%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET935+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 : n006.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 02:49:09 PM UTC 2026
% Result : Theorem 4.01s 11.55s
% Output : CNFRefutation 4.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 13
% Syntax : Number of formulae : 79 ( 33 unt; 5 def)
% Number of atoms : 274 ( 50 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 237 ( 89 ~; 100 |; 40 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 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 : 10 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 118 ( 1 sgn 111 !; 7 ?; 28 :)
% 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(f3,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f4,axiom,
! [X0,X1] :
( X1 = powerset(X0)
<=> ! [X2] :
( in(X2,X1)
<=> subset(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(f5,axiom,
! [X0,X1,X2] :
( X2 = set_union2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f6,axiom,
! [X0,X1] :
( inclusion_comparable(X0,X1)
<=> ( subset(X1,X0)
| subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_xboole_0) ).
fof(f12,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f15,axiom,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(f16,conjecture,
! [X0,X1] :
( set_union2(powerset(X0),powerset(X1)) = powerset(set_union2(X0,X1))
=> inclusion_comparable(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_zfmisc_1) ).
fof(f17,negated_conjecture,
~ ! [X0,X1] :
( set_union2(powerset(X0),powerset(X1)) = powerset(set_union2(X0,X1))
=> inclusion_comparable(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f19,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f12]) ).
fof(f25,plain,
? [X0,X1] :
( set_union2(powerset(X0),powerset(X1)) = powerset(set_union2(X0,X1))
& ~ inclusion_comparable(X0,X1) ),
inference(ennf_transformation,[],[f17]) ).
fof(f26,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f27,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(flattening,[],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( ( powerset(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| subset(X2,X0) )
& ( ~ subset(X2,X0)
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| subset(X2,X0) )
& ( ~ in(X2,X1)
| ~ subset(X2,X0) ) )
| X1 = powerset(X0) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f29,plain,
! [X0,X1] :
( ( powerset(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| subset(X3,X0) )
& ( ~ subset(X3,X0)
| in(X3,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| subset(X2,X0) )
& ( ~ in(X2,X1)
| ~ subset(X2,X0) ) )
| X1 = powerset(X0) ) ),
inference(rectify,[],[f28]) ).
fof(f30,plain,
! [X0,X1] :
( ( powerset(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| subset(X3,X0) )
& ( ~ subset(X3,X0)
| in(X3,X1) ) ) )
& ( ( ( in(sK0(X0,X1),X1)
| subset(sK0(X0,X1),X0) )
& ( ~ in(sK0(X0,X1),X1)
| ~ subset(sK0(X0,X1),X0) ) )
| X1 = powerset(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f29]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f32,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(flattening,[],[f31]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| in(X4,X1)
| in(X4,X0) )
& ( ( ~ in(X4,X1)
& ~ in(X4,X0) )
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(rectify,[],[f32]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| in(X4,X1)
| in(X4,X0) )
& ( ( ~ in(X4,X1)
& ~ in(X4,X0) )
| in(X4,X2) ) ) )
& ( ( ( in(sK1(X0,X1,X2),X2)
| in(sK1(X0,X1,X2),X1)
| in(sK1(X0,X1,X2),X0) )
& ( ~ in(sK1(X0,X1,X2),X2)
| ( ~ in(sK1(X0,X1,X2),X1)
& ~ in(sK1(X0,X1,X2),X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1,X2))],[f33]) ).
fof(f35,plain,
! [X0,X1] :
( ( ~ inclusion_comparable(X0,X1)
| subset(X1,X0)
| subset(X0,X1) )
& ( ( ~ subset(X1,X0)
& ~ subset(X0,X1) )
| inclusion_comparable(X0,X1) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f36,plain,
! [X0,X1] :
( ( ~ inclusion_comparable(X0,X1)
| subset(X1,X0)
| subset(X0,X1) )
& ( ( ~ subset(X1,X0)
& ~ subset(X0,X1) )
| inclusion_comparable(X0,X1) ) ),
inference(flattening,[],[f35]) ).
fof(f39,plain,
( set_union2(powerset(sK4),powerset(sK5)) = powerset(set_union2(sK4,sK5))
& ~ inclusion_comparable(sK4,sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5]),skolemize(X0,sK4),skolemize(X1,sK5)],[f25]) ).
fof(f41,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f44,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f27]) ).
fof(f45,plain,
! [X3,X0,X1] :
( powerset(X0) != X1
| ~ in(X3,X1)
| subset(X3,X0) ),
inference(cnf_transformation,[],[f30]) ).
fof(f46,plain,
! [X3,X0,X1] :
( powerset(X0) != X1
| ~ subset(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f49,plain,
! [X2,X0,X1,X4] :
( set_union2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X1)
| in(X4,X0) ),
inference(cnf_transformation,[],[f34]) ).
fof(f56,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| inclusion_comparable(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f57,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| inclusion_comparable(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f63,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f19]) ).
fof(f66,plain,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[],[f15]) ).
fof(f67,plain,
set_union2(powerset(sK4),powerset(sK5)) = powerset(set_union2(sK4,sK5)),
inference(cnf_transformation,[],[f39]) ).
fof(f68,plain,
~ inclusion_comparable(sK4,sK5),
inference(cnf_transformation,[],[f39]) ).
fof(f71,plain,
! [X3,X0] :
( ~ subset(X3,X0)
| in(X3,powerset(X0)) ),
inference(equality_resolution,[],[f46]) ).
fof(f72,plain,
! [X3,X0] :
( ~ in(X3,powerset(X0))
| subset(X3,X0) ),
inference(equality_resolution,[],[f45]) ).
fof(f75,plain,
! [X0,X1,X4] :
( ~ in(X4,set_union2(X0,X1))
| in(X4,X1)
| in(X4,X0) ),
inference(equality_resolution,[],[f49]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f41]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( in(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| in(X0,X1)
| ~ in(X0,set_union2(X1,X2)) ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( inclusion_comparable(X0,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( inclusion_comparable(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_72,plain,
! [X0: $i] : subset(X0,X0),
inference(cnf_transformation,[],[f63]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[],[f66]) ).
tcf(c_76,negated_conjecture,
~ inclusion_comparable(sK4,sK5),
inference(cnf_transformation,[],[f68]) ).
tcf(c_77,negated_conjecture,
set_union2(powerset(sK4),powerset(sK5)) = powerset(set_union2(sK4,sK5)),
inference(cnf_transformation,[],[f67]) ).
tcf(c_658,definition,
iPr_def_10 = powerset(sK4),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_659,definition,
iPr_def_11 = powerset(sK5),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_660,definition,
iPr_def_12 = set_union2(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_661,definition,
iPr_def_13 = set_union2(sK4,sK5),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_662,definition,
iPr_def_14 = powerset(iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_663,negated_conjecture,
iPr_def_12 = iPr_def_14,
inference(demodulation,[status(thm)],[c_77,c_661,c_662,c_659,c_658,c_660]) ).
tcf(c_664,negated_conjecture,
~ inclusion_comparable(sK4,sK5),
inference(demodulation,[status(thm)],[c_76]) ).
tcf(c_1214,plain,
powerset(iPr_def_13) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_662,c_663]) ).
tcf(c_1217,plain,
subset(sK4,iPr_def_13),
inference(superposition,[status(thm)],[c_661,c_75]) ).
tcf(c_1223,plain,
inclusion_comparable(sK4,iPr_def_13),
inference(superposition,[status(thm)],[c_1217,c_64]) ).
tcf(c_1233,plain,
! [X0: $i,X1: $i] : inclusion_comparable(set_union2(X0,X1),X0),
inference(superposition,[status(thm)],[c_75,c_65]) ).
tcf(c_1260,plain,
! [X0: $i,X1: $i] : inclusion_comparable(set_union2(X0,X1),X1),
inference(superposition,[status(thm)],[c_50,c_1233]) ).
tcf(c_1262,plain,
! [X0: $i,X1: $i] : subset(X0,set_union2(X1,X0)),
inference(superposition,[status(thm)],[c_50,c_75]) ).
tcf(c_1297,plain,
! [X0: $i] :
( in(X0,iPr_def_12)
| ~ subset(X0,iPr_def_13) ),
inference(superposition,[status(thm)],[c_1214,c_56]) ).
tcf(c_1318,plain,
inclusion_comparable(iPr_def_13,sK5),
inference(superposition,[status(thm)],[c_661,c_1260]) ).
tcf(c_1327,plain,
in(iPr_def_13,iPr_def_12),
inference(superposition,[status(thm)],[c_72,c_1297]) ).
tcf(c_1355,plain,
! [X0: $i] :
( subset(X0,sK4)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_658,c_57]) ).
tcf(c_1356,plain,
! [X0: $i] :
( subset(X0,sK5)
| ~ in(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_659,c_57]) ).
tcf(c_1440,plain,
subset(sK5,iPr_def_13),
inference(superposition,[status(thm)],[c_661,c_1262]) ).
tcf(c_1509,plain,
( ( sK4 = iPr_def_13 )
| ~ subset(iPr_def_13,sK4) ),
inference(superposition,[status(thm)],[c_1217,c_51]) ).
tcf(c_1511,plain,
( ( sK5 = iPr_def_13 )
| ~ subset(iPr_def_13,sK5) ),
inference(superposition,[status(thm)],[c_1440,c_51]) ).
tcf(c_1545,plain,
! [X0: $i] :
( in(X0,iPr_def_11)
| in(X0,iPr_def_10)
| ~ in(X0,iPr_def_12) ),
inference(superposition,[status(thm)],[c_660,c_63]) ).
tcf(c_4458,plain,
( in(iPr_def_13,iPr_def_11)
| in(iPr_def_13,iPr_def_10) ),
inference(superposition,[status(thm)],[c_1327,c_1545]) ).
tcf(c_4623,plain,
( subset(iPr_def_13,sK5)
| in(iPr_def_13,iPr_def_10) ),
inference(superposition,[status(thm)],[c_4458,c_1356]) ).
tcf(c_4995,plain,
( in(iPr_def_13,iPr_def_10)
| ( sK5 = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_4623,c_1511]) ).
tcf(c_5319,plain,
( subset(iPr_def_13,sK4)
| ( sK5 = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_4995,c_1355]) ).
tcf(c_5333,plain,
( ( sK5 = iPr_def_13 )
| ( sK4 = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_5319,c_1509]) ).
tcf(c_5842,plain,
( ( sK4 = iPr_def_13 )
| ~ inclusion_comparable(sK4,iPr_def_13) ),
inference(superposition,[status(thm)],[c_5333,c_664]) ).
tcf(c_5845,plain,
sK4 = iPr_def_13,
inference(forward_subsumption_resolution,[status(thm)],[c_5842,c_1223]) ).
tcf(c_5873,plain,
~ inclusion_comparable(iPr_def_13,sK5),
inference(demodulation,[status(thm)],[c_664,c_5845]) ).
tcf(c_5874,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_5873,c_1318]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET935+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/10.60 % Computer : n006.cluster.edu
% 0.12/10.60 % Model : x86_64 x86_64
% 0.12/10.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/10.60 % Memory : 8046.5625MB
% 0.12/10.60 % OS : Linux 6.8.0-71-generic
% 0.12/10.61 % CPULimit : 300
% 0.12/10.61 % WCLimit : 300
% 0.12/10.61 % DateTime : Thu Sep 24 12:24:10 UTC 2026
% 0.12/10.61 % CPUTime :
% 0.12/10.61 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/10.65 Running first-order theorem proving
% 0.12/10.65 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
% 0.12/10.66
% 0.12/10.66 % ======== iProver multi-core TPTP/SMT =========
% 0.12/10.66
% 0.12/10.66 % Detected problem language: tptp
% 0.12/10.68 % Proving...
% 4.01/11.55 % SZS status Started for theBenchmark.p
% 4.01/11.55 % SZS status Theorem for theBenchmark.p
% 4.01/11.55
% 4.01/11.55 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.01/11.55
% 4.01/11.55 % ------ iProver source info
% 4.01/11.55
% 4.01/11.55 % git: date: 2026-07-19 20:42:38 +0200
% 4.01/11.55 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.01/11.55 % git: non_committed_changes: false
% 4.01/11.55
% 4.01/11.55 % ------ Parsing...
% 4.01/11.55 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.01/11.55
% 4.01/11.55 % ------ 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 %
% 4.01/11.55
% 4.01/11.55 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.01/11.55
% 4.01/11.55 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.01/11.55 % ------ Proving...
% 4.01/11.55 % ------ Problem Properties
% 4.01/11.55
% 4.01/11.55 %
% 4.01/11.55 % clauses 32
% 4.01/11.55 % conjectures 2
% 4.01/11.55 % EPR 12
% 4.01/11.55 % Horn 28
% 4.01/11.55 % unary 14
% 4.01/11.55 % binary 10
% 4.01/11.55 % lits 59
% 4.01/11.55 % lits eq 14
% 4.01/11.55 % fd_pure 0
% 4.01/11.55 % fd_pseudo 0
% 4.01/11.55 % fd_cond 0
% 4.01/11.55 % fd_pseudo_cond 6
% 4.01/11.55 % AC symbols 0
% 4.01/11.55
% 4.01/11.55 % ------ Schedule dynamic 5 is on
% 4.01/11.55
% 4.01/11.55 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.01/11.55
% 4.01/11.55
% 4.01/11.55 % ------
% 4.01/11.55 % Current options:
% 4.01/11.55 % ------
% 4.01/11.55
% 4.01/11.55
% 4.01/11.55 %
% 4.01/11.55
% 4.01/11.55 % ------ Proving...
% 4.01/11.55 %
% 4.01/11.55
% 4.01/11.55 % SZS status Theorem for theBenchmark.p
% 4.01/11.55
% 4.01/11.55 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.01/11.55
% 4.01/11.55
%------------------------------------------------------------------------------