%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET622+3 : 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 : n015.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 02:47:36 PM UTC 2026
% Result : Theorem 3.03s 1.28s
% Output : CNFRefutation 3.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 27 ( 27 unt; 0 def)
% Number of atoms : 27 ( 26 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 53 ( 0 sgn 50 !; 3 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] : intersection(intersection(X0,X1),X2) = intersection(X0,intersection(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_intersection) ).
fof(f2,axiom,
! [X0,X1,X2] : difference(X0,difference(X1,X2)) = union(difference(X0,X1),intersection(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_difference_union2) ).
fof(f3,axiom,
! [X0,X1] : symmetric_difference(X0,X1) = difference(union(X0,X1),intersection(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetric_difference_and_difference) ).
fof(f9,axiom,
! [X0,X1] : union(X0,X1) = union(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(f10,axiom,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(f15,conjecture,
! [X0,X1,X2] : difference(X0,symmetric_difference(X1,X2)) = union(difference(X0,union(X1,X2)),intersection(intersection(X0,X1),X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th98) ).
fof(f16,negated_conjecture,
~ ! [X0,X1,X2] : difference(X0,symmetric_difference(X1,X2)) = union(difference(X0,union(X1,X2)),intersection(intersection(X0,X1),X2)),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f17,plain,
? [X0,X1,X2] : difference(X0,symmetric_difference(X1,X2)) != union(difference(X0,union(X1,X2)),intersection(intersection(X0,X1),X2)),
inference(ennf_transformation,[],[f16]) ).
fof(f18,plain,
difference(sK0,symmetric_difference(sK1,sK2)) != union(difference(sK0,union(sK1,sK2)),intersection(intersection(sK0,sK1),sK2)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f17]) ).
fof(f28,plain,
difference(sK0,symmetric_difference(sK1,sK2)) != union(difference(sK0,union(sK1,sK2)),intersection(intersection(sK0,sK1),sK2)),
inference(cnf_transformation,[],[f18]) ).
fof(f29,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f10]) ).
fof(f33,plain,
! [X0,X1] : symmetric_difference(X0,X1) = difference(union(X0,X1),intersection(X0,X1)),
inference(cnf_transformation,[],[f3]) ).
fof(f34,plain,
! [X2,X0,X1] : difference(X0,difference(X1,X2)) = union(difference(X0,X1),intersection(X0,X2)),
inference(cnf_transformation,[],[f2]) ).
fof(f35,plain,
! [X2,X0,X1] : intersection(intersection(X0,X1),X2) = intersection(X0,intersection(X1,X2)),
inference(cnf_transformation,[],[f1]) ).
fof(f40,plain,
! [X0,X1] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f9]) ).
fof(f49,plain,
union(difference(sK0,union(sK1,sK2)),intersection(intersection(sK0,sK1),sK2)) != difference(sK0,difference(union(sK1,sK2),intersection(sK1,sK2))),
inference(definition_unfolding,[],[f28,f33]) ).
tcf(c_49,negated_conjecture,
union(difference(sK0,union(sK1,sK2)),intersection(intersection(sK0,sK1),sK2)) != difference(sK0,difference(union(sK1,sK2),intersection(sK1,sK2))),
inference(cnf_transformation,[],[f49]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f29]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] : union(difference(X0,X1),intersection(X0,X2)) = difference(X0,difference(X1,X2)),
inference(cnf_transformation,[],[f34]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] : intersection(intersection(X0,X1),X2) = intersection(X0,intersection(X1,X2)),
inference(cnf_transformation,[],[f35]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f40]) ).
tcf(c_81,negated_conjecture,
union(difference(sK0,union(sK1,sK2)),intersection(sK1,intersection(sK2,sK0))) != difference(sK0,difference(union(sK1,sK2),intersection(sK1,sK2))),
inference(theory_normalisation,[status(thm)],[c_49,c_55,c_50]) ).
tcf(c_202,plain,
union(intersection(sK1,intersection(sK2,sK0)),difference(sK0,union(sK1,sK2))) != difference(sK0,difference(union(sK1,sK2),intersection(sK1,sK2))),
inference(demodulation,[status(thm)],[c_81,c_60]) ).
tcf(c_829,plain,
! [X0: $i,X1: $i,X2: $i] : union(difference(X0,X1),intersection(X2,X0)) = difference(X0,difference(X1,X2)),
inference(superposition,[status(thm)],[c_50,c_54]) ).
tcf(c_1388,plain,
! [X0: $i,X1: $i,X2: $i] : union(intersection(X0,X1),difference(X1,X2)) = difference(X1,difference(X2,X0)),
inference(superposition,[status(thm)],[c_829,c_60]) ).
tcf(c_1564,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : union(intersection(X0,intersection(X1,X2)),difference(X2,X3)) = difference(X2,difference(X3,intersection(X0,X1))),
inference(superposition,[status(thm)],[c_55,c_1388]) ).
tcf(c_1572,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_202,c_1564]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET622+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n015.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 11:32:25 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 3.03/1.28 % SZS status Started for theBenchmark.p
% 3.03/1.28 % SZS status Theorem for theBenchmark.p
% 3.03/1.28
% 3.03/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.03/1.28
% 3.03/1.28 % ------ iProver source info
% 3.03/1.28
% 3.03/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 3.03/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.03/1.28 % git: non_committed_changes: false
% 3.03/1.28
% 3.03/1.28 % ------ Parsing...
% 3.03/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.03/1.28
% 3.03/1.28 % ------ Preprocessing... sup_sim: 2 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.03/1.28
% 3.03/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.03/1.28
% 3.03/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.03/1.28 % ------ Proving...
% 3.03/1.28 % ------ Problem Properties
% 3.03/1.28
% 3.03/1.28 %
% 3.03/1.28 % clauses 17
% 3.03/1.28 % conjectures 0
% 3.03/1.28 % EPR 0
% 3.03/1.28 % Horn 14
% 3.03/1.28 % unary 6
% 3.03/1.28 % binary 6
% 3.03/1.28 % lits 33
% 3.03/1.28 % lits eq 8
% 3.03/1.28 % fd_pure 0
% 3.03/1.28 % fd_pseudo 0
% 3.03/1.28 % fd_cond 0
% 3.03/1.28 % fd_pseudo_cond 2
% 3.03/1.28 % AC symbols 1
% 3.03/1.28
% 3.03/1.28 % ------ Schedule dynamic 5 is on
% 3.03/1.28
% 3.03/1.28 % ------ no conjectures: strip conj schedule
% 3.03/1.28
% 3.03/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 3.03/1.28
% 3.03/1.28
% 3.03/1.28 % ------
% 3.03/1.28 % Current options:
% 3.03/1.28 % ------
% 3.03/1.28
% 3.03/1.28
% 3.03/1.28 %
% 3.03/1.28
% 3.03/1.28 % ------ Proving...
% 3.03/1.28 %
% 3.03/1.28
% 3.03/1.28 % SZS status Theorem for theBenchmark.p
% 3.03/1.28
% 3.03/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.03/1.28
% 3.03/1.28
%------------------------------------------------------------------------------