%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU137+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 : n018.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 02:55:32 PM UTC 2026
% Result : Theorem 3.38s 1.16s
% Output : CNFRefutation 3.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 19 unt; 1 def)
% Number of atoms : 40 ( 23 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 20 ( 12 ~; 3 |; 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 : 4 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn 24 !; 2 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f25,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_union2(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(f38,axiom,
! [X0,X1] : set_union2(X0,set_difference(X1,X0)) = set_union2(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_xboole_1) ).
fof(f43,conjecture,
! [X0,X1] :
( subset(X0,X1)
=> X1 = set_union2(X0,set_difference(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_xboole_1) ).
fof(f44,negated_conjecture,
~ ! [X0,X1] :
( subset(X0,X1)
=> X1 = set_union2(X0,set_difference(X1,X0)) ),
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f62,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 ),
inference(ennf_transformation,[],[f25]) ).
fof(f73,plain,
? [X0,X1] :
( subset(X0,X1)
& set_union2(X0,set_difference(X1,X0)) != X1 ),
inference(ennf_transformation,[],[f44]) ).
fof(f108,plain,
( subset(sK9,sK10)
& sK10 != set_union2(sK9,set_difference(sK10,sK9)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10]),skolemize(X0,sK9),skolemize(X1,sK10)],[f73]) ).
fof(f111,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f152,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 ),
inference(cnf_transformation,[],[f62]) ).
fof(f167,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X0,set_difference(X1,X0)),
inference(cnf_transformation,[],[f38]) ).
fof(f174,plain,
subset(sK9,sK10),
inference(cnf_transformation,[],[f108]) ).
fof(f175,plain,
sK10 != set_union2(sK9,set_difference(sK10,sK9)),
inference(cnf_transformation,[],[f108]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f111]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i] :
( ( set_union2(X0,X1) = X1 )
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f152]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i] : set_union2(X0,set_difference(X1,X0)) = set_union2(X0,X1),
inference(cnf_transformation,[],[f167]) ).
tcf(c_113,negated_conjecture,
set_union2(sK9,set_difference(sK10,sK9)) != sK10,
inference(cnf_transformation,[],[f175]) ).
tcf(c_114,negated_conjecture,
subset(sK9,sK10),
inference(cnf_transformation,[],[f174]) ).
tcf(c_720,plain,
set_union2(sK9,sK10) != sK10,
inference(demodulation,[status(thm)],[c_113,c_106]) ).
tcf(c_721,plain,
set_union2(sK10,sK9) != sK10,
inference(demodulation,[status(thm)],[c_720,c_50]) ).
tcf(c_1633,definition,
iPr_def_10 = set_union2(sK10,sK9),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1634,plain,
iPr_def_10 != sK10,
inference(demodulation,[status(thm)],[c_721,c_1633]) ).
tcf(c_1635,negated_conjecture,
subset(sK9,sK10),
inference(demodulation,[status(thm)],[c_114]) ).
tcf(c_3317,plain,
set_union2(sK9,sK10) = sK10,
inference(superposition,[status(thm)],[c_1635,c_91]) ).
tcf(c_3366,plain,
sK10 = iPr_def_10,
inference(demodulation,[status(thm)],[c_3317,c_50,c_1633]) ).
tcf(c_3377,plain,
iPr_def_10 != iPr_def_10,
inference(demodulation,[status(thm)],[c_1634,c_3366]) ).
tcf(c_3379,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_3377]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU137+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n018.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 12:55:33 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.39 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
% 0.14/0.41
% 0.14/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.41
% 0.14/0.41 % Detected problem language: tptp
% 0.14/0.42 % Proving...
% 3.38/1.16 % SZS status Started for theBenchmark.p
% 3.38/1.16 % SZS status Theorem for theBenchmark.p
% 3.38/1.16
% 3.38/1.16 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.38/1.16
% 3.38/1.16 % ------ iProver source info
% 3.38/1.16
% 3.38/1.16 % git: date: 2026-07-19 20:42:38 +0200
% 3.38/1.16 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.38/1.16 % git: non_committed_changes: false
% 3.38/1.16
% 3.38/1.16 % ------ Parsing...
% 3.38/1.16 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.38/1.16
% 3.38/1.16 % ------ Preprocessing... sup_sim: 2 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 %
% 3.38/1.16
% 3.38/1.16 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.38/1.16
% 3.38/1.16 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.38/1.16 % ------ Proving...
% 3.38/1.16 % ------ Problem Properties
% 3.38/1.16
% 3.38/1.16 %
% 3.38/1.16 % clauses 71
% 3.38/1.16 % conjectures 1
% 3.38/1.16 % EPR 18
% 3.38/1.16 % Horn 57
% 3.38/1.16 % unary 22
% 3.38/1.16 % binary 28
% 3.38/1.16 % lits 144
% 3.38/1.16 % lits eq 34
% 3.38/1.16 % fd_pure 0
% 3.38/1.16 % fd_pseudo 0
% 3.38/1.16 % fd_cond 3
% 3.38/1.16 % fd_pseudo_cond 13
% 3.38/1.16 % AC symbols 0
% 3.38/1.16
% 3.38/1.16 % ------ Schedule dynamic 5 is on
% 3.38/1.16
% 3.38/1.16 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.38/1.16
% 3.38/1.16
% 3.38/1.16 % ------
% 3.38/1.16 % Current options:
% 3.38/1.16 % ------
% 3.38/1.16
% 3.38/1.16
% 3.38/1.16 %
% 3.38/1.16
% 3.38/1.16 % ------ Proving...
% 3.38/1.16 %
% 3.38/1.16
% 3.38/1.16 % SZS status Theorem for theBenchmark.p
% 3.38/1.16
% 3.38/1.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.38/1.16
% 3.38/1.16
%------------------------------------------------------------------------------