%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET620+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n006.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 3.56s 1.28s
% Output : CNFRefutation 3.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 34 ( 34 unt; 6 def)
% Number of atoms : 60 ( 33 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 7 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 32 !; 2 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_difference_defn) ).
fof(f2,axiom,
! [X0,X1] : difference(X0,intersection(X0,X1)) = difference(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_into_intersection) ).
fof(f3,axiom,
! [X0,X1,X2] : difference(union(X0,X1),X2) = union(difference(X0,X2),difference(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_distributes_over_union) ).
fof(f9,axiom,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(f14,conjecture,
! [X0,X1] : symmetric_difference(X0,X1) = difference(union(X0,X1),intersection(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th96) ).
fof(f15,negated_conjecture,
~ ! [X0,X1] : symmetric_difference(X0,X1) = difference(union(X0,X1),intersection(X0,X1)),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f17,plain,
? [X0,X1] : symmetric_difference(X0,X1) != difference(union(X0,X1),intersection(X0,X1)),
inference(ennf_transformation,[],[f15]) ).
fof(f32,plain,
symmetric_difference(sK2,sK3) != difference(union(sK2,sK3),intersection(sK2,sK3)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f17]) ).
fof(f33,plain,
! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
inference(cnf_transformation,[],[f1]) ).
fof(f34,plain,
! [X0,X1] : difference(X0,X1) = difference(X0,intersection(X0,X1)),
inference(cnf_transformation,[],[f2]) ).
fof(f35,plain,
! [X2,X0,X1] : difference(union(X0,X1),X2) = union(difference(X0,X2),difference(X1,X2)),
inference(cnf_transformation,[],[f3]) ).
fof(f49,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f9]) ).
fof(f59,plain,
symmetric_difference(sK2,sK3) != difference(union(sK2,sK3),intersection(sK2,sK3)),
inference(cnf_transformation,[],[f32]) ).
fof(f61,plain,
difference(union(sK2,sK3),intersection(sK2,sK3)) != union(difference(sK2,sK3),difference(sK3,sK2)),
inference(definition_unfolding,[],[f59,f33]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : difference(X0,intersection(X0,X1)) = difference(X0,X1),
inference(cnf_transformation,[],[f34]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] : union(difference(X0,X1),difference(X2,X1)) = difference(union(X0,X2),X1),
inference(cnf_transformation,[],[f35]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f49]) ).
tcf(c_72,negated_conjecture,
difference(union(sK2,sK3),intersection(sK2,sK3)) != union(difference(sK2,sK3),difference(sK3,sK2)),
inference(cnf_transformation,[],[f61]) ).
tcf(c_418,definition,
iPr_def_10 = union(sK2,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_419,definition,
iPr_def_11 = intersection(sK2,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_420,definition,
iPr_def_12 = difference(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_421,definition,
iPr_def_13 = difference(sK2,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_422,definition,
iPr_def_14 = difference(sK3,sK2),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_423,definition,
iPr_def_15 = union(iPr_def_13,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_424,negated_conjecture,
iPr_def_12 != iPr_def_15,
inference(demodulation,[status(thm)],[c_72,c_422,c_421,c_423,c_419,c_418,c_420]) ).
tcf(c_701,plain,
difference(sK2,sK3) = difference(sK2,iPr_def_11),
inference(superposition,[status(thm)],[c_419,c_49]) ).
tcf(c_702,plain,
difference(sK2,iPr_def_11) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_701,c_421]) ).
tcf(c_703,plain,
! [X0: $i,X1: $i] : difference(X0,intersection(X1,X0)) = difference(X0,X1),
inference(superposition,[status(thm)],[c_64,c_49]) ).
tcf(c_806,plain,
difference(sK3,sK2) = difference(sK3,iPr_def_11),
inference(superposition,[status(thm)],[c_419,c_703]) ).
tcf(c_807,plain,
difference(sK3,iPr_def_11) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_806,c_422]) ).
tcf(c_972,plain,
! [X0: $i] : difference(union(sK2,X0),iPr_def_11) = union(iPr_def_13,difference(X0,iPr_def_11)),
inference(superposition,[status(thm)],[c_702,c_50]) ).
tcf(c_4564,plain,
difference(union(sK2,sK3),iPr_def_11) = union(iPr_def_13,iPr_def_14),
inference(superposition,[status(thm)],[c_807,c_972]) ).
tcf(c_4571,plain,
iPr_def_12 = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_4564,c_418,c_420,c_423]) ).
tcf(c_4572,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4571,c_424]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET620+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n006.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
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 11:28:41 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/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...
% 3.56/1.28 % SZS status Started for theBenchmark.p
% 3.56/1.28 % SZS status Theorem for theBenchmark.p
% 3.56/1.28
% 3.56/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.56/1.28
% 3.56/1.28 % ------ iProver source info
% 3.56/1.28
% 3.56/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 3.56/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.56/1.28 % git: non_committed_changes: false
% 3.56/1.28
% 3.56/1.28 % ------ Parsing...
% 3.56/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.56/1.28
% 3.56/1.28 % ------ Preprocessing... sup_sim: 0 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 %
% 3.56/1.28
% 3.56/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.56/1.28
% 3.56/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.56/1.28 % ------ Proving...
% 3.56/1.28 % ------ Problem Properties
% 3.56/1.28
% 3.56/1.28 %
% 3.56/1.28 % clauses 27
% 3.56/1.28 % conjectures 1
% 3.56/1.28 % EPR 4
% 3.56/1.28 % Horn 23
% 3.56/1.28 % unary 12
% 3.56/1.28 % binary 8
% 3.56/1.28 % lits 49
% 3.56/1.28 % lits eq 14
% 3.56/1.28 % fd_pure 0
% 3.56/1.28 % fd_pseudo 0
% 3.56/1.28 % fd_cond 0
% 3.56/1.28 % fd_pseudo_cond 3
% 3.56/1.28 % AC symbols 0
% 3.56/1.28
% 3.56/1.28 % ------ Schedule dynamic 5 is on
% 3.56/1.28
% 3.56/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.56/1.28
% 3.56/1.28
% 3.56/1.28 % ------
% 3.56/1.28 % Current options:
% 3.56/1.28 % ------
% 3.56/1.28
% 3.56/1.28
% 3.56/1.28 %
% 3.56/1.28
% 3.56/1.28 % ------ Proving...
% 3.56/1.28 %
% 3.56/1.28
% 3.56/1.28 % SZS status Theorem for theBenchmark.p
% 3.56/1.28
% 3.56/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.56/1.28
% 3.56/1.28
%------------------------------------------------------------------------------