%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU094+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 : n005.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 02:55:24 PM UTC 2026
% Result : Theorem 2.83s 1.28s
% Output : CNFRefutation 2.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 7
% Syntax : Number of formulae : 63 ( 9 unt; 1 def)
% Number of atoms : 194 ( 3 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 203 ( 85 ~; 87 |; 21 &)
% ( 3 <=>; 6 =>; 0 <=; 1 <~>)
% Maximal formula depth : 10 ( 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 : 6 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-1 aty)
% Number of variables : 65 ( 0 sgn 56 !; 9 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
fof(f21,axiom,
! [X0] :
( ( ! [X1] :
( in(X1,X0)
=> finite(X1) )
& finite(X0) )
=> finite(union(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l22_finset_1) ).
fof(f48,axiom,
! [X0] : subset(X0,powerset(union(X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t100_zfmisc_1) ).
fof(f49,axiom,
! [X0,X1] :
( ( finite(X1)
& subset(X0,X1) )
=> finite(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_finset_1) ).
fof(f51,axiom,
! [X0] :
( finite(X0)
<=> finite(powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_finset_1) ).
fof(f52,conjecture,
! [X0] :
( ( ! [X1] :
( in(X1,X0)
=> finite(X1) )
& finite(X0) )
<=> finite(union(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_finset_1) ).
fof(f53,negated_conjecture,
~ ! [X0] :
( ( ! [X1] :
( in(X1,X0)
=> finite(X1) )
& finite(X0) )
<=> finite(union(X0)) ),
inference(negated_conjecture,[status(cth)],[f52]) ).
fof(f61,axiom,
! [X0,X1] :
( in(X0,X1)
=> subset(X0,union(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_zfmisc_1) ).
fof(f100,plain,
! [X0] :
( ? [X1] :
( in(X1,X0)
& ~ finite(X1) )
| ~ finite(X0)
| finite(union(X0)) ),
inference(ennf_transformation,[],[f21]) ).
fof(f101,plain,
! [X0] :
( ? [X1] :
( in(X1,X0)
& ~ finite(X1) )
| ~ finite(X0)
| finite(union(X0)) ),
inference(flattening,[],[f100]) ).
fof(f104,plain,
! [X0,X1] :
( ~ finite(X1)
| ~ subset(X0,X1)
| finite(X0) ),
inference(ennf_transformation,[],[f49]) ).
fof(f105,plain,
! [X0,X1] :
( ~ finite(X1)
| ~ subset(X0,X1)
| finite(X0) ),
inference(flattening,[],[f104]) ).
fof(f107,plain,
? [X0] :
( ( ! [X1] :
( ~ in(X1,X0)
| finite(X1) )
& finite(X0) )
<~> finite(union(X0)) ),
inference(ennf_transformation,[],[f53]) ).
fof(f116,plain,
! [X0,X1] :
( ~ in(X0,X1)
| subset(X0,union(X1)) ),
inference(ennf_transformation,[],[f61]) ).
fof(f118,plain,
! [X0] :
( ( in(sK1(X0),X0)
& ~ finite(sK1(X0)) )
| ~ finite(X0)
| finite(union(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1(X0))],[f101]) ).
fof(f144,plain,
! [X0] :
( ( ~ finite(X0)
| finite(powerset(X0)) )
& ( ~ finite(powerset(X0))
| finite(X0) ) ),
inference(nnf_transformation,[],[f51]) ).
fof(f145,plain,
? [X0] :
( ( ( ! [X1] :
( ~ in(X1,X0)
| finite(X1) )
& finite(X0) )
| finite(union(X0)) )
& ( ? [X1] :
( in(X1,X0)
& ~ finite(X1) )
| ~ finite(X0)
| ~ finite(union(X0)) ) ),
inference(nnf_transformation,[],[f107]) ).
fof(f146,plain,
? [X0] :
( ( ( ! [X1] :
( ~ in(X1,X0)
| finite(X1) )
& finite(X0) )
| finite(union(X0)) )
& ( ? [X1] :
( in(X1,X0)
& ~ finite(X1) )
| ~ finite(X0)
| ~ finite(union(X0)) ) ),
inference(flattening,[],[f145]) ).
fof(f147,plain,
? [X0] :
( ( ( ! [X2] :
( ~ in(X2,X0)
| finite(X2) )
& finite(X0) )
| finite(union(X0)) )
& ( ? [X1] :
( in(X1,X0)
& ~ finite(X1) )
| ~ finite(X0)
| ~ finite(union(X0)) ) ),
inference(rectify,[],[f146]) ).
fof(f148,plain,
( ( ( ! [X2] :
( ~ in(X2,sK27)
| finite(X2) )
& finite(sK27) )
| finite(union(sK27)) )
& ( ( in(sK28,sK27)
& ~ finite(sK28) )
| ~ finite(sK27)
| ~ finite(union(sK27)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27,sK28]),skolemize(X0,sK27),skolemize(X1,sK28)],[f147]) ).
fof(f189,plain,
! [X0] :
( in(sK1(X0),X0)
| ~ finite(X0)
| finite(union(X0)) ),
inference(cnf_transformation,[],[f118]) ).
fof(f190,plain,
! [X0] :
( ~ finite(sK1(X0))
| ~ finite(X0)
| finite(union(X0)) ),
inference(cnf_transformation,[],[f118]) ).
fof(f263,plain,
! [X0] : subset(X0,powerset(union(X0))),
inference(cnf_transformation,[],[f48]) ).
fof(f264,plain,
! [X0,X1] :
( ~ finite(X1)
| ~ subset(X0,X1)
| finite(X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f266,plain,
! [X0] :
( ~ finite(X0)
| finite(powerset(X0)) ),
inference(cnf_transformation,[],[f144]) ).
fof(f268,plain,
! [X2] :
( ~ in(X2,sK27)
| finite(X2)
| finite(union(sK27)) ),
inference(cnf_transformation,[],[f148]) ).
fof(f269,plain,
( finite(sK27)
| finite(union(sK27)) ),
inference(cnf_transformation,[],[f148]) ).
fof(f270,plain,
( in(sK28,sK27)
| ~ finite(sK27)
| ~ finite(union(sK27)) ),
inference(cnf_transformation,[],[f148]) ).
fof(f271,plain,
( ~ finite(sK28)
| ~ finite(sK27)
| ~ finite(union(sK27)) ),
inference(cnf_transformation,[],[f148]) ).
fof(f280,plain,
! [X0,X1] :
( ~ in(X0,X1)
| subset(X0,union(X1)) ),
inference(cnf_transformation,[],[f116]) ).
tcf(c_84,plain,
! [X0: $i] :
( finite(union(X0))
| ~ finite(X0)
| ~ finite(sK1(X0)) ),
inference(cnf_transformation,[],[f190]) ).
tcf(c_85,plain,
! [X0: $i] :
( finite(union(X0))
| in(sK1(X0),X0)
| ~ finite(X0) ),
inference(cnf_transformation,[],[f189]) ).
tcf(c_158,plain,
! [X0: $i] : subset(X0,powerset(union(X0))),
inference(cnf_transformation,[],[f263]) ).
tcf(c_159,plain,
! [X0: $i,X1: $i] :
( finite(X0)
| ~ finite(X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f264]) ).
tcf(c_162,plain,
! [X0: $i] :
( finite(powerset(X0))
| ~ finite(X0) ),
inference(cnf_transformation,[],[f266]) ).
tcf(c_163,negated_conjecture,
( ~ finite(sK28)
| ~ finite(sK27)
| ~ finite(union(sK27)) ),
inference(cnf_transformation,[],[f271]) ).
tcf(c_164,negated_conjecture,
( in(sK28,sK27)
| ~ finite(sK27)
| ~ finite(union(sK27)) ),
inference(cnf_transformation,[],[f270]) ).
tcf(c_165,negated_conjecture,
( finite(sK27)
| finite(union(sK27)) ),
inference(cnf_transformation,[],[f269]) ).
tcf(c_166,negated_conjecture,
! [X0: $i] :
( finite(X0)
| finite(union(sK27))
| ~ in(X0,sK27) ),
inference(cnf_transformation,[],[f268]) ).
tcf(c_175,plain,
! [X0: $i,X1: $i] :
( subset(X0,union(X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f280]) ).
tcf(c_227,plain,
! [X0: $i,X1: $i] :
( subset(X0,union(X1))
| ~ in(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_175]) ).
tcf(c_1038,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( finite(X0)
| ~ finite(X3)
| ~ in(X1,X2)
| ( X0 != X1 )
| ( union(X2) != X3 ) ),
inference(resolution_lifted,[status(thm)],[c_159,c_227]) ).
tcf(c_1039,plain,
! [X0: $i,X1: $i] :
( finite(X0)
| ~ finite(union(X1))
| ~ in(X0,X1) ),
inference(unflattening,[status(thm)],[c_1038]) ).
tcf(c_1110,plain,
! [X0: $i] :
( finite(X0)
| ~ in(X0,sK27) ),
inference(backward_subsumption_resolution,[status(thm)],[c_166,c_1039]) ).
tcf(c_1377,plain,
! [X0: $i] :
( ~ in(X0,sK27)
| finite(X0) ),
inference(prop_impl_just,[status(thm)],[c_1110]) ).
tcf(c_1378,plain,
! [X0: $i] :
( finite(X0)
| ~ in(X0,sK27) ),
inference(renaming,[status(thm)],[c_1377]) ).
tcf(c_2105,definition,
iPr_def_10 = union(sK27),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2106,negated_conjecture,
( finite(iPr_def_10)
| finite(sK27) ),
inference(demodulation,[status(thm)],[c_165,c_2105]) ).
tcf(c_2107,negated_conjecture,
( in(sK28,sK27)
| ~ finite(iPr_def_10)
| ~ finite(sK27) ),
inference(demodulation,[status(thm)],[c_164]) ).
tcf(c_2108,negated_conjecture,
( ~ finite(iPr_def_10)
| ~ finite(sK28)
| ~ finite(sK27) ),
inference(demodulation,[status(thm)],[c_163]) ).
tcf(c_2891,plain,
( finite(sK28)
| ~ finite(iPr_def_10)
| ~ finite(sK27) ),
inference(superposition,[status(thm)],[c_2107,c_1378]) ).
tcf(c_2895,plain,
( ~ finite(sK27)
| ~ finite(iPr_def_10) ),
inference(global_subsumption_just,[status(thm)],[c_2891,c_2108,c_2891]) ).
tcf(c_2896,plain,
( ~ finite(iPr_def_10)
| ~ finite(sK27) ),
inference(renaming,[status(thm)],[c_2895]) ).
tcf(c_2919,plain,
subset(sK27,powerset(iPr_def_10)),
inference(superposition,[status(thm)],[c_2105,c_158]) ).
tcf(c_3022,plain,
( finite(sK27)
| ~ finite(powerset(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_2919,c_159]) ).
tcf(c_3052,plain,
( finite(sK27)
| ~ finite(iPr_def_10) ),
inference(superposition,[status(thm)],[c_162,c_3022]) ).
tcf(c_3055,plain,
finite(sK27),
inference(global_subsumption_just,[status(thm)],[c_3052,c_2106,c_3052]) ).
tcf(c_3057,plain,
~ finite(iPr_def_10),
inference(backward_subsumption_resolution,[status(thm)],[c_2896,c_3055]) ).
tcf(c_3136,plain,
( finite(sK1(sK27))
| finite(union(sK27))
| ~ finite(sK27) ),
inference(superposition,[status(thm)],[c_85,c_1378]) ).
tcf(c_3137,plain,
( finite(iPr_def_10)
| finite(sK1(sK27))
| ~ finite(sK27) ),
inference(light_normalisation,[status(thm)],[c_3136,c_2105]) ).
tcf(c_3138,plain,
finite(sK1(sK27)),
inference(forward_subsumption_resolution,[status(thm)],[c_3137,c_3057,c_3055]) ).
tcf(c_3170,plain,
( finite(union(sK27))
| ~ finite(sK27) ),
inference(superposition,[status(thm)],[c_3138,c_84]) ).
tcf(c_3171,plain,
( finite(iPr_def_10)
| ~ finite(sK27) ),
inference(light_normalisation,[status(thm)],[c_3170,c_2105]) ).
tcf(c_3172,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3171,c_3057,c_3055]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU094+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n005.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 12:43:47 UTC 2026
% 0.14/0.37 % CPUTime :
% 0.14/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 0.14/0.42
% 0.14/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.42
% 0.14/0.42 % Detected problem language: tptp
% 0.14/0.43 % Proving...
% 2.83/1.28 % SZS status Started for theBenchmark.p
% 2.83/1.28 % SZS status Theorem for theBenchmark.p
% 2.83/1.28
% 2.83/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.83/1.28
% 2.83/1.28 % ------ iProver source info
% 2.83/1.28
% 2.83/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 2.83/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.83/1.28 % git: non_committed_changes: false
% 2.83/1.28
% 2.83/1.28 % ------ Parsing...
% 2.83/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.83/1.28
% 2.83/1.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 72 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 6 0s sf_e pe_s pe_e %
% 2.83/1.28
% 2.83/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.83/1.28
% 2.83/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.83/1.28 % ------ Proving...
% 2.83/1.28 % ------ Problem Properties
% 2.83/1.28
% 2.83/1.28 %
% 2.83/1.28 % clauses 52
% 2.83/1.28 % conjectures 3
% 2.83/1.28 % EPR 31
% 2.83/1.28 % Horn 46
% 2.83/1.28 % unary 26
% 2.83/1.28 % binary 17
% 2.83/1.28 % lits 87
% 2.83/1.28 % lits eq 3
% 2.83/1.28 % fd_pure 0
% 2.83/1.28 % fd_pseudo 0
% 2.83/1.28 % fd_cond 1
% 2.83/1.28 % fd_pseudo_cond 1
% 2.83/1.28 % AC symbols 0
% 2.83/1.28
% 2.83/1.28 % ------ Schedule dynamic 5 is on
% 2.83/1.28
% 2.83/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.83/1.28
% 2.83/1.28
% 2.83/1.28 % ------
% 2.83/1.28 % Current options:
% 2.83/1.28 % ------
% 2.83/1.28
% 2.83/1.28
% 2.83/1.28 %
% 2.83/1.28
% 2.83/1.28 % ------ Proving...
% 2.83/1.28 %
% 2.83/1.28
% 2.83/1.28 % SZS status Theorem for theBenchmark.p
% 2.83/1.28
% 2.83/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.83/1.28
% 2.83/1.28
%------------------------------------------------------------------------------