3,X0,X1] :
( ~ apply(X0,X3,X2)
| ~ member(X3,X1)
| member(X2,image2(X0,X1)) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_49,negated_conjecture,
~ subset(image2(sK0,intersection(sK3,sK4)),intersection(image2(sK0,sK3),image2(sK0,sK4))),
inference(cnf_transformation,[],[f51]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK5(X0,X1),X1) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK5(X0,X1),X0) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X2,image2(X0,X3))
| ~ member(X1,X3)
| ~ apply(X0,X1,X2) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(sK7(X1,X2,X0),X2)
| ~ member(X0,image2(X1,X2)) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( apply(X1,sK7(X1,X2,X0),X0)
| ~ member(X0,image2(X1,X2)) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_311,plain,
! [X0: $i,X1: $i] :
( member(sK5(X1,X0),X1)
| ( image2(sK0,intersection(sK3,sK4)) != X1 )
| ( intersection(image2(sK0,sK3),image2(sK0,sK4)) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_54]) ).
tcf(c_312,plain,
member(sK5(image2(sK0,intersection(sK3,sK4)),intersection(image2(sK0,sK3),image2(sK0,sK4))),image2(sK0,intersection(sK3,sK4))),
inference(unflattening,[status(thm)],[c_311]) ).
tcf(c_316,plain,
! [X0: $i,X1: $i] :
( ~ member(sK5(X1,X0),X0)
| ( image2(sK0,intersection(sK3,sK4)) != X1 )
| ( intersection(image2(sK0,sK3),image2(sK0,sK4)) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_53]) ).
tcf(c_317,plain,
~ member(sK5(image2(sK0,intersection(sK3,sK4)),intersection(image2(sK0,sK3),image2(sK0,sK4))),intersection(image2(sK0,sK3),image2(sK0,sK4))),
inference(unflattening,[status(thm)],[c_316]) ).
tcf(c_1064,plain,
( apply(sK0,sK7(sK0,intersection(sK3,sK4),sK5(image2(sK0,intersection(sK3,sK4)),intersection(image2(sK0,sK3),image2(sK0,sK4)))),sK5(image2(sK0,intersection(sK3,sK4)),intersection(image2(sK0,sK3),image2(sK0,sK4))))
| ~ member(sK5(image2(sK0,intersection(sK3,sK4)),intersection(image2(sK0,sK3),image2(sK0,sK4))),image2(sK0,intersection(sK3,sK4))) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_1065,plain,
( member(sK7(sK0,intersection(sK3,sK4),sK5(image2(sK0,intersection(sK3,sK4)),intersection(image2(sK0,sK3),image2(sK0,sK4)))),intersection(sK3,sK4))
| ~ member(sK5(image2(sK0,intersection(sK3,sK4)),intersection(image2(sK0,sK3),image2(sK0,sK4))),image2(sK0,intersection(sK3,sK4))) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_1281,plain,
( member(sK7(sK0,intersection(sK3,sK4),sK5(image2(sK0,intersection(sK3,sK4)),intersection(image2(sK0,sK3),image2(sK0,sK4)))),sK4)
| ~ member(sK7(sK0,intersection(sK3,sK4),sK5(image2(sK0,intersection(sK3,sK4)),intersection(image2(sK0,sK3),image2(sK0,sK4)))),intersection(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_1282,plain,
( member(sK7(sK0,intersection(sK3,sK4),sK5(image2(sK0,intersection(sK3,sK4)),intersection(image2(sK0,sK3),image2(sK0,sK4)))),sK3)
| ~ member(sK7(sK0,intersection(sK3,sK4),sK5(image2(sK0,intersection(sK3,sK4)),intersection(image2(sK0,sK3),image2(sK0,sK4)))),intersection(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_1806,plain,
! [X0: $i,X1: $i] :
( member(X1,image2(X0,sK4))
| ~ member(sK7(sK0,intersection(sK3,sK4),sK5(image2(sK0,intersection(sK3,sK4)),intersection(image2(sK0,sK3),image2(sK0,sK4)))),sK4)
| ~ apply(X0,sK7(sK0,intersection(sK3,sK4),sK5(image2(sK0,intersection(sK3,sK4)),intersection(image2(sK0,sK3),image2(sK0,sK4)))),X1) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_1885,plain,
! [X0: $i,X1: $i] :
( member(X1,image2(X0,sK3))
| ~ member(sK7(sK0,intersection(sK3,sK4),sK5(image2(sK0,intersection(sK3,sK4)),intersection(image2(sK0,sK3),image2(sK0,sK4)))),sK3)
| ~ apply(X0,sK7(sK0,intersection(sK3,sK4),sK5(image2(sK0,intersection(sK3,sK4)),intersection(image2(sK0,sK3),image2(sK0,sK4)))),X1) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_2104,plain,
! [X0: $i,X1: $i] :
( member(sK5(image2(sK0,intersection(sK3,sK4)),intersection(image2(sK0,sK3),image2(sK0,sK4))),intersection(X0,X1))
| ~ member(sK5(image2(sK0,intersection(sK3,sK4)),intersection(image2(sK0,sK3),image2(sK0,sK4))),X1)
| ~ member(sK5(image2(sK0,intersection(sK3,sK4)),intersection(image2(sK0,sK3),image2(sK0,sK4))),X0) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_4616,plain,
( member(sK5(image2(sK0,intersection(sK3,sK4)),intersection(image2(sK0,sK3),image2(sK0,sK4))),intersection(image2(sK0,sK3),image2(sK0,sK4)))
| ~ member(sK5(image2(sK0,intersection(sK3,sK4)),intersection(image2(sK0,sK3),image2(sK0,sK4))),image2(sK0,sK4))
| ~ member(sK5(image2(sK0,intersection(sK3,sK4)),intersection(image2(sK0,sK3),image2(sK0,sK4))),image2(sK0,sK3)) ),
inference(instantiation,[status(thm)],[c_2104]) ).
tcf(c_4783,plain,
( member(sK5(image2(sK0,intersection(sK3,sK4)),intersection(image2(sK0,sK3),image2(sK0,sK4))),image2(sK0,sK4))
| ~ member(sK7(sK0,intersection(sK3,sK4),sK5(image2(sK0,intersection(sK3,sK4)),intersection(image2(sK0,sK3),image2(sK0,sK4)))),sK4)
| ~ apply(sK0,sK7(sK0,intersection(sK3,sK4),sK5(image2(sK0,intersection(sK3,sK4)),intersection(image2(sK0,sK3),image2(sK0,sK4)))),sK5(image2(sK0,intersection(sK3,sK4)),intersection(image2(sK0,sK3),image2(sK0,sK4)))) ),
inference(instantiation,[status(thm)],[c_1806]) ).
tcf(c_4792,plain,
( member(sK5(image2(sK0,intersection(sK3,sK4)),intersection(image2(sK0,sK3),image2(sK0,sK4))),image2(sK0,sK3))
| ~ member(sK7(sK0,intersection(sK3,sK4),sK5(image2(sK0,intersection(sK3,sK4)),intersection(image2(sK0,sK3),image2(sK0,sK4)))),sK3)
| ~ apply(sK0,sK7(sK0,intersection(sK3,sK4),sK5(image2(sK0,intersection(sK3,sK4)),intersection(image2(sK0,sK3),image2(sK0,sK4)))),sK5(image2(sK0,intersection(sK3,sK4)),intersection(image2(sK0,sK3),image2(sK0,sK4)))) ),
inference(instantiation,[status(thm)],[c_1885]) ).
tcf(c_4793,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_4792,c_4783,c_4616,c_1281,c_1282,c_1064,c_1065,c_317,c_312]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET753+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 11:51:18 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 0.09/0.41
% 0.09/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.41
% 0.09/0.41 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 1.29/1.29 % SZS status Started for theBenchmark.p
% 1.29/1.29 % SZS status Theorem for theBenchmark.p
% 1.29/1.29
% 1.29/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.29/1.29
% 1.29/1.29 % ------ iProver source info
% 1.29/1.29
% 1.29/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 1.29/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.29/1.29 % git: non_committed_changes: false
% 1.29/1.29
% 1.29/1.29 % ------ Parsing...
% 1.29/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.29/1.29
% 1.29/1.29 % ------ 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 %
% 1.29/1.29
% 1.29/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.29/1.29
% 1.29/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.29/1.29 % ------ Proving...
% 1.29/1.29 % ------ Problem Properties
% 1.29/1.29
% 1.29/1.29 %
% 1.29/1.29 % clauses 15
% 1.29/1.29 % conjectures 3
% 1.29/1.29 % EPR 4
% 1.29/1.29 % Horn 14
% 1.29/1.29 % unary 3
% 1.29/1.29 % binary 8
% 1.29/1.29 % lits 34
% 1.29/1.29 % lits eq 1
% 1.29/1.29 % fd_pure 0
% 1.29/1.29 % fd_pseudo 0
% 1.29/1.29 % fd_cond 0
% 1.29/1.29 % fd_pseudo_cond 1
% 1.29/1.29 % AC symbols 0
% 1.29/1.29
% 1.29/1.29 % ------ Schedule dynamic 5 is on
% 1.29/1.29
% 1.29/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.29/1.29
% 1.29/1.29
% 1.29/1.29 % ------
% 1.29/1.29 % Current options:
% 1.29/1.29 % ------
% 1.29/1.29
% 1.29/1.29
% 1.29/1.29 %
% 1.29/1.29
% 1.29/1.29 % ------ Proving...
% 1.29/1.29 %
% 1.29/1.29
% 1.29/1.29 % SZS status Theorem for theBenchmark.p
% 1.29/1.29
% 1.29/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.29/1.29
% 1.29/1.29
%------------------------------------------------------------------------------