%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET902+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 : 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 02:49:04 PM UTC 2026
% Result : Theorem 1.74s 1.28s
% Output : CNFRefutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 59 ( 24 unt; 2 def)
% Number of atoms : 168 ( 121 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 136 ( 63 ~; 50 |; 22 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 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 : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 51 ( 1 sgn 48 !; 3 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f5,axiom,
! [X0,X1] : set_union2(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(f6,axiom,
! [X0] : singleton(X0) != empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_zfmisc_1) ).
fof(f7,axiom,
! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( X0 = singleton(X1)
| X0 = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4_zfmisc_1) ).
fof(f11,conjecture,
! [X0,X1,X2] :
~ ( ~ ( X2 = empty_set
& X1 = singleton(X0) )
& ~ ( X2 = singleton(X0)
& X1 = empty_set )
& ~ ( X2 = singleton(X0)
& X1 = singleton(X0) )
& singleton(X0) = set_union2(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_zfmisc_1) ).
fof(f12,negated_conjecture,
~ ! [X0,X1,X2] :
~ ( ~ ( X2 = empty_set
& X1 = singleton(X0) )
& ~ ( X2 = singleton(X0)
& X1 = empty_set )
& ~ ( X2 = singleton(X0)
& X1 = singleton(X0) )
& singleton(X0) = set_union2(X1,X2) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f13,axiom,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(f14,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(rectify,[],[f5]) ).
fof(f18,plain,
? [X0,X1,X2] :
( ( empty_set != X2
| singleton(X0) != X1 )
& ( singleton(X0) != X2
| empty_set != X1 )
& ( singleton(X0) != X2
| singleton(X0) != X1 )
& singleton(X0) = set_union2(X1,X2) ),
inference(ennf_transformation,[],[f12]) ).
fof(f19,plain,
! [X0,X1] :
( ( ~ subset(X0,singleton(X1))
| X0 = singleton(X1)
| X0 = empty_set )
& ( ( singleton(X1) != X0
& empty_set != X0 )
| subset(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f20,plain,
! [X0,X1] :
( ( ~ subset(X0,singleton(X1))
| X0 = singleton(X1)
| X0 = empty_set )
& ( ( singleton(X1) != X0
& empty_set != X0 )
| subset(X0,singleton(X1)) ) ),
inference(flattening,[],[f19]) ).
fof(f23,plain,
( ( empty_set != sK4
| sK3 != singleton(sK2) )
& ( sK4 != singleton(sK2)
| empty_set != sK3 )
& ( sK4 != singleton(sK2)
| sK3 != singleton(sK2) )
& singleton(sK2) = set_union2(sK3,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f18]) ).
fof(f24,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f28,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(cnf_transformation,[],[f14]) ).
fof(f29,plain,
! [X0] : empty_set != singleton(X0),
inference(cnf_transformation,[],[f6]) ).
fof(f30,plain,
! [X0,X1] :
( ~ subset(X0,singleton(X1))
| singleton(X1) = X0
| empty_set = X0 ),
inference(cnf_transformation,[],[f20]) ).
fof(f36,plain,
( empty_set != sK4
| sK3 != singleton(sK2) ),
inference(cnf_transformation,[],[f23]) ).
fof(f37,plain,
( sK4 != singleton(sK2)
| empty_set != sK3 ),
inference(cnf_transformation,[],[f23]) ).
fof(f38,plain,
( sK4 != singleton(sK2)
| sK3 != singleton(sK2) ),
inference(cnf_transformation,[],[f23]) ).
fof(f39,plain,
singleton(sK2) = set_union2(sK3,sK4),
inference(cnf_transformation,[],[f23]) ).
fof(f40,plain,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[],[f13]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f24]) ).
tcf(c_53,plain,
! [X0: $i] : set_union2(X0,X0) = X0,
inference(cnf_transformation,[],[f28]) ).
tcf(c_54,plain,
! [X0: $i] : singleton(X0) != empty_set,
inference(cnf_transformation,[],[f29]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( ( X0 = empty_set )
| ( singleton(X1) = X0 )
| ~ subset(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_61,negated_conjecture,
set_union2(sK3,sK4) = singleton(sK2),
inference(cnf_transformation,[],[f39]) ).
tcf(c_62,negated_conjecture,
( ( singleton(sK2) != sK4 )
| ( singleton(sK2) != sK3 ) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_63,negated_conjecture,
( ( empty_set != sK3 )
| ( singleton(sK2) != sK4 ) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_64,negated_conjecture,
( ( empty_set != sK4 )
| ( singleton(sK2) != sK3 ) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[],[f40]) ).
tcf(c_155,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = empty_set )
| ( singleton(X2) = X3 )
| ( X0 != X3 )
| ( set_union2(X0,X1) != singleton(X2) ) ),
inference(resolution_lifted,[status(thm)],[c_57,c_65]) ).
tcf(c_156,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = empty_set )
| ( singleton(X2) = X0 )
| ( set_union2(X0,X1) != singleton(X2) ) ),
inference(unflattening,[status(thm)],[c_155]) ).
tcf(c_240,definition,
iPr_def_10 = singleton(sK2),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_241,definition,
iPr_def_11 = set_union2(sK3,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_242,negated_conjecture,
( ( iPr_def_10 != sK3 )
| ( empty_set != sK4 ) ),
inference(demodulation,[status(thm)],[c_64,c_240]) ).
tcf(c_243,negated_conjecture,
( ( iPr_def_10 != sK4 )
| ( empty_set != sK3 ) ),
inference(demodulation,[status(thm)],[c_63]) ).
tcf(c_244,negated_conjecture,
( ( iPr_def_10 != sK4 )
| ( iPr_def_10 != sK3 ) ),
inference(demodulation,[status(thm)],[c_62]) ).
tcf(c_245,negated_conjecture,
iPr_def_11 = iPr_def_10,
inference(demodulation,[status(thm)],[c_61,c_241]) ).
tcf(c_410,plain,
empty_set != iPr_def_10,
inference(superposition,[status(thm)],[c_240,c_54]) ).
tcf(c_411,plain,
set_union2(sK3,sK4) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_241,c_245]) ).
tcf(c_412,plain,
! [X0: $i] :
( ( empty_set = sK3 )
| ( singleton(X0) = sK3 )
| ( singleton(X0) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_411,c_156]) ).
tcf(c_447,plain,
( ( empty_set = sK3 )
| ( singleton(sK2) = sK3 ) ),
inference(superposition,[status(thm)],[c_240,c_412]) ).
tcf(c_448,plain,
( ( sK3 = iPr_def_10 )
| ( empty_set = sK3 ) ),
inference(light_normalisation,[status(thm)],[c_447,c_240]) ).
tcf(c_455,plain,
( ( sK3 = iPr_def_10 )
| ( set_union2(empty_set,sK4) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_448,c_411]) ).
tcf(c_457,plain,
( ( sK3 = iPr_def_10 )
| ( sK4 != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_448,c_243]) ).
tcf(c_483,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = empty_set )
| ( singleton(X2) = X1 )
| ( set_union2(X0,X1) != singleton(X2) ) ),
inference(superposition,[status(thm)],[c_49,c_156]) ).
tcf(c_496,plain,
! [X0: $i] :
( ( empty_set = sK4 )
| ( singleton(X0) = sK4 )
| ( singleton(X0) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_411,c_483]) ).
tcf(c_508,plain,
( ( empty_set = sK4 )
| ( singleton(sK2) = sK4 ) ),
inference(superposition,[status(thm)],[c_240,c_496]) ).
tcf(c_509,plain,
( ( sK4 = iPr_def_10 )
| ( empty_set = sK4 ) ),
inference(light_normalisation,[status(thm)],[c_508,c_240]) ).
tcf(c_516,plain,
( ( sK4 = iPr_def_10 )
| ( sK3 = iPr_def_10 )
| ( set_union2(empty_set,empty_set) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_509,c_455]) ).
tcf(c_519,plain,
( ( sK4 = iPr_def_10 )
| ( sK3 != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_509,c_242]) ).
tcf(c_549,plain,
( ( sK4 = iPr_def_10 )
| ( set_union2(empty_set,empty_set) = iPr_def_10 ) ),
inference(global_subsumption_just,[status(thm)],[c_516,c_519,c_516]) ).
tcf(c_551,plain,
( ( sK4 = iPr_def_10 )
| ( empty_set = iPr_def_10 ) ),
inference(demodulation,[status(thm)],[c_549,c_53]) ).
tcf(c_552,plain,
sK4 = iPr_def_10,
inference(forward_subsumption_resolution,[status(thm)],[c_551,c_410]) ).
tcf(c_558,plain,
( ( sK3 = iPr_def_10 )
| ( iPr_def_10 != iPr_def_10 ) ),
inference(demodulation,[status(thm)],[c_457,c_552]) ).
tcf(c_561,plain,
( ( iPr_def_10 != iPr_def_10 )
| ( sK3 != iPr_def_10 ) ),
inference(demodulation,[status(thm)],[c_244,c_552]) ).
tcf(c_564,plain,
sK3 = iPr_def_10,
inference(equality_resolution_simp,[status(thm)],[c_558]) ).
tcf(c_566,plain,
sK3 != iPr_def_10,
inference(equality_resolution_simp,[status(thm)],[c_561]) ).
tcf(c_567,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_566,c_564]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET902+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.37 % Computer : n015.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Thu Sep 24 12:24:26 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.41 Running first-order theorem proving
% 0.08/0.41 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
% 0.08/0.42
% 0.08/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.42
% 0.08/0.42 % Detected problem language: tptp
% 0.08/0.43 % Proving...
% 1.74/1.28 % SZS status Started for theBenchmark.p
% 1.74/1.28 % SZS status Theorem for theBenchmark.p
% 1.74/1.28
% 1.74/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.74/1.28
% 1.74/1.28 % ------ iProver source info
% 1.74/1.28
% 1.74/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 1.74/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.74/1.28 % git: non_committed_changes: false
% 1.74/1.28
% 1.74/1.28 % ------ Parsing...
% 1.74/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.74/1.28
% 1.74/1.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 1.74/1.28
% 1.74/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.74/1.28
% 1.74/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.74/1.28 % ------ Proving...
% 1.74/1.28 % ------ Problem Properties
% 1.74/1.28
% 1.74/1.28 %
% 1.74/1.28 % clauses 15
% 1.74/1.28 % conjectures 4
% 1.74/1.28 % EPR 7
% 1.74/1.28 % Horn 14
% 1.74/1.28 % unary 9
% 1.74/1.28 % binary 5
% 1.74/1.28 % lits 22
% 1.74/1.28 % lits eq 15
% 1.74/1.28 % fd_pure 0
% 1.74/1.28 % fd_pseudo 0
% 1.74/1.28 % fd_cond 0
% 1.74/1.28 % fd_pseudo_cond 1
% 1.74/1.28 % AC symbols 0
% 1.74/1.28
% 1.74/1.28 % ------ Schedule dynamic 5 is on
% 1.74/1.28
% 1.74/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.74/1.28
% 1.74/1.28
% 1.74/1.28 % ------
% 1.74/1.28 % Current options:
% 1.74/1.28 % ------
% 1.74/1.28
% 1.74/1.28
% 1.74/1.28 %
% 1.74/1.28
% 1.74/1.28 % ------ Proving...
% 1.74/1.28 %
% 1.74/1.28
% 1.74/1.28 % SZS status Theorem for theBenchmark.p
% 1.74/1.28
% 1.74/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.74/1.28
% 1.74/1.28
%------------------------------------------------------------------------------