%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET012-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n003.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 02:46:00 PM UTC 2026
% Result : Unsatisfiable 2.56s 1.06s
% Output : CNFRefutation 2.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 56 ( 15 unt; 0 def)
% Number of atoms : 104 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 91 ( 43 ~; 48 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 63 ( 0 sgn 63 !; 0 ?; 46 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X2,X0,X1] :
( member(X0,X2)
| ~ subset(X1,X2)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET002-0.ax',membership_in_subsets) ).
fof(f3,axiom,
! [X0,X1] :
( member(member_of_1_not_of_2(X0,X1),X0)
| subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET002-0.ax',subsets_axiom1) ).
fof(f4,axiom,
! [X0,X1] :
( subset(X0,X1)
| ~ member(member_of_1_not_of_2(X0,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET002-0.ax',subsets_axiom2) ).
fof(f5,axiom,
! [X0,X1] :
( member(X0,complement(X1))
| member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET002-0.ax',member_of_set_or_complement) ).
fof(f6,axiom,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET002-0.ax',not_member_of_set_and_complement) ).
fof(f14,axiom,
! [X0,X1] :
( subset(X1,X0)
| ~ equal_sets(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET002-0.ax',set_equal_sets_are_subsets2) ).
fof(f15,axiom,
! [X0,X1] :
( equal_sets(X1,X0)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET002-0.ax',subsets_are_set_equal_sets) ).
fof(f17,axiom,
! [X0,X1] :
( equal_sets(X1,X0)
| ~ equal_sets(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET002-0.ax',symmetry_for_set_equal) ).
fof(f22,axiom,
equal_sets(complement(a),b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_of_a_is_b) ).
fof(f23,axiom,
equal_sets(complement(b),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_of_b_is_c) ).
fof(f24,negated_conjecture,
~ equal_sets(a,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_equals_c) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ subset(X1,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(member_of_1_not_of_2(X0,X1),X0) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(member_of_1_not_of_2(X0,X1),X1) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| member(X0,complement(X1)) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| ~ equal_sets(X0,X1) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i] :
( equal_sets(X1,X0)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i] :
( equal_sets(X1,X0)
| ~ equal_sets(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_94,plain,
equal_sets(complement(a),b),
inference(cnf_transformation,[],[f22]) ).
tcf(c_95,plain,
equal_sets(complement(b),c),
inference(cnf_transformation,[],[f23]) ).
tcf(c_96,negated_conjecture,
~ equal_sets(a,c),
inference(cnf_transformation,[],[f24]) ).
tcf(c_437,plain,
! [X0_iProver_equal_sets_1: iProver_equal_sets_1,X1_iProver_equal_sets_1: iProver_equal_sets_1] :
( equal_sets(X1_iProver_equal_sets_1,X0_iProver_equal_sets_1)
| ~ equal_sets(X0_iProver_equal_sets_1,X1_iProver_equal_sets_1) ),
inference(subtyping,[status(esa)],[c_89]) ).
tcf(c_439,plain,
! [X0_iProver_equal_sets_1: iProver_equal_sets_1,X1_iProver_equal_sets_1: iProver_equal_sets_1] :
( equal_sets(X1_iProver_equal_sets_1,X0_iProver_equal_sets_1)
| ~ subset(X1_iProver_equal_sets_1,X0_iProver_equal_sets_1)
| ~ subset(X0_iProver_equal_sets_1,X1_iProver_equal_sets_1) ),
inference(subtyping,[status(esa)],[c_87]) ).
tcf(c_440,plain,
! [X0_iProver_equal_sets_1: iProver_equal_sets_1,X1_iProver_equal_sets_1: iProver_equal_sets_1] :
( subset(X1_iProver_equal_sets_1,X0_iProver_equal_sets_1)
| ~ equal_sets(X0_iProver_equal_sets_1,X1_iProver_equal_sets_1) ),
inference(subtyping,[status(esa)],[c_86]) ).
tcf(c_448,plain,
! [X0_iProver_equal_sets_1: iProver_equal_sets_1,X0_iProver_member_1: iProver_member_1] :
( ~ member(X0_iProver_member_1,X0_iProver_equal_sets_1)
| ~ member(X0_iProver_member_1,complement(X0_iProver_equal_sets_1)) ),
inference(subtyping,[status(esa)],[c_78]) ).
tcf(c_449,plain,
! [X0_iProver_equal_sets_1: iProver_equal_sets_1,X0_iProver_member_1: iProver_member_1] :
( member(X0_iProver_member_1,X0_iProver_equal_sets_1)
| member(X0_iProver_member_1,complement(X0_iProver_equal_sets_1)) ),
inference(subtyping,[status(esa)],[c_77]) ).
tcf(c_450,plain,
! [X0_iProver_equal_sets_1: iProver_equal_sets_1,X1_iProver_equal_sets_1: iProver_equal_sets_1] :
( subset(X0_iProver_equal_sets_1,X1_iProver_equal_sets_1)
| ~ member(member_of_1_not_of_2(X0_iProver_equal_sets_1,X1_iProver_equal_sets_1),X1_iProver_equal_sets_1) ),
inference(subtyping,[status(esa)],[c_76]) ).
tcf(c_451,plain,
! [X0_iProver_equal_sets_1: iProver_equal_sets_1,X1_iProver_equal_sets_1: iProver_equal_sets_1] :
( subset(X0_iProver_equal_sets_1,X1_iProver_equal_sets_1)
| member(member_of_1_not_of_2(X0_iProver_equal_sets_1,X1_iProver_equal_sets_1),X0_iProver_equal_sets_1) ),
inference(subtyping,[status(esa)],[c_75]) ).
tcf(c_452,plain,
! [X0_iProver_equal_sets_1: iProver_equal_sets_1,X0_iProver_member_1: iProver_member_1,X1_iProver_equal_sets_1: iProver_equal_sets_1] :
( member(X0_iProver_member_1,X1_iProver_equal_sets_1)
| ~ subset(X0_iProver_equal_sets_1,X1_iProver_equal_sets_1)
| ~ member(X0_iProver_member_1,X0_iProver_equal_sets_1) ),
inference(subtyping,[status(esa)],[c_74]) ).
tcf(c_455,plain,
equal_sets(complement(b),c),
inference(subtyping,[status(esa)],[c_95]) ).
tcf(c_456,plain,
equal_sets(complement(a),b),
inference(subtyping,[status(esa)],[c_94]) ).
tcf(c_517,plain,
( equal_sets(a,c)
| ~ subset(c,a)
| ~ subset(a,c) ),
inference(instantiation,[status(thm)],[c_439]) ).
tcf(c_551,plain,
( subset(c,a)
| ~ member(member_of_1_not_of_2(c,a),a) ),
inference(instantiation,[status(thm)],[c_450]) ).
tcf(c_559,plain,
equal_sets(b,complement(a)),
inference(superposition,[status(thm)],[c_456,c_437]) ).
tcf(c_560,plain,
equal_sets(c,complement(b)),
inference(superposition,[status(thm)],[c_455,c_437]) ).
tcf(c_579,plain,
subset(b,complement(a)),
inference(superposition,[status(thm)],[c_456,c_440]) ).
tcf(c_580,plain,
subset(c,complement(b)),
inference(superposition,[status(thm)],[c_455,c_440]) ).
tcf(c_582,plain,
subset(complement(a),b),
inference(superposition,[status(thm)],[c_559,c_440]) ).
tcf(c_583,plain,
subset(complement(b),c),
inference(superposition,[status(thm)],[c_560,c_440]) ).
tcf(c_702,plain,
( subset(a,c)
| member(member_of_1_not_of_2(a,c),a) ),
inference(instantiation,[status(thm)],[c_451]) ).
tcf(c_757,plain,
! [X0_iProver_member_1: iProver_member_1] :
( member(X0_iProver_member_1,complement(a))
| ~ member(X0_iProver_member_1,b) ),
inference(superposition,[status(thm)],[c_579,c_452]) ).
tcf(c_758,plain,
! [X0_iProver_member_1: iProver_member_1] :
( member(X0_iProver_member_1,complement(b))
| ~ member(X0_iProver_member_1,c) ),
inference(superposition,[status(thm)],[c_580,c_452]) ).
tcf(c_760,plain,
! [X0_iProver_member_1: iProver_member_1] :
( member(X0_iProver_member_1,b)
| ~ member(X0_iProver_member_1,complement(a)) ),
inference(superposition,[status(thm)],[c_582,c_452]) ).
tcf(c_761,plain,
! [X0_iProver_member_1: iProver_member_1] :
( member(X0_iProver_member_1,c)
| ~ member(X0_iProver_member_1,complement(b)) ),
inference(superposition,[status(thm)],[c_583,c_452]) ).
tcf(c_1354,plain,
! [X0_iProver_member_1: iProver_member_1] :
( member(X0_iProver_member_1,b)
| member(X0_iProver_member_1,a) ),
inference(superposition,[status(thm)],[c_449,c_760]) ).
tcf(c_1359,plain,
! [X0_iProver_member_1: iProver_member_1] :
( ~ member(X0_iProver_member_1,b)
| ~ member(X0_iProver_member_1,a) ),
inference(superposition,[status(thm)],[c_757,c_448]) ).
tcf(c_1360,plain,
! [X0_iProver_member_1: iProver_member_1] :
( ~ member(X0_iProver_member_1,c)
| ~ member(X0_iProver_member_1,b) ),
inference(superposition,[status(thm)],[c_758,c_448]) ).
tcf(c_1404,plain,
! [X0_iProver_member_1: iProver_member_1] :
( member(X0_iProver_member_1,c)
| member(X0_iProver_member_1,b) ),
inference(superposition,[status(thm)],[c_449,c_761]) ).
tcf(c_1407,plain,
! [X0_iProver_equal_sets_1: iProver_equal_sets_1] :
( subset(X0_iProver_equal_sets_1,c)
| member(member_of_1_not_of_2(X0_iProver_equal_sets_1,c),b) ),
inference(superposition,[status(thm)],[c_1404,c_450]) ).
tcf(c_1417,plain,
! [X0_iProver_member_1: iProver_member_1] :
( member(X0_iProver_member_1,a)
| ~ member(X0_iProver_member_1,c) ),
inference(superposition,[status(thm)],[c_1354,c_1360]) ).
tcf(c_1420,plain,
! [X0_iProver_equal_sets_1: iProver_equal_sets_1] :
( subset(c,X0_iProver_equal_sets_1)
| member(member_of_1_not_of_2(c,X0_iProver_equal_sets_1),a) ),
inference(superposition,[status(thm)],[c_451,c_1417]) ).
tcf(c_1422,plain,
( subset(c,a)
| member(member_of_1_not_of_2(c,a),a) ),
inference(instantiation,[status(thm)],[c_1420]) ).
tcf(c_1460,plain,
! [X0_iProver_equal_sets_1: iProver_equal_sets_1] :
( subset(X0_iProver_equal_sets_1,c)
| ~ member(member_of_1_not_of_2(X0_iProver_equal_sets_1,c),a) ),
inference(superposition,[status(thm)],[c_1407,c_1359]) ).
tcf(c_1461,plain,
( subset(a,c)
| ~ member(member_of_1_not_of_2(a,c),a) ),
inference(instantiation,[status(thm)],[c_1460]) ).
tcf(c_1643,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1461,c_1422,c_702,c_551,c_517,c_96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET012-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n003.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Thu Sep 24 09:07:21 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 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
% 0.12/0.40
% 0.12/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.40
% 0.12/0.40 % Detected problem language: tptp
% 0.12/0.42 % Proving...
% 2.56/1.06 % SZS status Started for theBenchmark.p
% 2.56/1.06 % SZS status Unsatisfiable for theBenchmark.p
% 2.56/1.06
% 2.56/1.06 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.56/1.06
% 2.56/1.06 % ------ iProver source info
% 2.56/1.06
% 2.56/1.06 % git: date: 2026-07-19 20:42:38 +0200
% 2.56/1.06 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.56/1.06 % git: non_committed_changes: false
% 2.56/1.06
% 2.56/1.06 % ------ Parsing...% successful
% 2.56/1.06
% 2.56/1.06
% 2.56/1.06 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.56/1.06
% 2.56/1.06 % ------ Preprocessing... sf_s rm: 3 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.56/1.06
% 2.56/1.06 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.56/1.06 % ------ Proving...
% 2.56/1.06 % ------ Problem Properties
% 2.56/1.06
% 2.56/1.06 %
% 2.56/1.06 % clauses 21
% 2.56/1.06 % conjectures 1
% 2.56/1.06 % EPR 9
% 2.56/1.06 % Horn 18
% 2.56/1.06 % unary 5
% 2.56/1.06 % binary 11
% 2.56/1.06 % lits 42
% 2.56/1.06 % lits eq 0
% 2.56/1.06 % fd_pure 0
% 2.56/1.06 % fd_pseudo 0
% 2.56/1.06 % fd_cond 0
% 2.56/1.06 % fd_pseudo_cond 0
% 2.56/1.06 % AC symbols 0
% 2.56/1.06
% 2.56/1.06 % ------ Input Options Time Limit: Unbounded
% 2.56/1.06
% 2.56/1.06
% 2.56/1.06 % ------
% 2.56/1.06 % Current options:
% 2.56/1.06 % ------
% 2.56/1.06
% 2.56/1.06
% 2.56/1.06 %
% 2.56/1.06
% 2.56/1.06 % ------ Proving...
% 2.56/1.06 %
% 2.56/1.06
% 2.56/1.06 % SZS status Unsatisfiable for theBenchmark.p
% 2.56/1.06
% 2.56/1.06 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.56/1.06
% 2.56/1.06
%------------------------------------------------------------------------------