%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET688+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n010.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 02:47:48 PM UTC 2026
% Result : Theorem 3.80s 21.54s
% Output : CNFRefutation 3.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 41 ( 13 unt; 0 def)
% Number of atoms : 115 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 129 ( 55 ~; 39 |; 29 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 59 ( 0 sgn 51 !; 8 ?; 13 :)
% 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(f12,conjecture,
! [X0,X1,X2] :
( ( ~ equal_set(X1,X2)
& subset(X1,X2)
& ~ equal_set(X0,X1)
& subset(X0,X1) )
=> ~ equal_set(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI04) ).
fof(f13,negated_conjecture,
~ ! [X0,X1,X2] :
( ( ~ equal_set(X1,X2)
& subset(X1,X2)
& ~ equal_set(X0,X1)
& subset(X0,X1) )
=> ~ equal_set(X0,X2) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
? [X0,X1,X2] :
( ~ equal_set(X1,X2)
& subset(X1,X2)
& ~ equal_set(X0,X1)
& subset(X0,X1)
& equal_set(X0,X2) ),
inference(ennf_transformation,[],[f13]) ).
fof(f15,plain,
? [X0,X1,X2] :
( ~ equal_set(X1,X2)
& subset(X1,X2)
& ~ equal_set(X0,X1)
& subset(X0,X1)
& equal_set(X0,X2) ),
inference(flattening,[],[f14]) ).
fof(f16,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f17,plain,
( ~ equal_set(sK1,sK2)
& subset(sK1,sK2)
& ~ equal_set(sK0,sK1)
& subset(sK0,sK1)
& equal_set(sK0,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f15]) ).
fof(f18,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,[],[f16]) ).
fof(f19,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,[],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ( member(sK3(X0,X1),X0)
& ~ member(sK3(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ( ~ equal_set(X0,X1)
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f22,plain,
! [X0,X1] :
( ( ~ equal_set(X0,X1)
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ) ),
inference(flattening,[],[f21]) ).
fof(f23,plain,
~ equal_set(sK1,sK2),
inference(cnf_transformation,[],[f17]) ).
fof(f24,plain,
subset(sK1,sK2),
inference(cnf_transformation,[],[f17]) ).
fof(f26,plain,
subset(sK0,sK1),
inference(cnf_transformation,[],[f17]) ).
fof(f27,plain,
equal_set(sK0,sK2),
inference(cnf_transformation,[],[f17]) ).
fof(f28,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f29,plain,
! [X0,X1] :
( member(sK3(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f30,plain,
! [X0,X1] :
( ~ member(sK3(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f31,plain,
! [X0,X1] :
( ~ equal_set(X0,X1)
| subset(X1,X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f33,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_49,negated_conjecture,
equal_set(sK0,sK2),
inference(cnf_transformation,[],[f27]) ).
tcf(c_50,negated_conjecture,
subset(sK0,sK1),
inference(cnf_transformation,[],[f26]) ).
tcf(c_52,negated_conjecture,
subset(sK1,sK2),
inference(cnf_transformation,[],[f24]) ).
tcf(c_53,negated_conjecture,
~ equal_set(sK1,sK2),
inference(cnf_transformation,[],[f23]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK3(X0,X1),X1) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK3(X0,X1),X0) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| ~ equal_set(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_104,plain,
subset(sK2,sK0),
inference(resolution,[status(thm)],[c_49,c_59]) ).
tcf(c_118,plain,
( ~ subset(sK1,sK2)
| ~ subset(sK2,sK1) ),
inference(resolution,[status(thm)],[c_53,c_57]) ).
tcf(c_119,plain,
~ subset(sK2,sK1),
inference(global_subsumption_just,[status(thm)],[c_118,c_52,c_118]) ).
tcf(c_188,plain,
member(sK3(sK2,sK1),sK2),
inference(resolution,[status(thm)],[c_55,c_119]) ).
tcf(c_192,plain,
~ member(sK3(sK2,sK1),sK1),
inference(resolution,[status(thm)],[c_54,c_119]) ).
tcf(c_327,plain,
! [X0: $i] :
( member(sK3(sK2,sK1),X0)
| ~ subset(sK2,X0)
| ~ member(sK3(sK2,sK1),sK2) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_332,plain,
( member(sK3(sK2,sK1),sK0)
| ~ subset(sK2,sK0)
| ~ member(sK3(sK2,sK1),sK2) ),
inference(instantiation,[status(thm)],[c_327]) ).
tcf(c_333,plain,
! [X0: $i] :
( member(sK3(sK2,sK1),X0)
| ~ subset(sK0,X0)
| ~ member(sK3(sK2,sK1),sK0) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_334,plain,
( member(sK3(sK2,sK1),sK1)
| ~ subset(sK0,sK1)
| ~ member(sK3(sK2,sK1),sK0) ),
inference(instantiation,[status(thm)],[c_333]) ).
tcf(c_335,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_334,c_332,c_192,c_188,c_104,c_50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET688+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/20.62 % Computer : n010.cluster.edu
% 0.11/20.62 % Model : x86_64 x86_64
% 0.11/20.62 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/20.62 % Memory : 8046.5625MB
% 0.11/20.62 % OS : Linux 6.8.0-71-generic
% 0.11/20.62 % CPULimit : 300
% 0.11/20.62 % WCLimit : 300
% 0.11/20.62 % DateTime : Thu Sep 24 11:41:12 UTC 2026
% 0.11/20.62 % CPUTime :
% 0.11/20.62 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/20.66 Running first-order theorem proving
% 0.11/20.66 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
% 0.11/20.67
% 0.11/20.67 % ======== iProver multi-core TPTP/SMT =========
% 0.11/20.67
% 0.11/20.67 % Detected problem language: tptp
% 0.11/20.68 % Proving...
% 3.80/21.54 % SZS status Started for theBenchmark.p
% 3.80/21.54 % SZS status Theorem for theBenchmark.p
% 3.80/21.54
% 3.80/21.54 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.80/21.54
% 3.80/21.54 % ------ iProver source info
% 3.80/21.54
% 3.80/21.54 % git: date: 2026-07-19 20:42:38 +0200
% 3.80/21.54 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.80/21.54 % git: non_committed_changes: false
% 3.80/21.54
% 3.80/21.54 % ------ Parsing...
% 3.80/21.54 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.80/21.54
% 3.80/21.54 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.80/21.54
% 3.80/21.54 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.80/21.54 % ------ Proving...
% 3.80/21.54 % ------ Problem Properties
% 3.80/21.54
% 3.80/21.54 %
% 3.80/21.54 % clauses 9
% 3.80/21.54 % conjectures 2
% 3.80/21.54 % EPR 7
% 3.80/21.54 % Horn 8
% 3.80/21.54 % unary 6
% 3.80/21.54 % binary 2
% 3.80/21.54 % lits 13
% 3.80/21.54 % lits eq 0
% 3.80/21.54 % fd_pure 0
% 3.80/21.54 % fd_pseudo 0
% 3.80/21.54 % fd_cond 0
% 3.80/21.54 % fd_pseudo_cond 0
% 3.80/21.54 % AC symbols 0
% 3.80/21.54
% 3.80/21.54 % ------ Schedule dynamic 5 is on
% 3.80/21.54
% 3.80/21.54 % ------ no equalities: superposition off
% 3.80/21.54
% 3.80/21.54 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.80/21.54
% 3.80/21.54
% 3.80/21.54 % ------
% 3.80/21.54 % Current options:
% 3.80/21.54 % ------
% 3.80/21.54
% 3.80/21.54
% 3.80/21.54 %
% 3.80/21.54
% 3.80/21.54 % ------ Proving...
% 3.80/21.54 %
% 3.80/21.54
% 3.80/21.54 % SZS status Theorem for theBenchmark.p
% 3.80/21.54
% 3.80/21.54 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.80/21.54
% 3.80/21.54
%------------------------------------------------------------------------------