%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET605+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 : 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 02:47:32 PM UTC 2026
% Result : Theorem 0.45s 1.29s
% Output : CNFRefutation 0.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 17 unt; 2 def)
% Number of atoms : 36 ( 17 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 17 ( 11 ~; 4 |; 1 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 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 : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 20 ( 0 sgn 18 !; 2 ?; 4 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : subset(X0,union(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_of_union) ).
fof(f2,axiom,
! [X0,X1] :
( difference(X0,X1) = empty_set
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_empty_set) ).
fof(f12,conjecture,
! [X0,X1] : difference(X0,union(X0,X1)) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th76) ).
fof(f13,negated_conjecture,
~ ! [X0,X1] : difference(X0,union(X0,X1)) = empty_set,
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f15,plain,
? [X0,X1] : empty_set != difference(X0,union(X0,X1)),
inference(ennf_transformation,[],[f13]) ).
fof(f16,plain,
! [X0,X1] :
( ( difference(X0,X1) != empty_set
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| difference(X0,X1) = empty_set ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f29,plain,
empty_set != difference(sK2,union(sK2,sK3)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f15]) ).
fof(f30,plain,
! [X0,X1] : subset(X0,union(X0,X1)),
inference(cnf_transformation,[],[f1]) ).
fof(f32,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| difference(X0,X1) = empty_set ),
inference(cnf_transformation,[],[f16]) ).
fof(f52,plain,
empty_set != difference(sK2,union(sK2,sK3)),
inference(cnf_transformation,[],[f29]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : subset(X0,union(X0,X1)),
inference(cnf_transformation,[],[f30]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( ( difference(X0,X1) = empty_set )
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_69,negated_conjecture,
difference(sK2,union(sK2,sK3)) != empty_set,
inference(cnf_transformation,[],[f52]) ).
tcf(c_498,definition,
iPr_def_10 = union(sK2,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_499,definition,
iPr_def_11 = difference(sK2,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_500,negated_conjecture,
iPr_def_11 != empty_set,
inference(demodulation,[status(thm)],[c_69,c_498,c_499]) ).
tcf(c_886,plain,
subset(sK2,iPr_def_10),
inference(superposition,[status(thm)],[c_498,c_49]) ).
tcf(c_893,plain,
difference(sK2,iPr_def_10) = empty_set,
inference(superposition,[status(thm)],[c_886,c_50]) ).
tcf(c_894,plain,
empty_set = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_893,c_499]) ).
tcf(c_897,plain,
iPr_def_11 != iPr_def_11,
inference(demodulation,[status(thm)],[c_500,c_894]) ).
tcf(c_898,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_897]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET605+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.37 % Computer : n009.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Thu Sep 24 11:25:29 UTC 2026
% 0.16/0.37 % CPUTime :
% 0.16/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/0.41 Running first-order theorem proving
% 0.16/0.41 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
% 0.16/0.43
% 0.16/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.16/0.43
% 0.16/0.43 % Detected problem language: tptp
% 0.16/0.44 % Proving...
% 0.45/1.29 % SZS status Started for theBenchmark.p
% 0.45/1.29 % SZS status Theorem for theBenchmark.p
% 0.45/1.29
% 0.45/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.45/1.29
% 0.45/1.29 % ------ iProver source info
% 0.45/1.29
% 0.45/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 0.45/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.45/1.29 % git: non_committed_changes: false
% 0.45/1.29
% 0.45/1.29 % ------ Parsing...
% 0.45/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.45/1.29
% 0.45/1.29 % ------ 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 %
% 0.45/1.29
% 0.45/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.45/1.29
% 0.45/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.45/1.29 % ------ Proving...
% 0.45/1.29 % ------ Problem Properties
% 0.45/1.29
% 0.45/1.29 %
% 0.45/1.29 % clauses 21
% 0.45/1.29 % conjectures 1
% 0.45/1.29 % EPR 5
% 0.45/1.29 % Horn 17
% 0.45/1.29 % unary 7
% 0.45/1.29 % binary 8
% 0.45/1.29 % lits 41
% 0.45/1.29 % lits eq 9
% 0.45/1.29 % fd_pure 0
% 0.45/1.29 % fd_pseudo 0
% 0.45/1.29 % fd_cond 0
% 0.45/1.29 % fd_pseudo_cond 3
% 0.45/1.29 % AC symbols 0
% 0.45/1.29
% 0.45/1.29 % ------ Schedule dynamic 5 is on
% 0.45/1.29
% 0.45/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.45/1.29
% 0.45/1.29
% 0.45/1.29 % ------
% 0.45/1.29 % Current options:
% 0.45/1.29 % ------
% 0.45/1.29
% 0.45/1.29
% 0.45/1.29 %
% 0.45/1.29
% 0.45/1.29 % ------ Proving...
% 0.45/1.29 %
% 0.45/1.29
% 0.45/1.29 % SZS status Theorem for theBenchmark.p
% 0.45/1.29
% 0.45/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.45/1.29
% 0.45/1.29
%------------------------------------------------------------------------------