TSTP Solution File: SET766+4 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET766+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 : 600s
% DateTime : Tue Jul 19 05:28:32 EDT 2022
% Result : Theorem 0.44s 0.63s
% Output : Refutation 0.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of clauses : 12 ( 7 unt; 0 nHn; 12 RR)
% Number of literals : 19 ( 0 equ; 11 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equivalence(skc5,skc3),
file('SET766+4.p',unknown),
[] ).
cnf(2,axiom,
member(skc4,skc3),
file('SET766+4.p',unknown),
[] ).
cnf(7,axiom,
~ member(skc4,equivalence_class(skc4,skc3,skc5)),
file('SET766+4.p',unknown),
[] ).
cnf(12,axiom,
( ~ equivalence(u,v)
| skP2(u,v) ),
file('SET766+4.p',unknown),
[] ).
cnf(52,axiom,
( ~ member(u,v)
| ~ skP2(w,v)
| apply(w,u,u) ),
file('SET766+4.p',unknown),
[] ).
cnf(65,axiom,
( ~ member(u,v)
| ~ apply(w,x,u)
| member(u,equivalence_class(x,v,w)) ),
file('SET766+4.p',unknown),
[] ).
cnf(97,plain,
( ~ skP2(u,skc3)
| apply(u,skc4,skc4) ),
inference(res,[status(thm),theory(equality)],[2,52]),
[iquote('0:Res:2.0,52.1')] ).
cnf(112,plain,
skP2(skc5,skc3),
inference(res,[status(thm),theory(equality)],[1,12]),
[iquote('0:Res:1.0,12.0')] ).
cnf(124,plain,
( ~ apply(skc5,skc4,skc4)
| ~ member(skc4,skc3) ),
inference(res,[status(thm),theory(equality)],[65,7]),
[iquote('0:Res:65.2,7.0')] ).
cnf(125,plain,
~ apply(skc5,skc4,skc4),
inference(mrr,[status(thm)],[124,2]),
[iquote('0:MRR:124.1,2.0')] ).
cnf(162,plain,
~ skP2(skc5,skc3),
inference(res,[status(thm),theory(equality)],[97,125]),
[iquote('0:Res:97.1,125.0')] ).
cnf(163,plain,
$false,
inference(mrr,[status(thm)],[162,112]),
[iquote('0:MRR:162.0,112.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET766+4 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 10 08:10:41 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.44/0.63
% 0.44/0.63 SPASS V 3.9
% 0.44/0.63 SPASS beiseite: Proof found.
% 0.44/0.63 % SZS status Theorem
% 0.44/0.63 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.44/0.63 SPASS derived 72 clauses, backtracked 0 clauses, performed 0 splits and kept 128 clauses.
% 0.44/0.63 SPASS allocated 88194 KBytes.
% 0.44/0.63 SPASS spent 0:00:00.28 on the problem.
% 0.44/0.63 0:00:00.03 for the input.
% 0.44/0.63 0:00:00.21 for the FLOTTER CNF translation.
% 0.44/0.63 0:00:00.00 for inferences.
% 0.44/0.63 0:00:00.00 for the backtracking.
% 0.44/0.63 0:00:00.00 for the reduction.
% 0.44/0.63
% 0.44/0.63
% 0.44/0.63 Here is a proof with depth 2, length 12 :
% 0.44/0.63 % SZS output start Refutation
% See solution above
% 0.44/0.63 Formulae used in the proof : thIII02 equivalence equivalence_class
% 0.44/0.63
%------------------------------------------------------------------------------