%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET015+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 : n016.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 02:46:03 PM UTC 2026
% Result : Theorem 4.28s 1.50s
% Output : CNFRefutation 4.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 45 ( 7 unt; 0 def)
% Number of atoms : 106 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 104 ( 43 ~; 46 |; 8 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 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; 2 con; 0-2 aty)
% Number of variables : 68 ( 0 sgn 65 !; 3 ?; 19 :)
% 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(f5,axiom,
! [X0,X1,X2] :
( member(X0,union(X1,X2))
<=> ( member(X0,X2)
| member(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',union) ).
fof(f12,conjecture,
! [X0,X1] : equal_set(union(X0,X1),union(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI07) ).
fof(f13,negated_conjecture,
~ ! [X0,X1] : equal_set(union(X0,X1),union(X1,X0)),
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] :
( member(X2,X0)
=> member(X2,X1) )
=> subset(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f16,plain,
? [X0,X1] : ~ equal_set(union(X0,X1),union(X1,X0)),
inference(ennf_transformation,[],[f13]) ).
fof(f17,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f18,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(flattening,[],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f20,plain,
~ equal_set(union(sK0,sK1),union(sK1,sK0)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f16]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( ~ member(X0,union(X1,X2))
| member(X0,X2)
| member(X0,X1) )
& ( ( ~ member(X0,X2)
& ~ member(X0,X1) )
| member(X0,union(X1,X2)) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( ~ member(X0,union(X1,X2))
| member(X0,X2)
| member(X0,X1) )
& ( ( ~ member(X0,X2)
& ~ member(X0,X1) )
| member(X0,union(X1,X2)) ) ),
inference(flattening,[],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( ( member(sK2(X0,X1),X0)
& ~ member(sK2(X0,X1),X1) )
| subset(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f19]) ).
fof(f24,plain,
~ equal_set(union(sK0,sK1),union(sK1,sK0)),
inference(cnf_transformation,[],[f20]) ).
fof(f25,plain,
! [X2,X0,X1] :
( ~ member(X0,union(X1,X2))
| member(X0,X2)
| member(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f26,plain,
! [X2,X0,X1] :
( ~ member(X0,X2)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f22]) ).
fof(f27,plain,
! [X2,X0,X1] :
( ~ member(X0,X1)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f22]) ).
fof(f28,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f29,plain,
! [X0,X1] :
( member(sK2(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f30,plain,
! [X0,X1] :
( ~ member(sK2(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_49,negated_conjecture,
~ equal_set(union(sK0,sK1),union(sK1,sK0)),
inference(cnf_transformation,[],[f24]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,union(X2,X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_91,plain,
( ~ subset(union(sK1,sK0),union(sK0,sK1))
| ~ subset(union(sK0,sK1),union(sK1,sK0)) ),
inference(resolution,[status(thm)],[c_49,c_53]) ).
tcf(c_126,plain,
( subset(union(sK0,sK1),union(sK1,sK0))
| ~ member(sK2(union(sK0,sK1),union(sK1,sK0)),union(sK1,sK0)) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_127,plain,
( subset(union(sK0,sK1),union(sK1,sK0))
| member(sK2(union(sK0,sK1),union(sK1,sK0)),union(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_128,plain,
( subset(union(sK1,sK0),union(sK0,sK1))
| member(sK2(union(sK1,sK0),union(sK0,sK1)),union(sK1,sK0)) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_129,plain,
( subset(union(sK1,sK0),union(sK0,sK1))
| ~ member(sK2(union(sK1,sK0),union(sK0,sK1)),union(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_134,plain,
( member(sK2(union(sK1,sK0),union(sK0,sK1)),sK1)
| member(sK2(union(sK1,sK0),union(sK0,sK1)),sK0)
| ~ member(sK2(union(sK1,sK0),union(sK0,sK1)),union(sK1,sK0)) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_141,plain,
( member(sK2(union(sK0,sK1),union(sK1,sK0)),sK1)
| member(sK2(union(sK0,sK1),union(sK1,sK0)),sK0)
| ~ member(sK2(union(sK0,sK1),union(sK1,sK0)),union(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_143,plain,
! [X0: $i] :
( member(sK2(union(sK1,sK0),union(sK0,sK1)),union(sK0,X0))
| ~ member(sK2(union(sK1,sK0),union(sK0,sK1)),sK0) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_168,plain,
( member(sK2(union(sK1,sK0),union(sK0,sK1)),union(sK0,sK1))
| ~ member(sK2(union(sK1,sK0),union(sK0,sK1)),sK0) ),
inference(instantiation,[status(thm)],[c_143]) ).
tcf(c_232,plain,
! [X0: $i] :
( member(sK2(union(sK0,sK1),union(sK1,sK0)),union(X0,sK0))
| ~ member(sK2(union(sK0,sK1),union(sK1,sK0)),sK0) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_253,plain,
( member(sK2(union(sK0,sK1),union(sK1,sK0)),union(sK1,sK0))
| ~ member(sK2(union(sK0,sK1),union(sK1,sK0)),sK0) ),
inference(instantiation,[status(thm)],[c_232]) ).
tcf(c_344,plain,
! [X0: $i] :
( member(sK2(union(sK1,sK0),union(sK0,sK1)),union(X0,sK1))
| ~ member(sK2(union(sK1,sK0),union(sK0,sK1)),sK1) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_347,plain,
( member(sK2(union(sK1,sK0),union(sK0,sK1)),union(sK0,sK1))
| ~ member(sK2(union(sK1,sK0),union(sK0,sK1)),sK1) ),
inference(instantiation,[status(thm)],[c_344]) ).
tcf(c_391,plain,
! [X0: $i] :
( member(sK2(union(sK0,sK1),union(sK1,sK0)),union(sK1,X0))
| ~ member(sK2(union(sK0,sK1),union(sK1,sK0)),sK1) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_392,plain,
( member(sK2(union(sK0,sK1),union(sK1,sK0)),union(sK1,sK0))
| ~ member(sK2(union(sK0,sK1),union(sK1,sK0)),sK1) ),
inference(instantiation,[status(thm)],[c_391]) ).
tcf(c_782,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_392,c_347,c_253,c_168,c_141,c_134,c_128,c_129,c_127,c_126,c_91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET015+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.58 % Computer : n016.cluster.edu
% 0.10/0.58 % Model : x86_64 x86_64
% 0.10/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.58 % Memory : 8046.5625MB
% 0.10/0.58 % OS : Linux 6.8.0-71-generic
% 0.10/0.58 % CPULimit : 300
% 0.10/0.58 % WCLimit : 300
% 0.10/0.58 % DateTime : Thu Sep 24 09:13:43 UTC 2026
% 0.10/0.59 % CPUTime :
% 0.10/0.59 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.63 Running first-order theorem proving
% 0.10/0.63 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
% 0.15/0.64
% 0.15/0.64 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.64
% 0.15/0.64 % Detected problem language: tptp
% 0.15/0.65 % Proving...
% 4.28/1.50 % SZS status Started for theBenchmark.p
% 4.28/1.50 % SZS status Theorem for theBenchmark.p
% 4.28/1.50
% 4.28/1.50 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.28/1.50
% 4.28/1.50 % ------ iProver source info
% 4.28/1.50
% 4.28/1.50 % git: date: 2026-07-19 20:42:38 +0200
% 4.28/1.50 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.28/1.50 % git: non_committed_changes: false
% 4.28/1.50
% 4.28/1.50 % ------ Parsing...
% 4.28/1.50 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.28/1.50
% 4.28/1.50 % ------ 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 %
% 4.28/1.50
% 4.28/1.50 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 4.28/1.50 % ------ Proving...
% 4.28/1.50 % ------ Problem Properties
% 4.28/1.50
% 4.28/1.50 %
% 4.28/1.50 % clauses 6
% 4.28/1.50 % conjectures 0
% 4.28/1.50 % EPR 0
% 4.28/1.50 % Horn 4
% 4.28/1.50 % unary 0
% 4.28/1.50 % binary 5
% 4.28/1.50 % lits 13
% 4.28/1.50 % lits eq 0
% 4.28/1.50 % fd_pure 0
% 4.28/1.50 % fd_pseudo 0
% 4.28/1.50 % fd_cond 0
% 4.28/1.50 % fd_pseudo_cond 0
% 4.28/1.50 % AC symbols 0
% 4.28/1.50
% 4.28/1.50 % ------ Schedule dynamic 5 is on
% 4.28/1.50
% 4.28/1.50 % ------ no conjectures: strip conj schedule
% 4.28/1.50
% 4.28/1.50 % ------ no equalities: superposition off
% 4.28/1.50
% 4.28/1.50 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 4.28/1.50
% 4.28/1.50
% 4.28/1.50 % ------
% 4.28/1.50 % Current options:
% 4.28/1.50 % ------
% 4.28/1.50
% 4.28/1.50
% 4.28/1.50 %
% 4.28/1.50
% 4.28/1.50 % ------ Proving...
% 4.28/1.50 %
% 4.28/1.50
% 4.28/1.50 % SZS status Theorem for theBenchmark.p
% 4.28/1.50
% 4.28/1.50 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.28/1.50
% 4.28/1.50
%------------------------------------------------------------------------------