%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET762+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/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 02:48:31 PM UTC 2026
% Result : Theorem 4.37s 1.52s
% Output : CNFRefutation 4.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 10 unt; 0 def)
% Number of atoms : 97 ( 2 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 108 ( 47 ~; 36 |; 17 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 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; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 76 ( 0 sgn 68 !; 8 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',subset) ).
fof(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',equal_set) ).
fof(f6,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',empty_set) ).
fof(f22,axiom,
! [X0,X1,X2] :
( member(X2,image2(X0,X1))
<=> ? [X3] :
( apply(X0,X3,X2)
& member(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',image2) ).
fof(f29,conjecture,
! [X0,X1,X2] :
( maps(X0,X1,X2)
=> equal_set(image2(X0,empty_set),empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIIa12) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2] :
( maps(X0,X1,X2)
=> equal_set(image2(X0,empty_set),empty_set) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f33,plain,
! [X0,X1] :
( ( subset(X1,X0)
& subset(X0,X1) )
=> equal_set(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f34,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f35,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(ennf_transformation,[],[f33]) ).
fof(f36,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(flattening,[],[f35]) ).
fof(f44,plain,
? [X0,X1,X2] :
( maps(X0,X1,X2)
& ~ equal_set(image2(X0,empty_set),empty_set) ),
inference(ennf_transformation,[],[f30]) ).
fof(f45,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,[],[f34]) ).
fof(f46,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,[],[f45]) ).
fof(f47,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ( member(sK0(X0,X1),X0)
& ~ member(sK0(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f46]) ).
fof(f69,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(f70,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,[],[f69]) ).
fof(f71,plain,
! [X0,X1,X2] :
( ( ~ member(X2,image2(X0,X1))
| ( apply(X0,sK5(X0,X1,X2),X2)
& member(sK5(X0,X1,X2),X1) ) )
& ( ! [X3] :
( ~ apply(X0,X3,X2)
| ~ member(X3,X1) )
| member(X2,image2(X0,X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X4,sK5(X0,X1,X2))],[f70]) ).
fof(f83,plain,
( maps(sK9,sK10,sK11)
& ~ equal_set(image2(sK9,empty_set),empty_set) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11]),skolemize(X0,sK9),skolemize(X1,sK10),skolemize(X2,sK11)],[f44]) ).
fof(f85,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f87,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f96,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f6]) ).
fof(f121,plain,
! [X2,X0,X1] :
( ~ member(X2,image2(X0,X1))
| member(sK5(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f135,plain,
~ equal_set(image2(sK9,empty_set),empty_set),
inference(cnf_transformation,[],[f83]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f87]) ).
tcf(c_61,plain,
! [X0: $i] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f96]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(sK5(X1,X2,X0),X2)
| ~ member(X0,image2(X1,X2)) ),
inference(cnf_transformation,[],[f121]) ).
tcf(c_99,negated_conjecture,
~ equal_set(image2(sK9,empty_set),empty_set),
inference(cnf_transformation,[],[f135]) ).
tcf(c_839,plain,
! [X0: $i,X1: $i] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| ( X1 != empty_set )
| ( image2(sK9,empty_set) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_99]) ).
tcf(c_840,plain,
( ~ subset(empty_set,image2(sK9,empty_set))
| ~ subset(image2(sK9,empty_set),empty_set) ),
inference(unflattening,[status(thm)],[c_839]) ).
tcf(c_994,plain,
( ~ subset(empty_set,image2(sK9,empty_set))
| ~ subset(image2(sK9,empty_set),empty_set) ),
inference(prop_impl_just,[status(thm)],[c_840]) ).
tcf(c_2639,plain,
! [X0: $i] : subset(empty_set,X0),
inference(superposition,[status(thm)],[c_50,c_61]) ).
tcf(c_2645,plain,
~ subset(image2(sK9,empty_set),empty_set),
inference(forward_subsumption_resolution,[status(thm)],[c_994,c_2639]) ).
tcf(c_3258,plain,
! [X0: $i,X1: $i] : ~ member(X0,image2(X1,empty_set)),
inference(superposition,[status(thm)],[c_86,c_61]) ).
tcf(c_3340,plain,
! [X0: $i,X1: $i] : subset(image2(X0,empty_set),X1),
inference(superposition,[status(thm)],[c_50,c_3258]) ).
tcf(c_3344,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_2645,c_3340]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET762+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/0.43 % Computer : n008.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Thu Sep 24 11:53:55 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/0.50 Running first-order theorem proving
% 0.16/0.50 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.27/0.52
% 0.27/0.52 % ======== iProver multi-core TPTP/SMT =========
% 0.27/0.52
% 0.27/0.52 % Detected problem language: tptp
% 0.27/0.54 % Proving...
% 4.37/1.52 % SZS status Started for theBenchmark.p
% 4.37/1.52 % SZS status Theorem for theBenchmark.p
% 4.37/1.52
% 4.37/1.52 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.37/1.52
% 4.37/1.52 % ------ iProver source info
% 4.37/1.52
% 4.37/1.52 % git: date: 2026-07-19 20:42:38 +0200
% 4.37/1.52 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.37/1.52 % git: non_committed_changes: false
% 4.37/1.52
% 4.37/1.52 % ------ Parsing...
% 4.37/1.52 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.37/1.52
% 4.37/1.52 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 4.37/1.52
% 4.37/1.52 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.37/1.52
% 4.37/1.52 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.37/1.52 % ------ Proving...
% 4.37/1.52 % ------ Problem Properties
% 4.37/1.52
% 4.37/1.52 %
% 4.37/1.52 % clauses 50
% 4.37/1.52 % conjectures 0
% 4.37/1.52 % EPR 3
% 4.37/1.52 % Horn 45
% 4.37/1.52 % unary 4
% 4.37/1.52 % binary 28
% 4.37/1.52 % lits 127
% 4.37/1.52 % lits eq 4
% 4.37/1.52 % fd_pure 0
% 4.37/1.52 % fd_pseudo 0
% 4.37/1.52 % fd_cond 0
% 4.37/1.52 % fd_pseudo_cond 3
% 4.37/1.52 % AC symbols 0
% 4.37/1.52
% 4.37/1.52 % ------ Schedule dynamic 5 is on
% 4.37/1.52
% 4.37/1.52 % ------ no conjectures: strip conj schedule
% 4.37/1.52
% 4.37/1.52 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 4.37/1.52
% 4.37/1.52
% 4.37/1.52 % ------
% 4.37/1.52 % Current options:
% 4.37/1.52 % ------
% 4.37/1.52
% 4.37/1.52
% 4.37/1.52 %
% 4.37/1.52
% 4.37/1.52 % ------ Proving...
% 4.37/1.52 %
% 4.37/1.52
% 4.37/1.52 % SZS status Theorem for theBenchmark.p
% 4.37/1.52
% 4.37/1.52 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.37/1.52
% 4.37/1.52
%------------------------------------------------------------------------------