%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET942+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n013.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 02:49:10 PM UTC 2026
% Result : Theorem 3.15s 1.28s
% Output : CNFRefutation 3.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 45 ( 10 unt; 2 def)
% Number of atoms : 159 ( 12 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 169 ( 69 ~; 69 |; 24 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 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 : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 100 ( 0 sgn 89 !; 11 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f3,axiom,
! [X0,X1] :
( X1 = union(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,X0)
& in(X2,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
fof(f7,conjecture,
! [X0,X1] :
( subset(X0,X1)
=> subset(union(X0),union(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t95_zfmisc_1) ).
fof(f8,negated_conjecture,
~ ! [X0,X1] :
( subset(X0,X1)
=> subset(union(X0),union(X1)) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f11,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f12,plain,
? [X0,X1] :
( subset(X0,X1)
& ~ subset(union(X0),union(X1)) ),
inference(ennf_transformation,[],[f8]) ).
fof(f13,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,[],[f11]) ).
fof(f14,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,[],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK0(X0,X1),X0)
& ~ in(sK0(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f14]) ).
fof(f16,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,[],[f3]) ).
fof(f17,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,[],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( ( union(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ( in(sK3(X0,X5),X0)
& in(X5,sK3(X0,X5)) ) )
& ( ! [X6] :
( ~ in(X6,X0)
| ~ in(X5,X6) )
| in(X5,X1) ) ) )
& ( ( ( in(sK1(X0,X1),X1)
| ( in(sK2(X0,X1),X0)
& in(sK1(X0,X1),sK2(X0,X1)) ) )
& ( ~ in(sK1(X0,X1),X1)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(sK1(X0,X1),X3) ) ) )
| X1 = union(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X2,sK1(X0,X1)),skolemize(X4,sK2(X0,X1)),skolemize(X7,sK3(X0,X5))],[f17]) ).
fof(f21,plain,
( subset(sK6,sK7)
& ~ subset(union(sK6),union(sK7)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X0,sK6),skolemize(X1,sK7)],[f12]) ).
fof(f23,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f24,plain,
! [X0,X1] :
( in(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f25,plain,
! [X0,X1] :
( ~ in(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f26,plain,
! [X0,X1,X5] :
( union(X0) != X1
| ~ in(X5,X1)
| in(sK3(X0,X5),X0) ),
inference(cnf_transformation,[],[f18]) ).
fof(f27,plain,
! [X0,X1,X5] :
( union(X0) != X1
| ~ in(X5,X1)
| in(X5,sK3(X0,X5)) ),
inference(cnf_transformation,[],[f18]) ).
fof(f28,plain,
! [X0,X1,X6,X5] :
( union(X0) != X1
| ~ in(X6,X0)
| ~ in(X5,X6)
| in(X5,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f35,plain,
subset(sK6,sK7),
inference(cnf_transformation,[],[f21]) ).
fof(f36,plain,
~ subset(union(sK6),union(sK7)),
inference(cnf_transformation,[],[f21]) ).
fof(f37,plain,
! [X0,X6,X5] :
( ~ in(X6,X0)
| ~ in(X5,X6)
| in(X5,union(X0)) ),
inference(equality_resolution,[],[f28]) ).
fof(f38,plain,
! [X0,X5] :
( ~ in(X5,union(X0))
| in(X5,sK3(X0,X5)) ),
inference(equality_resolution,[],[f27]) ).
fof(f39,plain,
! [X0,X5] :
( ~ in(X5,union(X0))
| in(sK3(X0,X5),X0) ),
inference(equality_resolution,[],[f26]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,union(X2))
| ~ in(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( in(X0,sK3(X1,X0))
| ~ in(X0,union(X1)) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( in(sK3(X1,X0),X1)
| ~ in(X0,union(X1)) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_62,negated_conjecture,
~ subset(union(sK6),union(sK7)),
inference(cnf_transformation,[],[f36]) ).
tcf(c_63,negated_conjecture,
subset(sK6,sK7),
inference(cnf_transformation,[],[f35]) ).
tcf(c_444,definition,
iPr_def_10 = union(sK6),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_445,definition,
iPr_def_11 = union(sK7),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_446,negated_conjecture,
subset(sK6,sK7),
inference(demodulation,[status(thm)],[c_63]) ).
tcf(c_447,negated_conjecture,
~ subset(iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_62,c_445,c_444]) ).
tcf(c_681,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X1,X0),X2)
| ~ subset(X1,X2)
| ~ in(X0,union(X1)) ),
inference(superposition,[status(thm)],[c_58,c_52]) ).
tcf(c_699,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,union(X2))
| ~ in(X1,union(X0))
| ~ in(sK3(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_57,c_56]) ).
tcf(c_1352,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,union(X2))
| ~ subset(X1,X2)
| ~ in(X0,union(X1)) ),
inference(superposition,[status(thm)],[c_681,c_699]) ).
tcf(c_1605,plain,
! [X0: $i,X1: $i] :
( in(X0,union(X1))
| ~ subset(sK6,X1)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_444,c_1352]) ).
tcf(c_1684,plain,
! [X0: $i] :
( in(X0,iPr_def_11)
| ~ subset(sK6,sK7)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_445,c_1605]) ).
tcf(c_1695,plain,
! [X0: $i] :
( in(X0,iPr_def_11)
| ~ in(X0,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1684,c_446]) ).
tcf(c_1796,plain,
! [X0: $i] :
( subset(iPr_def_10,X0)
| in(sK0(iPr_def_10,X0),iPr_def_11) ),
inference(superposition,[status(thm)],[c_51,c_1695]) ).
tcf(c_1872,plain,
subset(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_1796,c_50]) ).
tcf(c_1873,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1872,c_447]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET942+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n013.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 12:25:21 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.41 Running first-order theorem proving
% 0.08/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/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...
% 3.15/1.28 % SZS status Started for theBenchmark.p
% 3.15/1.28 % SZS status Theorem for theBenchmark.p
% 3.15/1.28
% 3.15/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.15/1.28
% 3.15/1.28 % ------ iProver source info
% 3.15/1.28
% 3.15/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 3.15/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.15/1.28 % git: non_committed_changes: false
% 3.15/1.28
% 3.15/1.28 % ------ Parsing...
% 3.15/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.15/1.28
% 3.15/1.28 % ------ 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 %
% 3.15/1.28
% 3.15/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.15/1.28
% 3.15/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.15/1.28 % ------ Proving...
% 3.15/1.28 % ------ Problem Properties
% 3.15/1.28
% 3.15/1.28 %
% 3.15/1.28 % clauses 16
% 3.15/1.28 % conjectures 2
% 3.15/1.28 % EPR 6
% 3.15/1.28 % Horn 13
% 3.15/1.28 % unary 6
% 3.15/1.28 % binary 5
% 3.15/1.28 % lits 32
% 3.15/1.28 % lits eq 6
% 3.15/1.28 % fd_pure 0
% 3.15/1.28 % fd_pseudo 0
% 3.15/1.28 % fd_cond 0
% 3.15/1.28 % fd_pseudo_cond 3
% 3.15/1.28 % AC symbols 0
% 3.15/1.28
% 3.15/1.28 % ------ Schedule dynamic 5 is on
% 3.15/1.28
% 3.15/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.15/1.28
% 3.15/1.28
% 3.15/1.28 % ------
% 3.15/1.28 % Current options:
% 3.15/1.28 % ------
% 3.15/1.28
% 3.15/1.28
% 3.15/1.28 %
% 3.15/1.28
% 3.15/1.28 % ------ Proving...
% 3.15/1.28 %
% 3.15/1.28
% 3.15/1.28 % SZS status Theorem for theBenchmark.p
% 3.15/1.28
% 3.15/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.15/1.28
% 3.15/1.28
%------------------------------------------------------------------------------