%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET617+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 : 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 1.82s 1.25s
% Output : CNFRefutation 1.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 28 ( 21 unt; 1 def)
% Number of atoms : 40 ( 34 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 21 ( 14 ~; 5 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 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 : 3 ( 1 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 23 ( 0 sgn 22 !; 1 ?; 6 :)
% 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] : union(X0,empty_set) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_empty_set) ).
fof(f3,axiom,
! [X0] : difference(X0,empty_set) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_difference_with_empty_set1) ).
fof(f4,axiom,
! [X0] : difference(empty_set,X0) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_difference_with_empty_set2) ).
fof(f7,axiom,
! [X0,X1] : union(X0,X1) = union(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(f13,conjecture,
! [X0] :
( symmetric_difference(empty_set,X0) = X0
& symmetric_difference(X0,empty_set) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th92) ).
fof(f14,negated_conjecture,
~ ! [X0] :
( symmetric_difference(empty_set,X0) = X0
& symmetric_difference(X0,empty_set) = X0 ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f16,plain,
? [X0] :
( symmetric_difference(empty_set,X0) != X0
| symmetric_difference(X0,empty_set) != X0 ),
inference(ennf_transformation,[],[f14]) ).
fof(f25,plain,
( sK2 != symmetric_difference(empty_set,sK2)
| sK2 != symmetric_difference(sK2,empty_set) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f16]) ).
fof(f26,plain,
! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
inference(cnf_transformation,[],[f1]) ).
fof(f27,plain,
! [X0] : union(X0,empty_set) = X0,
inference(cnf_transformation,[],[f2]) ).
fof(f28,plain,
! [X0] : difference(X0,empty_set) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f29,plain,
! [X0] : empty_set = difference(empty_set,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f34,plain,
! [X0,X1] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f7]) ).
fof(f44,plain,
( sK2 != symmetric_difference(empty_set,sK2)
| sK2 != symmetric_difference(sK2,empty_set) ),
inference(cnf_transformation,[],[f25]) ).
fof(f46,plain,
( sK2 != union(difference(empty_set,sK2),difference(sK2,empty_set))
| sK2 != union(difference(sK2,empty_set),difference(empty_set,sK2)) ),
inference(definition_unfolding,[],[f44,f26,f26]) ).
tcf(c_49,plain,
! [X0: $i] : union(X0,empty_set) = X0,
inference(cnf_transformation,[],[f27]) ).
tcf(c_50,plain,
! [X0: $i] : difference(X0,empty_set) = X0,
inference(cnf_transformation,[],[f28]) ).
tcf(c_51,plain,
! [X0: $i] : difference(empty_set,X0) = empty_set,
inference(cnf_transformation,[],[f29]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f34]) ).
tcf(c_64,negated_conjecture,
( ( union(difference(sK2,empty_set),difference(empty_set,sK2)) != sK2 )
| ( union(difference(empty_set,sK2),difference(sK2,empty_set)) != sK2 ) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_152,plain,
union(empty_set,sK2) != sK2,
inference(demodulation,[status(thm)],[c_64,c_50,c_51,c_56]) ).
tcf(c_241,definition,
iPr_def_10 = union(empty_set,sK2),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_242,plain,
iPr_def_10 != sK2,
inference(demodulation,[status(thm)],[c_152,c_241]) ).
tcf(c_406,plain,
! [X0: $i] : union(empty_set,X0) = X0,
inference(superposition,[status(thm)],[c_49,c_56]) ).
tcf(c_410,plain,
sK2 = iPr_def_10,
inference(demodulation,[status(thm)],[c_241,c_406]) ).
tcf(c_411,plain,
iPr_def_10 != iPr_def_10,
inference(demodulation,[status(thm)],[c_242,c_410]) ).
tcf(c_412,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_411]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET617+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 : n004.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 11:28:21 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.13/0.40
% 0.13/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40
% 0.13/0.40 % Detected problem language: tptp
% 0.13/0.41 % Proving...
% 1.82/1.25 % SZS status Started for theBenchmark.p
% 1.82/1.25 % SZS status Theorem for theBenchmark.p
% 1.82/1.25
% 1.82/1.25 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.82/1.25
% 1.82/1.25 % ------ iProver source info
% 1.82/1.25
% 1.82/1.25 % git: date: 2026-07-19 20:42:38 +0200
% 1.82/1.25 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.82/1.25 % git: non_committed_changes: false
% 1.82/1.25
% 1.82/1.25 % ------ Parsing...
% 1.82/1.25 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.82/1.25
% 1.82/1.25 % ------ 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 %
% 1.82/1.25
% 1.82/1.25 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.82/1.25
% 1.82/1.25 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.82/1.25 % ------ Proving...
% 1.82/1.25 % ------ Problem Properties
% 1.82/1.25
% 1.82/1.25 %
% 1.82/1.25 % clauses 14
% 1.82/1.25 % conjectures 0
% 1.82/1.25 % EPR 5
% 1.82/1.25 % Horn 12
% 1.82/1.25 % unary 8
% 1.82/1.25 % binary 2
% 1.82/1.25 % lits 24
% 1.82/1.25 % lits eq 9
% 1.82/1.25 % fd_pure 0
% 1.82/1.25 % fd_pseudo 0
% 1.82/1.25 % fd_cond 0
% 1.82/1.25 % fd_pseudo_cond 3
% 1.82/1.25 % AC symbols 0
% 1.82/1.25
% 1.82/1.25 % ------ Schedule dynamic 5 is on
% 1.82/1.25
% 1.82/1.25 % ------ no conjectures: strip conj schedule
% 1.82/1.25
% 1.82/1.25 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 1.82/1.25
% 1.82/1.25
% 1.82/1.25 % ------
% 1.82/1.25 % Current options:
% 1.82/1.25 % ------
% 1.82/1.25
% 1.82/1.25
% 1.82/1.25 %
% 1.82/1.25
% 1.82/1.25 % ------ Proving...
% 1.82/1.25 %
% 1.82/1.25
% 1.82/1.25 % SZS status Theorem for theBenchmark.p
% 1.82/1.25
% 1.82/1.25 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.82/1.25
% 1.82/1.25
%------------------------------------------------------------------------------