%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET904+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n008.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 02:49:04 PM UTC 2026
% Result : Theorem 0.52s 6.29s
% Output : CNFRefutation 0.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 14 unt; 2 def)
% Number of atoms : 42 ( 6 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 21 ( 11 ~; 5 |; 2 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 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 : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 21 ( 0 sgn 19 !; 2 ?; 5 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f9,conjecture,
! [X0,X1] :
( subset(set_union2(singleton(X0),X1),X1)
=> in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_zfmisc_1) ).
fof(f10,negated_conjecture,
~ ! [X0,X1] :
( subset(set_union2(singleton(X0),X1),X1)
=> in(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,axiom,
! [X0,X1] :
( subset(set_union2(singleton(X0),X1),X1)
=> in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l21_zfmisc_1) ).
fof(f17,plain,
? [X0,X1] :
( subset(set_union2(singleton(X0),X1),X1)
& ~ in(X0,X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f18,plain,
! [X0,X1] :
( ~ subset(set_union2(singleton(X0),X1),X1)
| in(X0,X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f21,plain,
( subset(set_union2(singleton(sK2),sK3),sK3)
& ~ in(sK2,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f17]) ).
fof(f24,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f30,plain,
subset(set_union2(singleton(sK2),sK3),sK3),
inference(cnf_transformation,[],[f21]) ).
fof(f31,plain,
~ in(sK2,sK3),
inference(cnf_transformation,[],[f21]) ).
fof(f32,plain,
! [X0,X1] :
( ~ subset(set_union2(singleton(X0),X1),X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f24]) ).
tcf(c_57,negated_conjecture,
~ in(sK2,sK3),
inference(cnf_transformation,[],[f31]) ).
tcf(c_58,negated_conjecture,
subset(set_union2(singleton(sK2),sK3),sK3),
inference(cnf_transformation,[],[f30]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ subset(set_union2(singleton(X0),X1),X1) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_106,plain,
subset(set_union2(sK3,singleton(sK2)),sK3),
inference(demodulation,[status(thm)],[c_58,c_51]) ).
tcf(c_141,definition,
iPr_def_10 = singleton(sK2),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_142,definition,
iPr_def_11 = set_union2(sK3,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_143,plain,
subset(iPr_def_11,sK3),
inference(demodulation,[status(thm)],[c_106,c_141,c_142]) ).
tcf(c_144,negated_conjecture,
~ in(sK2,sK3),
inference(demodulation,[status(thm)],[c_57]) ).
tcf(c_306,plain,
set_union2(iPr_def_10,sK3) = iPr_def_11,
inference(demodulation,[status(thm)],[c_142,c_51]) ).
tcf(c_336,plain,
! [X0: $i] :
( in(sK2,X0)
| ~ subset(set_union2(iPr_def_10,X0),X0) ),
inference(superposition,[status(thm)],[c_141,c_59]) ).
tcf(c_365,plain,
( in(sK2,sK3)
| ~ subset(iPr_def_11,sK3) ),
inference(superposition,[status(thm)],[c_306,c_336]) ).
tcf(c_366,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_365,c_144,c_143]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET904+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/5.38 % Computer : n008.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Thu Sep 24 12:22:02 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/5.42 Running first-order theorem proving
% 0.15/5.42 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
% 0.15/5.43
% 0.15/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.43
% 0.15/5.43 % Detected problem language: tptp
% 0.15/5.45 % Proving...
% 0.52/6.29 % SZS status Started for theBenchmark.p
% 0.52/6.29 % SZS status Theorem for theBenchmark.p
% 0.52/6.29
% 0.52/6.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.52/6.29
% 0.52/6.29 % ------ iProver source info
% 0.52/6.29
% 0.52/6.29 % git: date: 2026-07-19 20:42:38 +0200
% 0.52/6.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.52/6.29 % git: non_committed_changes: false
% 0.52/6.29
% 0.52/6.29 % ------ Parsing...
% 0.52/6.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.52/6.29
% 0.52/6.29 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe_e %
% 0.52/6.29
% 0.52/6.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.52/6.29
% 0.52/6.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.52/6.29 % ------ Proving...
% 0.52/6.29 % ------ Problem Properties
% 0.52/6.29
% 0.52/6.29 %
% 0.52/6.29 % clauses 13
% 0.52/6.29 % conjectures 1
% 0.52/6.29 % EPR 6
% 0.52/6.29 % Horn 13
% 0.52/6.29 % unary 9
% 0.52/6.29 % binary 4
% 0.52/6.29 % lits 17
% 0.52/6.29 % lits eq 4
% 0.52/6.29 % fd_pure 0
% 0.52/6.29 % fd_pseudo 0
% 0.52/6.29 % fd_cond 0
% 0.52/6.29 % fd_pseudo_cond 0
% 0.52/6.29 % AC symbols 0
% 0.52/6.29
% 0.52/6.29 % ------ Schedule dynamic 5 is on
% 0.52/6.29
% 0.52/6.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.52/6.29
% 0.52/6.29
% 0.52/6.29 % ------
% 0.52/6.29 % Current options:
% 0.52/6.29 % ------
% 0.52/6.29
% 0.52/6.29
% 0.52/6.29 %
% 0.52/6.29
% 0.52/6.29 % ------ Proving...
% 0.52/6.29 %
% 0.52/6.29
% 0.52/6.29 % SZS status Theorem for theBenchmark.p
% 0.52/6.29
% 0.52/6.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.52/6.29
% 0.52/6.29
%------------------------------------------------------------------------------