%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET618+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 : n009.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 1.54s 1.28s
% Output : CNFRefutation 1.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 17 unt; 0 def)
% Number of atoms : 17 ( 16 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 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 : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 13 ( 0 sgn 12 !; 1 ?; 2 :)
% 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,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotency_of_union) ).
fof(f3,axiom,
! [X0] : difference(X0,X0) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',self_difference_is_empty_set) ).
fof(f12,conjecture,
! [X0] : symmetric_difference(X0,X0) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th93) ).
fof(f13,negated_conjecture,
~ ! [X0] : symmetric_difference(X0,X0) = empty_set,
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f15,plain,
? [X0] : empty_set != symmetric_difference(X0,X0),
inference(ennf_transformation,[],[f13]) ).
fof(f24,plain,
empty_set != symmetric_difference(sK2,sK2),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f15]) ).
fof(f25,plain,
! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
inference(cnf_transformation,[],[f1]) ).
fof(f26,plain,
! [X0] : union(X0,X0) = X0,
inference(cnf_transformation,[],[f2]) ).
fof(f27,plain,
! [X0] : difference(X0,X0) = empty_set,
inference(cnf_transformation,[],[f3]) ).
fof(f42,plain,
empty_set != symmetric_difference(sK2,sK2),
inference(cnf_transformation,[],[f24]) ).
fof(f44,plain,
empty_set != union(difference(sK2,sK2),difference(sK2,sK2)),
inference(definition_unfolding,[],[f42,f25]) ).
tcf(c_49,plain,
! [X0: $i] : union(X0,X0) = X0,
inference(cnf_transformation,[],[f26]) ).
tcf(c_50,plain,
! [X0: $i] : difference(X0,X0) = empty_set,
inference(cnf_transformation,[],[f27]) ).
tcf(c_63,negated_conjecture,
union(difference(sK2,sK2),difference(sK2,sK2)) != empty_set,
inference(cnf_transformation,[],[f44]) ).
tcf(c_123,plain,
empty_set != empty_set,
inference(demodulation,[status(thm)],[c_63,c_49,c_50]) ).
tcf(c_124,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_123]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET618+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n009.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 11:28:44 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 1.54/1.28 % SZS status Started for theBenchmark.p
% 1.54/1.28 % SZS status Theorem for theBenchmark.p
% 1.54/1.28
% 1.54/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.54/1.28
% 1.54/1.28 % ------ iProver source info
% 1.54/1.28
% 1.54/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 1.54/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.54/1.28 % git: non_committed_changes: false
% 1.54/1.28
% 1.54/1.28 % ------ Parsing...
% 1.54/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.54/1.28
% 1.54/1.28 % ------ Preprocessing...%
% 1.54/1.28
% 1.54/1.28 % SZS status Theorem for theBenchmark.p
% 1.54/1.28
% 1.54/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.54/1.28
% 1.54/1.28
%------------------------------------------------------------------------------