%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET162+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 : n018.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 02:46:48 PM UTC 2026
% Result : Theorem 3.94s 1.28s
% Output : CNFRefutation 3.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 42 ( 11 unt; 0 def)
% Number of atoms : 107 ( 2 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 115 ( 50 ~; 47 |; 12 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 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 : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 67 ( 0 sgn 64 !; 3 ?; 16 :)
% 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(f6,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',empty_set) ).
fof(f12,conjecture,
! [X0] : equal_set(union(X0,empty_set),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI18) ).
fof(f13,negated_conjecture,
~ ! [X0] : equal_set(union(X0,empty_set),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] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f16,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f17,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(flattening,[],[f16]) ).
fof(f19,plain,
? [X0] : ~ equal_set(union(X0,empty_set),X0),
inference(ennf_transformation,[],[f13]) ).
fof(f20,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,[],[f15]) ).
fof(f21,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,[],[f20]) ).
fof(f22,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))],[f21]) ).
fof(f26,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(f27,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,[],[f26]) ).
fof(f39,plain,
~ equal_set(union(sK3,empty_set),sK3),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X0,sK3)],[f19]) ).
fof(f41,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f42,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f43,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f49,plain,
! [X2,X0,X1] :
( ~ member(X0,union(X1,X2))
| member(X0,X2)
| member(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f51,plain,
! [X2,X0,X1] :
( ~ member(X0,X1)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f27]) ).
fof(f52,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f6]) ).
fof(f67,plain,
~ equal_set(union(sK3,empty_set),sK3),
inference(cnf_transformation,[],[f39]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_61,plain,
! [X0: $i] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f52]) ).
tcf(c_76,negated_conjecture,
~ equal_set(union(sK3,empty_set),sK3),
inference(cnf_transformation,[],[f67]) ).
tcf(c_422,plain,
! [X0: $i,X1: $i] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| ( X1 != sK3 )
| ( union(sK3,empty_set) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_76]) ).
tcf(c_423,plain,
( ~ subset(sK3,union(sK3,empty_set))
| ~ subset(union(sK3,empty_set),sK3) ),
inference(unflattening,[status(thm)],[c_422]) ).
tcf(c_1431,plain,
( subset(union(sK3,empty_set),sK3)
| ~ member(sK0(union(sK3,empty_set),sK3),sK3) ),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_1432,plain,
( subset(union(sK3,empty_set),sK3)
| member(sK0(union(sK3,empty_set),sK3),union(sK3,empty_set)) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_1874,plain,
( subset(sK3,union(sK3,empty_set))
| member(sK0(sK3,union(sK3,empty_set)),sK3) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_1875,plain,
( subset(sK3,union(sK3,empty_set))
| ~ member(sK0(sK3,union(sK3,empty_set)),union(sK3,empty_set)) ),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_1954,plain,
! [X0: $i] :
( member(sK0(sK3,union(sK3,empty_set)),union(sK3,X0))
| ~ member(sK0(sK3,union(sK3,empty_set)),sK3) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_1955,plain,
( member(sK0(sK3,union(sK3,empty_set)),union(sK3,empty_set))
| ~ member(sK0(sK3,union(sK3,empty_set)),sK3) ),
inference(instantiation,[status(thm)],[c_1954]) ).
tcf(c_2135,plain,
( member(sK0(union(sK3,empty_set),sK3),sK3)
| member(sK0(union(sK3,empty_set),sK3),empty_set)
| ~ member(sK0(union(sK3,empty_set),sK3),union(sK3,empty_set)) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_9087,plain,
~ member(sK0(union(sK3,empty_set),sK3),empty_set),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_9088,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_9087,c_2135,c_1955,c_1874,c_1875,c_1432,c_1431,c_423]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET162+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n018.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 10:07:33 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 3.94/1.28 % SZS status Started for theBenchmark.p
% 3.94/1.28 % SZS status Theorem for theBenchmark.p
% 3.94/1.28
% 3.94/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.94/1.28
% 3.94/1.28 % ------ iProver source info
% 3.94/1.28
% 3.94/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 3.94/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.94/1.28 % git: non_committed_changes: false
% 3.94/1.28
% 3.94/1.28 % ------ Parsing...
% 3.94/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.94/1.28
% 3.94/1.28 % ------ 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 %
% 3.94/1.28
% 3.94/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.94/1.28
% 3.94/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.94/1.28 % ------ Proving...
% 3.94/1.28 % ------ Problem Properties
% 3.94/1.28
% 3.94/1.28 %
% 3.94/1.28 % clauses 27
% 3.94/1.28 % conjectures 0
% 3.94/1.28 % EPR 2
% 3.94/1.28 % Horn 22
% 3.94/1.28 % unary 4
% 3.94/1.28 % binary 16
% 3.94/1.28 % lits 57
% 3.94/1.28 % lits eq 3
% 3.94/1.28 % fd_pure 0
% 3.94/1.28 % fd_pseudo 0
% 3.94/1.28 % fd_cond 0
% 3.94/1.28 % fd_pseudo_cond 2
% 3.94/1.28 % AC symbols 0
% 3.94/1.28
% 3.94/1.28 % ------ Schedule dynamic 5 is on
% 3.94/1.28
% 3.94/1.28 % ------ no conjectures: strip conj schedule
% 3.94/1.28
% 3.94/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 3.94/1.28
% 3.94/1.28
% 3.94/1.28 % ------
% 3.94/1.28 % Current options:
% 3.94/1.28 % ------
% 3.94/1.28
% 3.94/1.28
% 3.94/1.28 %
% 3.94/1.28
% 3.94/1.28 % ------ Proving...
% 3.94/1.28 %
% 3.94/1.28
% 3.94/1.28 % SZS status Theorem for theBenchmark.p
% 3.94/1.28
% 3.94/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.94/1.28
% 3.94/1.28
%------------------------------------------------------------------------------