TSTP Solution File: SET018+1 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET018+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 15:05:33 EDT 2023
% Result : Theorem 1.38s 1.17s
% Output : CNFRefutation 1.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 6
% Syntax : Number of formulae : 77 ( 26 unt; 0 def)
% Number of atoms : 180 ( 102 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 148 ( 45 ~; 76 |; 21 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 75 ( 4 sgn; 49 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X2,X0,X1] :
( member(X2,unordered_pair(X0,X1))
<=> ( ( X1 = X2
| X0 = X2 )
& member(X2,universal_class) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_defn) ).
fof(f5,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair) ).
fof(f6,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set_defn) ).
fof(f7,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair_defn) ).
fof(f44,conjecture,
! [X6,X0,X1,X4] :
( ( member(X0,universal_class)
& ordered_pair(X6,X0) = ordered_pair(X1,X4) )
=> X0 = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair_determines_components2) ).
fof(f45,negated_conjecture,
~ ! [X6,X0,X1,X4] :
( ( member(X0,universal_class)
& ordered_pair(X6,X0) = ordered_pair(X1,X4) )
=> X0 = X4 ),
inference(negated_conjecture,[],[f44]) ).
fof(f46,plain,
! [X0,X1,X2] :
( member(X0,unordered_pair(X1,X2))
<=> ( ( X0 = X2
| X0 = X1 )
& member(X0,universal_class) ) ),
inference(rectify,[],[f4]) ).
fof(f70,plain,
~ ! [X0,X1,X2,X3] :
( ( member(X1,universal_class)
& ordered_pair(X0,X1) = ordered_pair(X2,X3) )
=> X1 = X3 ),
inference(rectify,[],[f45]) ).
fof(f85,plain,
? [X0,X1,X2,X3] :
( X1 != X3
& member(X1,universal_class)
& ordered_pair(X0,X1) = ordered_pair(X2,X3) ),
inference(ennf_transformation,[],[f70]) ).
fof(f86,plain,
? [X0,X1,X2,X3] :
( X1 != X3
& member(X1,universal_class)
& ordered_pair(X0,X1) = ordered_pair(X2,X3) ),
inference(flattening,[],[f85]) ).
fof(f93,plain,
! [X0,X1,X2] :
( ( member(X0,unordered_pair(X1,X2))
| ( X0 != X2
& X0 != X1 )
| ~ member(X0,universal_class) )
& ( ( ( X0 = X2
| X0 = X1 )
& member(X0,universal_class) )
| ~ member(X0,unordered_pair(X1,X2)) ) ),
inference(nnf_transformation,[],[f46]) ).
fof(f94,plain,
! [X0,X1,X2] :
( ( member(X0,unordered_pair(X1,X2))
| ( X0 != X2
& X0 != X1 )
| ~ member(X0,universal_class) )
& ( ( ( X0 = X2
| X0 = X1 )
& member(X0,universal_class) )
| ~ member(X0,unordered_pair(X1,X2)) ) ),
inference(flattening,[],[f93]) ).
fof(f135,plain,
( ? [X0,X1,X2,X3] :
( X1 != X3
& member(X1,universal_class)
& ordered_pair(X0,X1) = ordered_pair(X2,X3) )
=> ( sK7 != sK9
& member(sK7,universal_class)
& ordered_pair(sK6,sK7) = ordered_pair(sK8,sK9) ) ),
introduced(choice_axiom,[]) ).
fof(f136,plain,
( sK7 != sK9
& member(sK7,universal_class)
& ordered_pair(sK6,sK7) = ordered_pair(sK8,sK9) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9])],[f86,f135]) ).
fof(f145,plain,
! [X2,X0,X1] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f94]) ).
fof(f146,plain,
! [X2,X0,X1] :
( member(X0,unordered_pair(X1,X2))
| X0 != X1
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f94]) ).
fof(f147,plain,
! [X2,X0,X1] :
( member(X0,unordered_pair(X1,X2))
| X0 != X2
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f94]) ).
fof(f148,plain,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[],[f5]) ).
fof(f149,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f150,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
inference(cnf_transformation,[],[f7]) ).
fof(f224,plain,
ordered_pair(sK6,sK7) = ordered_pair(sK8,sK9),
inference(cnf_transformation,[],[f136]) ).
fof(f225,plain,
member(sK7,universal_class),
inference(cnf_transformation,[],[f136]) ).
fof(f226,plain,
sK7 != sK9,
inference(cnf_transformation,[],[f136]) ).
fof(f227,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
inference(definition_unfolding,[],[f150,f149,f149]) ).
fof(f264,plain,
unordered_pair(unordered_pair(sK6,sK6),unordered_pair(sK6,unordered_pair(sK7,sK7))) = unordered_pair(unordered_pair(sK8,sK8),unordered_pair(sK8,unordered_pair(sK9,sK9))),
inference(definition_unfolding,[],[f224,f227,f227]) ).
fof(f267,plain,
! [X2,X1] :
( member(X2,unordered_pair(X1,X2))
| ~ member(X2,universal_class) ),
inference(equality_resolution,[],[f147]) ).
fof(f268,plain,
! [X2,X1] :
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
inference(equality_resolution,[],[f146]) ).
cnf(c_56,plain,
( ~ member(X0,universal_class)
| member(X0,unordered_pair(X1,X0)) ),
inference(cnf_transformation,[],[f267]) ).
cnf(c_57,plain,
( ~ member(X0,universal_class)
| member(X0,unordered_pair(X0,X1)) ),
inference(cnf_transformation,[],[f268]) ).
cnf(c_58,plain,
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
inference(cnf_transformation,[],[f145]) ).
cnf(c_60,plain,
member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[],[f148]) ).
cnf(c_128,negated_conjecture,
sK7 != sK9,
inference(cnf_transformation,[],[f226]) ).
cnf(c_129,negated_conjecture,
member(sK7,universal_class),
inference(cnf_transformation,[],[f225]) ).
cnf(c_130,negated_conjecture,
unordered_pair(unordered_pair(sK6,sK6),unordered_pair(sK6,unordered_pair(sK7,sK7))) = unordered_pair(unordered_pair(sK8,sK8),unordered_pair(sK8,unordered_pair(sK9,sK9))),
inference(cnf_transformation,[],[f264]) ).
cnf(c_2397,plain,
( ~ member(unordered_pair(sK8,unordered_pair(sK9,sK9)),universal_class)
| member(unordered_pair(sK8,unordered_pair(sK9,sK9)),unordered_pair(unordered_pair(sK6,sK6),unordered_pair(sK6,unordered_pair(sK7,sK7)))) ),
inference(superposition,[status(thm)],[c_130,c_56]) ).
cnf(c_2398,plain,
( ~ member(unordered_pair(sK8,sK8),universal_class)
| member(unordered_pair(sK8,sK8),unordered_pair(unordered_pair(sK6,sK6),unordered_pair(sK6,unordered_pair(sK7,sK7)))) ),
inference(superposition,[status(thm)],[c_130,c_57]) ).
cnf(c_2400,plain,
( ~ member(X0,unordered_pair(unordered_pair(sK6,sK6),unordered_pair(sK6,unordered_pair(sK7,sK7))))
| unordered_pair(sK8,unordered_pair(sK9,sK9)) = X0
| unordered_pair(sK8,sK8) = X0 ),
inference(superposition,[status(thm)],[c_130,c_58]) ).
cnf(c_2412,plain,
member(unordered_pair(sK8,sK8),unordered_pair(unordered_pair(sK6,sK6),unordered_pair(sK6,unordered_pair(sK7,sK7)))),
inference(forward_subsumption_resolution,[status(thm)],[c_2398,c_60]) ).
cnf(c_2413,plain,
( unordered_pair(sK6,unordered_pair(sK7,sK7)) = unordered_pair(sK8,sK8)
| unordered_pair(sK6,sK6) = unordered_pair(sK8,sK8) ),
inference(superposition,[status(thm)],[c_2412,c_58]) ).
cnf(c_2418,plain,
member(unordered_pair(sK8,unordered_pair(sK9,sK9)),unordered_pair(unordered_pair(sK6,sK6),unordered_pair(sK6,unordered_pair(sK7,sK7)))),
inference(forward_subsumption_resolution,[status(thm)],[c_2397,c_60]) ).
cnf(c_2419,plain,
( unordered_pair(sK6,unordered_pair(sK7,sK7)) = unordered_pair(sK8,unordered_pair(sK9,sK9))
| unordered_pair(sK8,unordered_pair(sK9,sK9)) = unordered_pair(sK6,sK6) ),
inference(superposition,[status(thm)],[c_2418,c_58]) ).
cnf(c_2453,plain,
( ~ member(unordered_pair(sK6,unordered_pair(sK7,sK7)),universal_class)
| unordered_pair(sK6,unordered_pair(sK7,sK7)) = unordered_pair(sK8,unordered_pair(sK9,sK9))
| unordered_pair(sK6,unordered_pair(sK7,sK7)) = unordered_pair(sK8,sK8) ),
inference(superposition,[status(thm)],[c_56,c_2400]) ).
cnf(c_2462,plain,
( ~ member(sK6,universal_class)
| unordered_pair(sK6,sK6) = unordered_pair(sK8,sK8)
| member(sK6,unordered_pair(sK8,sK8)) ),
inference(superposition,[status(thm)],[c_2413,c_57]) ).
cnf(c_2489,plain,
( ~ member(unordered_pair(sK9,sK9),universal_class)
| unordered_pair(sK8,unordered_pair(sK9,sK9)) = unordered_pair(sK6,sK6)
| member(unordered_pair(sK9,sK9),unordered_pair(sK6,unordered_pair(sK7,sK7))) ),
inference(superposition,[status(thm)],[c_2419,c_56]) ).
cnf(c_2548,plain,
( unordered_pair(sK6,unordered_pair(sK7,sK7)) = unordered_pair(sK8,unordered_pair(sK9,sK9))
| unordered_pair(sK6,unordered_pair(sK7,sK7)) = unordered_pair(sK8,sK8) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2453,c_60]) ).
cnf(c_2557,plain,
( ~ member(X0,unordered_pair(sK6,unordered_pair(sK7,sK7)))
| unordered_pair(sK6,unordered_pair(sK7,sK7)) = unordered_pair(sK8,sK8)
| unordered_pair(sK9,sK9) = X0
| X0 = sK8 ),
inference(superposition,[status(thm)],[c_2548,c_58]) ).
cnf(c_2580,plain,
( ~ member(sK6,universal_class)
| unordered_pair(sK6,sK6) = unordered_pair(sK8,sK8)
| sK6 = sK8 ),
inference(superposition,[status(thm)],[c_2462,c_58]) ).
cnf(c_2688,plain,
( unordered_pair(sK8,unordered_pair(sK9,sK9)) = unordered_pair(sK6,sK6)
| member(unordered_pair(sK9,sK9),unordered_pair(sK6,unordered_pair(sK7,sK7))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2489,c_60]) ).
cnf(c_2694,plain,
( unordered_pair(sK8,unordered_pair(sK9,sK9)) = unordered_pair(sK6,sK6)
| unordered_pair(sK7,sK7) = unordered_pair(sK9,sK9)
| unordered_pair(sK9,sK9) = sK6 ),
inference(superposition,[status(thm)],[c_2688,c_58]) ).
cnf(c_2871,plain,
( ~ member(unordered_pair(sK7,sK7),universal_class)
| unordered_pair(sK6,unordered_pair(sK7,sK7)) = unordered_pair(sK8,sK8)
| unordered_pair(sK7,sK7) = unordered_pair(sK9,sK9)
| unordered_pair(sK7,sK7) = sK8 ),
inference(superposition,[status(thm)],[c_56,c_2557]) ).
cnf(c_2950,plain,
( ~ member(unordered_pair(sK9,sK9),universal_class)
| unordered_pair(sK7,sK7) = unordered_pair(sK9,sK9)
| unordered_pair(sK9,sK9) = sK6
| member(unordered_pair(sK9,sK9),unordered_pair(sK6,sK6)) ),
inference(superposition,[status(thm)],[c_2694,c_56]) ).
cnf(c_3356,plain,
( unordered_pair(sK6,unordered_pair(sK7,sK7)) = unordered_pair(sK8,sK8)
| unordered_pair(sK7,sK7) = unordered_pair(sK9,sK9)
| unordered_pair(sK7,sK7) = sK8 ),
inference(forward_subsumption_resolution,[status(thm)],[c_2871,c_60]) ).
cnf(c_3363,plain,
( ~ member(unordered_pair(sK7,sK7),universal_class)
| unordered_pair(sK7,sK7) = unordered_pair(sK9,sK9)
| unordered_pair(sK7,sK7) = sK8
| member(unordered_pair(sK7,sK7),unordered_pair(sK8,sK8)) ),
inference(superposition,[status(thm)],[c_3356,c_56]) ).
cnf(c_3557,plain,
( unordered_pair(sK7,sK7) = unordered_pair(sK9,sK9)
| unordered_pair(sK9,sK9) = sK6
| member(unordered_pair(sK9,sK9),unordered_pair(sK6,sK6)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2950,c_60]) ).
cnf(c_3564,plain,
( unordered_pair(sK7,sK7) = unordered_pair(sK9,sK9)
| unordered_pair(sK9,sK9) = sK6 ),
inference(superposition,[status(thm)],[c_3557,c_58]) ).
cnf(c_3854,plain,
( unordered_pair(sK7,sK7) = unordered_pair(sK9,sK9)
| unordered_pair(sK7,sK7) = sK8
| member(unordered_pair(sK7,sK7),unordered_pair(sK8,sK8)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3363,c_60]) ).
cnf(c_3863,plain,
( unordered_pair(sK7,sK7) = unordered_pair(sK9,sK9)
| unordered_pair(sK7,sK7) = sK8 ),
inference(superposition,[status(thm)],[c_3854,c_58]) ).
cnf(c_3925,plain,
( ~ member(X0,unordered_pair(sK7,sK7))
| unordered_pair(sK9,sK9) = sK6
| X0 = sK9 ),
inference(superposition,[status(thm)],[c_3564,c_58]) ).
cnf(c_3937,plain,
( unordered_pair(sK9,sK9) = sK6
| member(unordered_pair(sK8,unordered_pair(sK7,sK7)),unordered_pair(unordered_pair(sK6,sK6),unordered_pair(sK6,unordered_pair(sK7,sK7)))) ),
inference(superposition,[status(thm)],[c_3564,c_2418]) ).
cnf(c_4003,plain,
( ~ member(X0,unordered_pair(sK7,sK7))
| unordered_pair(sK7,sK7) = sK8
| X0 = sK9 ),
inference(superposition,[status(thm)],[c_3863,c_58]) ).
cnf(c_4015,plain,
( unordered_pair(sK7,sK7) = sK8
| member(unordered_pair(sK8,unordered_pair(sK7,sK7)),unordered_pair(unordered_pair(sK6,sK6),unordered_pair(sK6,unordered_pair(sK7,sK7)))) ),
inference(superposition,[status(thm)],[c_3863,c_2418]) ).
cnf(c_4139,plain,
( ~ member(sK7,universal_class)
| unordered_pair(sK9,sK9) = sK6
| sK7 = sK9 ),
inference(superposition,[status(thm)],[c_56,c_3925]) ).
cnf(c_4142,plain,
unordered_pair(sK9,sK9) = sK6,
inference(global_subsumption_just,[status(thm)],[c_3937,c_129,c_128,c_4139]) ).
cnf(c_4148,plain,
member(sK6,universal_class),
inference(superposition,[status(thm)],[c_4142,c_60]) ).
cnf(c_4149,plain,
( ~ member(X0,sK6)
| X0 = sK9 ),
inference(superposition,[status(thm)],[c_4142,c_58]) ).
cnf(c_4168,plain,
( unordered_pair(sK6,sK6) = unordered_pair(sK8,sK8)
| sK6 = sK8 ),
inference(backward_subsumption_resolution,[status(thm)],[c_2580,c_4148]) ).
cnf(c_4272,plain,
( ~ member(sK7,universal_class)
| unordered_pair(sK7,sK7) = sK8
| sK7 = sK9 ),
inference(superposition,[status(thm)],[c_56,c_4003]) ).
cnf(c_4276,plain,
unordered_pair(sK7,sK7) = sK8,
inference(global_subsumption_just,[status(thm)],[c_4015,c_129,c_128,c_4272]) ).
cnf(c_4278,plain,
( ~ member(sK7,universal_class)
| member(sK7,sK8) ),
inference(superposition,[status(thm)],[c_4276,c_56]) ).
cnf(c_4280,plain,
member(sK8,universal_class),
inference(superposition,[status(thm)],[c_4276,c_60]) ).
cnf(c_4360,plain,
( ~ member(sK8,universal_class)
| sK6 = sK8
| member(sK8,unordered_pair(sK6,sK6)) ),
inference(superposition,[status(thm)],[c_4168,c_56]) ).
cnf(c_4837,plain,
member(sK7,sK8),
inference(global_subsumption_just,[status(thm)],[c_4278,c_129,c_4278]) ).
cnf(c_5150,plain,
( sK6 = sK8
| member(sK8,unordered_pair(sK6,sK6)) ),
inference(global_subsumption_just,[status(thm)],[c_4360,c_4280,c_4360]) ).
cnf(c_5156,plain,
sK6 = sK8,
inference(superposition,[status(thm)],[c_5150,c_58]) ).
cnf(c_5172,plain,
member(sK7,sK6),
inference(demodulation,[status(thm)],[c_4837,c_5156]) ).
cnf(c_5778,plain,
sK7 = sK9,
inference(superposition,[status(thm)],[c_5172,c_4149]) ).
cnf(c_5780,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_128,c_5778]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET018+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.13/0.35 % Computer : n020.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 10:58:00 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.48 Running first-order theorem proving
% 0.20/0.48 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 1.38/1.17 % SZS status Started for theBenchmark.p
% 1.38/1.17 % SZS status Theorem for theBenchmark.p
% 1.38/1.17
% 1.38/1.17 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 1.38/1.17
% 1.38/1.17 ------ iProver source info
% 1.38/1.17
% 1.38/1.17 git: date: 2023-05-31 18:12:56 +0000
% 1.38/1.17 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 1.38/1.17 git: non_committed_changes: false
% 1.38/1.17 git: last_make_outside_of_git: false
% 1.38/1.17
% 1.38/1.17 ------ Parsing...
% 1.38/1.17 ------ Clausification by vclausify_rel & Parsing by iProver...
% 1.38/1.17
% 1.38/1.17 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e
% 1.38/1.17
% 1.38/1.17 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.38/1.17
% 1.38/1.17 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.38/1.17 ------ Proving...
% 1.38/1.17 ------ Problem Properties
% 1.38/1.17
% 1.38/1.17
% 1.38/1.17 clauses 77
% 1.38/1.17 conjectures 3
% 1.38/1.17 EPR 9
% 1.38/1.17 Horn 69
% 1.38/1.17 unary 17
% 1.38/1.17 binary 39
% 1.38/1.17 lits 159
% 1.38/1.17 lits eq 16
% 1.38/1.17 fd_pure 0
% 1.38/1.17 fd_pseudo 0
% 1.38/1.17 fd_cond 4
% 1.38/1.17 fd_pseudo_cond 3
% 1.38/1.17 AC symbols 0
% 1.38/1.17
% 1.38/1.17 ------ Input Options Time Limit: Unbounded
% 1.38/1.17
% 1.38/1.17
% 1.38/1.17 ------
% 1.38/1.17 Current options:
% 1.38/1.17 ------
% 1.38/1.17
% 1.38/1.17
% 1.38/1.17
% 1.38/1.17
% 1.38/1.17 ------ Proving...
% 1.38/1.17
% 1.38/1.17
% 1.38/1.17 % SZS status Theorem for theBenchmark.p
% 1.38/1.17
% 1.38/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.38/1.17
% 1.38/1.17
%------------------------------------------------------------------------------