%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET619+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 : n004.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 02:47:35 PM UTC 2026
% Result : Theorem 2.67s 1.18s
% Output : CNFRefutation 2.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 40 ( 40 unt; 3 def)
% Number of atoms : 54 ( 39 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 10 ( 10 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 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 : 5 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 49 ( 0 sgn 47 !; 2 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetric_difference_defn) ).
fof(f2,axiom,
! [X0,X1,X2] : union(union(X0,X1),X2) = union(X0,union(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_union) ).
fof(f3,axiom,
! [X0,X1] : union(X0,intersection(X0,X1)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_intersection) ).
fof(f4,axiom,
! [X0,X1] : union(intersection(X0,X1),difference(X0,X1)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_intersection_difference) ).
fof(f8,axiom,
! [X0,X1] : union(X0,X1) = union(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(f9,axiom,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(f14,conjecture,
! [X0,X1] : union(X0,X1) = union(symmetric_difference(X0,X1),intersection(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th95) ).
fof(f15,negated_conjecture,
~ ! [X0,X1] : union(X0,X1) = union(symmetric_difference(X0,X1),intersection(X0,X1)),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f17,plain,
? [X0,X1] : union(X0,X1) != union(symmetric_difference(X0,X1),intersection(X0,X1)),
inference(ennf_transformation,[],[f15]) ).
fof(f30,plain,
union(sK2,sK3) != union(symmetric_difference(sK2,sK3),intersection(sK2,sK3)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f17]) ).
fof(f31,plain,
! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
inference(cnf_transformation,[],[f1]) ).
fof(f32,plain,
! [X2,X0,X1] : union(union(X0,X1),X2) = union(X0,union(X1,X2)),
inference(cnf_transformation,[],[f2]) ).
fof(f33,plain,
! [X0,X1] : union(X0,intersection(X0,X1)) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f34,plain,
! [X0,X1] : union(intersection(X0,X1),difference(X0,X1)) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f44,plain,
! [X0,X1] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f8]) ).
fof(f45,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f9]) ).
fof(f55,plain,
union(sK2,sK3) != union(symmetric_difference(sK2,sK3),intersection(sK2,sK3)),
inference(cnf_transformation,[],[f30]) ).
fof(f57,plain,
union(sK2,sK3) != union(union(difference(sK2,sK3),difference(sK3,sK2)),intersection(sK2,sK3)),
inference(definition_unfolding,[],[f55,f31]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i] : union(union(X0,X1),X2) = union(X0,union(X1,X2)),
inference(cnf_transformation,[],[f32]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] : union(X0,intersection(X0,X1)) = X0,
inference(cnf_transformation,[],[f33]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] : union(intersection(X0,X1),difference(X0,X1)) = X0,
inference(cnf_transformation,[],[f34]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f44]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f45]) ).
tcf(c_70,negated_conjecture,
union(union(difference(sK2,sK3),difference(sK3,sK2)),intersection(sK2,sK3)) != union(sK2,sK3),
inference(cnf_transformation,[],[f57]) ).
tcf(c_85,negated_conjecture,
union(intersection(sK2,sK3),union(difference(sK2,sK3),difference(sK3,sK2))) != union(sK2,sK3),
inference(theory_normalisation,[status(thm)],[c_70,c_49,c_61]) ).
tcf(c_218,plain,
union(difference(sK3,sK2),sK2) != union(sK2,sK3),
inference(ac_demodulation,[status(thm)],[c_85,c_51,c_49,c_61]) ).
tcf(c_219,plain,
union(sK2,difference(sK3,sK2)) != union(sK2,sK3),
inference(theory_normalisation,[status(thm)],[c_218,c_49,c_61]) ).
tcf(c_364,definition,
iPr_def_10 = difference(sK3,sK2),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_365,definition,
iPr_def_11 = union(sK2,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_366,definition,
iPr_def_12 = union(sK2,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_367,plain,
iPr_def_11 != iPr_def_12,
inference(demodulation,[status(thm)],[c_219,c_366,c_364,c_365]) ).
tcf(c_595,plain,
! [X0: $i,X1: $i,X2: $i] : union(X0,union(X1,X2)) = union(X1,union(X0,X2)),
inference(superposition,[status(thm)],[c_49,c_61]) ).
tcf(c_598,plain,
union(iPr_def_10,sK2) = iPr_def_11,
inference(theory_normalisation,[status(thm)],[c_365,c_49,c_61]) ).
tcf(c_604,plain,
! [X0: $i,X1: $i,X2: $i] : union(X0,union(X1,intersection(X0,X2))) = union(X1,X0),
inference(superposition,[status(thm)],[c_50,c_595]) ).
tcf(c_763,plain,
union(intersection(sK3,sK2),iPr_def_10) = sK3,
inference(superposition,[status(thm)],[c_364,c_51]) ).
tcf(c_768,plain,
union(iPr_def_10,intersection(sK3,sK2)) = sK3,
inference(theory_normalisation,[status(thm)],[c_763,c_49,c_61]) ).
tcf(c_915,plain,
union(iPr_def_10,intersection(sK2,sK3)) = sK3,
inference(demodulation,[status(thm)],[c_768,c_62]) ).
tcf(c_922,plain,
union(sK2,sK3) = union(iPr_def_10,sK2),
inference(superposition,[status(thm)],[c_915,c_604]) ).
tcf(c_925,plain,
iPr_def_11 = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_922,c_366,c_598]) ).
tcf(c_926,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_925,c_367]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET619+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n004.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 11:28:37 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 2.67/1.18 % SZS status Started for theBenchmark.p
% 2.67/1.18 % SZS status Theorem for theBenchmark.p
% 2.67/1.18
% 2.67/1.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.67/1.18
% 2.67/1.18 % ------ iProver source info
% 2.67/1.18
% 2.67/1.18 % git: date: 2026-07-19 20:42:38 +0200
% 2.67/1.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.67/1.18 % git: non_committed_changes: false
% 2.67/1.18
% 2.67/1.18 % ------ Parsing...
% 2.67/1.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.67/1.18
% 2.67/1.18 % ------ Preprocessing... sup_sim: 1 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 %
% 2.67/1.18
% 2.67/1.18 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.67/1.18
% 2.67/1.18 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.67/1.18 % ------ Proving...
% 2.67/1.18 % ------ Problem Properties
% 2.67/1.18
% 2.67/1.18 %
% 2.67/1.18 % clauses 22
% 2.67/1.18 % conjectures 0
% 2.67/1.18 % EPR 4
% 2.67/1.18 % Horn 19
% 2.67/1.18 % unary 10
% 2.67/1.18 % binary 6
% 2.67/1.18 % lits 40
% 2.67/1.18 % lits eq 12
% 2.67/1.18 % fd_pure 0
% 2.67/1.18 % fd_pseudo 0
% 2.67/1.18 % fd_cond 0
% 2.67/1.18 % fd_pseudo_cond 3
% 2.67/1.18 % AC symbols 1
% 2.67/1.18
% 2.67/1.18 % ------ Schedule dynamic 5 is on
% 2.67/1.18
% 2.67/1.18 % ------ no conjectures: strip conj schedule
% 2.67/1.18
% 2.67/1.18 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.67/1.18
% 2.67/1.18
% 2.67/1.18 % ------
% 2.67/1.18 % Current options:
% 2.67/1.18 % ------
% 2.67/1.18
% 2.67/1.18
% 2.67/1.18 %
% 2.67/1.18
% 2.67/1.18 % ------ Proving...
% 2.67/1.18 %
% 2.67/1.18
% 2.67/1.18 % SZS status Theorem for theBenchmark.p
% 2.67/1.18
% 2.67/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.67/1.18
% 2.67/1.18
%------------------------------------------------------------------------------