%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU161+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n015.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 02:55:40 PM UTC 2026
% Result : Theorem 3.97s 1.31s
% Output : CNFRefutation 3.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 35 ( 21 unt; 2 def)
% Number of atoms : 63 ( 24 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 34 ( 18 ~; 9 |; 3 &)
% ( 1 <=>; 3 =>; 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 : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn 31 !; 2 ?; 7 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f52,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_union2(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(f67,axiom,
! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_zfmisc_1) ).
fof(f76,conjecture,
! [X0,X1] :
( in(X0,X1)
=> set_union2(singleton(X0),X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_zfmisc_1) ).
fof(f77,negated_conjecture,
~ ! [X0,X1] :
( in(X0,X1)
=> set_union2(singleton(X0),X1) = X1 ),
inference(negated_conjecture,[status(cth)],[f76]) ).
fof(f83,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f115,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 ),
inference(ennf_transformation,[],[f52]) ).
fof(f128,plain,
? [X0,X1] :
( in(X0,X1)
& set_union2(singleton(X0),X1) != X1 ),
inference(ennf_transformation,[],[f77]) ).
fof(f189,plain,
! [X0,X1] :
( ( ~ subset(singleton(X0),X1)
| in(X0,X1) )
& ( ~ in(X0,X1)
| subset(singleton(X0),X1) ) ),
inference(nnf_transformation,[],[f67]) ).
fof(f195,plain,
( in(sK20,sK21)
& sK21 != set_union2(singleton(sK20),sK21) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20,sK21]),skolemize(X0,sK20),skolemize(X1,sK21)],[f128]) ).
fof(f201,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f289,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 ),
inference(cnf_transformation,[],[f115]) ).
fof(f308,plain,
! [X0,X1] :
( ~ in(X0,X1)
| subset(singleton(X0),X1) ),
inference(cnf_transformation,[],[f189]) ).
fof(f323,plain,
in(sK20,sK21),
inference(cnf_transformation,[],[f195]) ).
fof(f324,plain,
sK21 != set_union2(singleton(sK20),sK21),
inference(cnf_transformation,[],[f195]) ).
fof(f331,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f83]) ).
fof(f383,plain,
! [X0,X1] :
( ~ in(X0,X1)
| subset(unordered_pair(X0,X0),X1) ),
inference(definition_unfolding,[],[f308,f331]) ).
fof(f388,plain,
sK21 != set_union2(unordered_pair(sK20,sK20),sK21),
inference(definition_unfolding,[],[f324,f331]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f201]) ).
tcf(c_139,plain,
! [X0: $i,X1: $i] :
( ( set_union2(X0,X1) = X1 )
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f289]) ).
tcf(c_157,plain,
! [X0: $i,X1: $i] :
( subset(unordered_pair(X0,X0),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f383]) ).
tcf(c_173,negated_conjecture,
set_union2(unordered_pair(sK20,sK20),sK21) != sK21,
inference(cnf_transformation,[],[f388]) ).
tcf(c_174,negated_conjecture,
in(sK20,sK21),
inference(cnf_transformation,[],[f323]) ).
tcf(c_1267,plain,
set_union2(sK21,unordered_pair(sK20,sK20)) != sK21,
inference(demodulation,[status(thm)],[c_173,c_52]) ).
tcf(c_3131,definition,
iPr_def_10 = unordered_pair(sK20,sK20),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_3132,definition,
iPr_def_11 = set_union2(sK21,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_3133,plain,
iPr_def_11 != sK21,
inference(demodulation,[status(thm)],[c_1267,c_3131,c_3132]) ).
tcf(c_3134,negated_conjecture,
in(sK20,sK21),
inference(demodulation,[status(thm)],[c_174]) ).
tcf(c_5160,plain,
set_union2(iPr_def_10,sK21) = iPr_def_11,
inference(demodulation,[status(thm)],[c_3132,c_52]) ).
tcf(c_5750,plain,
! [X0: $i] :
( subset(iPr_def_10,X0)
| ~ in(sK20,X0) ),
inference(superposition,[status(thm)],[c_3131,c_157]) ).
tcf(c_5868,plain,
subset(iPr_def_10,sK21),
inference(superposition,[status(thm)],[c_3134,c_5750]) ).
tcf(c_6297,plain,
set_union2(iPr_def_10,sK21) = sK21,
inference(superposition,[status(thm)],[c_5868,c_139]) ).
tcf(c_6298,plain,
sK21 = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_6297,c_5160]) ).
tcf(c_6309,plain,
iPr_def_11 != iPr_def_11,
inference(demodulation,[status(thm)],[c_3133,c_6298]) ).
tcf(c_6311,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_6309]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU161+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.19/0.44 % Computer : n015.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Thu Sep 24 13:03:10 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.23/0.51 Running first-order theorem proving
% 0.23/0.51 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
% 0.23/0.52
% 0.23/0.52 % ======== iProver multi-core TPTP/SMT =========
% 0.23/0.52
% 0.23/0.53 % Detected problem language: tptp
% 0.23/0.54 % Proving...
% 3.97/1.31 % SZS status Started for theBenchmark.p
% 3.97/1.31 % SZS status Theorem for theBenchmark.p
% 3.97/1.31
% 3.97/1.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.97/1.31
% 3.97/1.31 % ------ iProver source info
% 3.97/1.31
% 3.97/1.31 % git: date: 2026-07-19 20:42:38 +0200
% 3.97/1.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.97/1.31 % git: non_committed_changes: false
% 3.97/1.31
% 3.97/1.31 % ------ Parsing...
% 3.97/1.31 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.97/1.31
% 3.97/1.31 % ------ Preprocessing... sup_sim: 6 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 %
% 3.97/1.31
% 3.97/1.31 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.97/1.31
% 3.97/1.31 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.97/1.31 % ------ Proving...
% 3.97/1.31 % ------ Problem Properties
% 3.97/1.31
% 3.97/1.31 %
% 3.97/1.31 % clauses 125
% 3.97/1.31 % conjectures 1
% 3.97/1.31 % EPR 23
% 3.97/1.31 % Horn 97
% 3.97/1.31 % unary 28
% 3.97/1.31 % binary 53
% 3.97/1.31 % lits 273
% 3.97/1.31 % lits eq 81
% 3.97/1.31 % fd_pure 0
% 3.97/1.31 % fd_pseudo 0
% 3.97/1.31 % fd_cond 3
% 3.97/1.31 % fd_pseudo_cond 35
% 3.97/1.31 % AC symbols 0
% 3.97/1.31
% 3.97/1.31 % ------ Schedule dynamic 5 is on
% 3.97/1.31
% 3.97/1.31 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.97/1.31
% 3.97/1.31
% 3.97/1.31 % ------
% 3.97/1.31 % Current options:
% 3.97/1.31 % ------
% 3.97/1.31
% 3.97/1.31
% 3.97/1.31 %
% 3.97/1.31
% 3.97/1.31 % ------ Proving...
% 3.97/1.31 %
% 3.97/1.31
% 3.97/1.31 % SZS status Theorem for theBenchmark.p
% 3.97/1.31
% 3.97/1.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.97/1.32
% 3.97/1.32
%------------------------------------------------------------------------------