%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET689+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 : n012.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 2.11s 26.00s
% Output : CNFRefutation 2.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 40 ( 12 unt; 0 def)
% Number of atoms : 105 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 109 ( 44 ~; 37 |; 21 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 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] :
( ( subset(X2,X0)
& subset(X1,X2)
& subset(X0,X1) )
=> equal_set(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI05) ).
fof(f13,negated_conjecture,
~ ! [X0,X1,X2] :
( ( subset(X2,X0)
& subset(X1,X2)
& subset(X0,X1) )
=> equal_set(X0,X2) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( ( subset(X1,X0)
& subset(X0,X1) )
=> equal_set(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f15,plain,
? [X0,X1,X2] :
( subset(X2,X0)
& subset(X1,X2)
& subset(X0,X1)
& ~ equal_set(X0,X2) ),
inference(ennf_transformation,[],[f13]) ).
fof(f16,plain,
? [X0,X1,X2] :
( subset(X2,X0)
& subset(X1,X2)
& subset(X0,X1)
& ~ equal_set(X0,X2) ),
inference(flattening,[],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f18,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f19,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(flattening,[],[f18]) ).
fof(f20,plain,
( subset(sK2,sK0)
& subset(sK1,sK2)
& 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)],[f16]) ).
fof(f21,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,[],[f17]) ).
fof(f22,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,[],[f21]) ).
fof(f23,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))],[f22]) ).
fof(f24,plain,
subset(sK2,sK0),
inference(cnf_transformation,[],[f20]) ).
fof(f25,plain,
subset(sK1,sK2),
inference(cnf_transformation,[],[f20]) ).
fof(f26,plain,
subset(sK0,sK1),
inference(cnf_transformation,[],[f20]) ).
fof(f27,plain,
~ equal_set(sK0,sK2),
inference(cnf_transformation,[],[f20]) ).
fof(f28,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f29,plain,
! [X0,X1] :
( member(sK3(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f30,plain,
! [X0,X1] :
( ~ member(sK3(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f31,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
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_51,negated_conjecture,
subset(sK1,sK2),
inference(cnf_transformation,[],[f25]) ).
tcf(c_52,negated_conjecture,
subset(sK2,sK0),
inference(cnf_transformation,[],[f24]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK3(X0,X1),X1) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK3(X0,X1),X0) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_88,plain,
( ~ subset(sK2,sK0)
| ~ subset(sK0,sK2) ),
inference(resolution,[status(thm)],[c_49,c_56]) ).
tcf(c_89,plain,
~ subset(sK0,sK2),
inference(global_subsumption_just,[status(thm)],[c_88,c_52,c_88]) ).
tcf(c_139,plain,
member(sK3(sK0,sK2),sK0),
inference(resolution,[status(thm)],[c_54,c_89]) ).
tcf(c_143,plain,
~ member(sK3(sK0,sK2),sK2),
inference(resolution,[status(thm)],[c_53,c_89]) ).
tcf(c_248,plain,
! [X0: $i] :
( member(sK3(sK0,sK2),X0)
| ~ subset(sK0,X0)
| ~ member(sK3(sK0,sK2),sK0) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_249,plain,
! [X0: $i,X1: $i] :
( member(sK3(sK0,sK2),X1)
| ~ subset(X0,X1)
| ~ member(sK3(sK0,sK2),X0) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_252,plain,
! [X0: $i] :
( member(sK3(sK0,sK2),sK2)
| ~ subset(X0,sK2)
| ~ member(sK3(sK0,sK2),X0) ),
inference(instantiation,[status(thm)],[c_249]) ).
tcf(c_253,plain,
( member(sK3(sK0,sK2),sK2)
| ~ subset(sK1,sK2)
| ~ member(sK3(sK0,sK2),sK1) ),
inference(instantiation,[status(thm)],[c_252]) ).
tcf(c_256,plain,
( member(sK3(sK0,sK2),sK1)
| ~ subset(sK0,sK1)
| ~ member(sK3(sK0,sK2),sK0) ),
inference(instantiation,[status(thm)],[c_248]) ).
tcf(c_257,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_256,c_253,c_143,c_139,c_50,c_51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET689+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/25.34 % Computer : n012.cluster.edu
% 0.03/25.34 % Model : x86_64 x86_64
% 0.03/25.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/25.34 % Memory : 8046.5625MB
% 0.03/25.34 % OS : Linux 6.8.0-71-generic
% 0.03/25.34 % CPULimit : 300
% 0.03/25.34 % WCLimit : 300
% 0.03/25.34 % DateTime : Thu Sep 24 11:40:43 UTC 2026
% 0.03/25.34 % CPUTime :
% 0.03/25.34 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/25.36 Running first-order theorem proving
% 0.03/25.36 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
% 0.03/25.36
% 0.03/25.36 % ======== iProver multi-core TPTP/SMT =========
% 0.03/25.36
% 0.03/25.36 % Detected problem language: tptp
% 0.03/25.37 % Proving...
% 2.11/26.00 % SZS status Started for theBenchmark.p
% 2.11/26.00 % SZS status Theorem for theBenchmark.p
% 2.11/26.00
% 2.11/26.00 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.11/26.00
% 2.11/26.00 % ------ iProver source info
% 2.11/26.00
% 2.11/26.00 % git: date: 2026-07-19 20:42:38 +0200
% 2.11/26.00 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.11/26.00 % git: non_committed_changes: false
% 2.11/26.00
% 2.11/26.00 % ------ Parsing...
% 2.11/26.00 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.11/26.00
% 2.11/26.00 % ------ 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 %
% 2.11/26.00
% 2.11/26.00 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.11/26.00 % ------ Proving...
% 2.11/26.00 % ------ Problem Properties
% 2.11/26.00
% 2.11/26.00 %
% 2.11/26.00 % clauses 7
% 2.11/26.00 % conjectures 3
% 2.11/26.00 % EPR 5
% 2.11/26.00 % Horn 6
% 2.11/26.00 % unary 4
% 2.11/26.00 % binary 2
% 2.11/26.00 % lits 11
% 2.11/26.00 % lits eq 0
% 2.11/26.00 % fd_pure 0
% 2.11/26.00 % fd_pseudo 0
% 2.11/26.00 % fd_cond 0
% 2.11/26.00 % fd_pseudo_cond 0
% 2.11/26.00 % AC symbols 0
% 2.11/26.00
% 2.11/26.00 % ------ Schedule dynamic 5 is on
% 2.11/26.00
% 2.11/26.00 % ------ no equalities: superposition off
% 2.11/26.00
% 2.11/26.00 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.11/26.00
% 2.11/26.00
% 2.11/26.00 % ------
% 2.11/26.00 % Current options:
% 2.11/26.00 % ------
% 2.11/26.00
% 2.11/26.00
% 2.11/26.00 %
% 2.11/26.00
% 2.11/26.00 % ------ Proving...
% 2.11/26.00 %
% 2.11/26.00
% 2.11/26.00 % SZS status Theorem for theBenchmark.p
% 2.11/26.00
% 2.11/26.00 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.11/26.00
% 2.11/26.00
%------------------------------------------------------------------------------