%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET890+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 : n001.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 02:48:54 PM UTC 2026
% Result : Theorem 1.65s 1.06s
% Output : CNFRefutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 65 ( 16 unt; 2 def)
% Number of atoms : 244 ( 59 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 236 ( 94 ~; 97 |; 36 &)
% ( 7 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 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 : 8 ( 8 usr; 1 con; 0-2 aty)
% Number of variables : 118 ( 0 sgn 106 !; 12 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f3,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f4,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f5,axiom,
! [X0,X1] :
( X1 = union(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,X0)
& in(X2,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
fof(f6,axiom,
! [X0,X1] :
( in(X0,X1)
=> subset(X0,union(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l50_zfmisc_1) ).
fof(f10,conjecture,
! [X0] : union(singleton(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_zfmisc_1) ).
fof(f11,negated_conjecture,
~ ! [X0] : union(singleton(X0)) = X0,
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f14,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f15,plain,
! [X0,X1] :
( ~ in(X0,X1)
| subset(X0,union(X1)) ),
inference(ennf_transformation,[],[f6]) ).
fof(f16,plain,
? [X0] : union(singleton(X0)) != X0,
inference(ennf_transformation,[],[f11]) ).
fof(f17,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f18,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(flattening,[],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| X2 = X0 )
& ( X0 != X2
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| X2 = X0 )
& ( ~ in(X2,X1)
| X0 != X2 ) )
| X1 = singleton(X0) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f20,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| X0 = X3 )
& ( X0 != X3
| in(X3,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| X2 = X0 )
& ( ~ in(X2,X1)
| X0 != X2 ) )
| X1 = singleton(X0) ) ),
inference(rectify,[],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| X0 = X3 )
& ( X0 != X3
| in(X3,X1) ) ) )
& ( ( ( in(sK0(X0,X1),X1)
| sK0(X0,X1) = X0 )
& ( ~ in(sK0(X0,X1),X1)
| sK0(X0,X1) != X0 ) )
| X1 = singleton(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f23,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(rectify,[],[f22]) ).
fof(f24,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK1(X0,X1),X0)
& ~ in(sK1(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f23]) ).
fof(f25,plain,
! [X0,X1] :
( ( union(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| ? [X3] :
( in(X3,X0)
& in(X2,X3) ) )
& ( ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) )
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X3] :
( in(X3,X0)
& in(X2,X3) ) )
& ( ~ in(X2,X1)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) ) ) )
| X1 = union(X0) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f26,plain,
! [X0,X1] :
( ( union(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ? [X7] :
( in(X7,X0)
& in(X5,X7) ) )
& ( ! [X6] :
( ~ in(X6,X0)
| ~ in(X5,X6) )
| in(X5,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X4] :
( in(X4,X0)
& in(X2,X4) ) )
& ( ~ in(X2,X1)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) ) ) )
| X1 = union(X0) ) ),
inference(rectify,[],[f25]) ).
fof(f27,plain,
! [X0,X1] :
( ( union(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ( in(sK4(X0,X5),X0)
& in(X5,sK4(X0,X5)) ) )
& ( ! [X6] :
( ~ in(X6,X0)
| ~ in(X5,X6) )
| in(X5,X1) ) ) )
& ( ( ( in(sK2(X0,X1),X1)
| ( in(sK3(X0,X1),X0)
& in(sK2(X0,X1),sK3(X0,X1)) ) )
& ( ~ in(sK2(X0,X1),X1)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(sK2(X0,X1),X3) ) ) )
| X1 = union(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X2,sK2(X0,X1)),skolemize(X4,sK3(X0,X1)),skolemize(X7,sK4(X0,X5))],[f26]) ).
fof(f30,plain,
sK7 != union(singleton(sK7)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X0,sK7)],[f16]) ).
fof(f34,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f18]) ).
fof(f35,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| ~ in(X3,X1)
| X0 = X3 ),
inference(cnf_transformation,[],[f21]) ).
fof(f36,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| X0 != X3
| in(X3,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f40,plain,
! [X0,X1] :
( in(sK1(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f41,plain,
! [X0,X1] :
( ~ in(sK1(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f42,plain,
! [X0,X1,X5] :
( union(X0) != X1
| ~ in(X5,X1)
| in(sK4(X0,X5),X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f43,plain,
! [X0,X1,X5] :
( union(X0) != X1
| ~ in(X5,X1)
| in(X5,sK4(X0,X5)) ),
inference(cnf_transformation,[],[f27]) ).
fof(f48,plain,
! [X0,X1] :
( ~ in(X0,X1)
| subset(X0,union(X1)) ),
inference(cnf_transformation,[],[f15]) ).
fof(f52,plain,
sK7 != union(singleton(sK7)),
inference(cnf_transformation,[],[f30]) ).
fof(f55,plain,
! [X3,X1] :
( singleton(X3) != X1
| in(X3,X1) ),
inference(equality_resolution,[],[f36]) ).
fof(f56,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f55]) ).
fof(f57,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f35]) ).
fof(f59,plain,
! [X0,X5] :
( ~ in(X5,union(X0))
| in(X5,sK4(X0,X5)) ),
inference(equality_resolution,[],[f43]) ).
fof(f60,plain,
! [X0,X5] :
( ~ in(X5,union(X0))
| in(sK4(X0,X5),X0) ),
inference(equality_resolution,[],[f42]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_55,plain,
! [X0: $i] : in(X0,singleton(X0)),
inference(cnf_transformation,[],[f56]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK1(X0,X1),X1) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( in(X0,sK4(X1,X0))
| ~ in(X0,union(X1)) ),
inference(cnf_transformation,[],[f59]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( in(sK4(X1,X0),X1)
| ~ in(X0,union(X1)) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( subset(X0,union(X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_70,negated_conjecture,
union(singleton(sK7)) != sK7,
inference(cnf_transformation,[],[f52]) ).
tcf(c_429,definition,
iPr_def_10 = singleton(sK7),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_430,definition,
iPr_def_11 = union(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_431,negated_conjecture,
iPr_def_11 != sK7,
inference(demodulation,[status(thm)],[c_70,c_429,c_430]) ).
tcf(c_685,plain,
in(sK7,iPr_def_10),
inference(superposition,[status(thm)],[c_429,c_55]) ).
tcf(c_708,plain,
! [X0: $i] :
( subset(X0,iPr_def_11)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_430,c_66]) ).
tcf(c_711,plain,
( subset(sK7,iPr_def_11)
| ~ in(sK7,iPr_def_10) ),
inference(instantiation,[status(thm)],[c_708]) ).
tcf(c_718,plain,
! [X0: $i] :
( ( X0 = sK7 )
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_429,c_56]) ).
tcf(c_735,plain,
subset(sK7,iPr_def_11),
inference(superposition,[status(thm)],[c_685,c_708]) ).
tcf(c_774,plain,
! [X0: $i] :
( ( sK4(iPr_def_10,X0) = sK7 )
| ~ in(X0,union(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_65,c_718]) ).
tcf(c_779,plain,
! [X0: $i] :
( ( sK4(iPr_def_10,X0) = sK7 )
| ~ in(X0,iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_774,c_430]) ).
tcf(c_798,plain,
! [X0: $i] :
( subset(iPr_def_11,X0)
| ( sK4(iPr_def_10,sK1(iPr_def_11,X0)) = sK7 ) ),
inference(superposition,[status(thm)],[c_58,c_779]) ).
tcf(c_881,plain,
( ( sK7 = iPr_def_11 )
| ~ subset(iPr_def_11,sK7) ),
inference(superposition,[status(thm)],[c_735,c_50]) ).
tcf(c_903,plain,
( ( iPr_def_11 = sK7 )
| ~ subset(iPr_def_11,sK7)
| ~ subset(sK7,iPr_def_11) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_1019,plain,
( subset(iPr_def_11,sK7)
| in(sK1(iPr_def_11,sK7),iPr_def_11) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_1020,plain,
( subset(iPr_def_11,sK7)
| ~ in(sK1(iPr_def_11,sK7),sK7) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_1045,plain,
~ subset(iPr_def_11,sK7),
inference(global_subsumption_just,[status(thm)],[c_881,c_431,c_685,c_711,c_903]) ).
tcf(c_1832,plain,
sK4(iPr_def_10,sK1(iPr_def_11,sK7)) = sK7,
inference(superposition,[status(thm)],[c_798,c_1045]) ).
tcf(c_1928,plain,
( in(sK1(iPr_def_11,sK7),sK7)
| ~ in(sK1(iPr_def_11,sK7),union(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_1832,c_64]) ).
tcf(c_1932,plain,
( in(sK1(iPr_def_11,sK7),sK7)
| ~ in(sK1(iPr_def_11,sK7),iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_1928,c_430]) ).
tcf(c_1938,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1932,c_1019,c_1020,c_903,c_711,c_685,c_431]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET890+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.35 % Computer : n001.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Thu Sep 24 12:26:09 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 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
% 0.14/0.40
% 0.14/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.40
% 0.14/0.40 % Detected problem language: tptp
% 0.14/0.41 % Proving...
% 1.65/1.06 % SZS status Started for theBenchmark.p
% 1.65/1.06 % SZS status Theorem for theBenchmark.p
% 1.65/1.06
% 1.65/1.06 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.65/1.06
% 1.65/1.06 % ------ iProver source info
% 1.65/1.06
% 1.65/1.06 % git: date: 2026-07-19 20:42:38 +0200
% 1.65/1.06 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.65/1.06 % git: non_committed_changes: false
% 1.65/1.06
% 1.65/1.06 % ------ Parsing...
% 1.65/1.06 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.65/1.06
% 1.65/1.06 % ------ 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 %
% 1.65/1.06
% 1.65/1.06 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.65/1.06
% 1.65/1.06 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.65/1.06 % ------ Proving...
% 1.65/1.06 % ------ Problem Properties
% 1.65/1.06
% 1.65/1.06 %
% 1.65/1.06 % clauses 21
% 1.65/1.06 % conjectures 1
% 1.65/1.06 % EPR 6
% 1.65/1.06 % Horn 17
% 1.65/1.06 % unary 6
% 1.65/1.06 % binary 7
% 1.65/1.06 % lits 45
% 1.65/1.06 % lits eq 13
% 1.65/1.06 % fd_pure 0
% 1.65/1.06 % fd_pseudo 0
% 1.65/1.06 % fd_cond 0
% 1.65/1.06 % fd_pseudo_cond 6
% 1.65/1.06 % AC symbols 0
% 1.65/1.06
% 1.65/1.06 % ------ Schedule dynamic 5 is on
% 1.65/1.06
% 1.65/1.06 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.65/1.06
% 1.65/1.06
% 1.65/1.06 % ------
% 1.65/1.06 % Current options:
% 1.65/1.06 % ------
% 1.65/1.06
% 1.65/1.06
% 1.65/1.06 %
% 1.65/1.06
% 1.65/1.06 % ------ Proving...
% 1.65/1.06 %
% 1.65/1.06
% 1.65/1.06 % SZS status Theorem for theBenchmark.p
% 1.65/1.06
% 1.65/1.06 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.65/1.06
% 1.65/1.06
%------------------------------------------------------------------------------