TSTP Solution File: SET764+4 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET764+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 05:28:31 EDT 2022
% Result : Theorem 2.06s 2.27s
% Output : Refutation 2.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of clauses : 11 ( 6 unt; 2 nHn; 11 RR)
% Number of literals : 17 ( 0 equ; 8 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
~ member(u,empty_set),
file('SET764+4.p',unknown),
[] ).
cnf(4,axiom,
~ equal_set(inverse_image2(skc3,empty_set),empty_set),
file('SET764+4.p',unknown),
[] ).
cnf(8,axiom,
( subset(u,v)
| member(skf39(v,u),u) ),
file('SET764+4.p',unknown),
[] ).
cnf(36,axiom,
( ~ subset(u,v)
| ~ subset(v,u)
| equal_set(v,u) ),
file('SET764+4.p',unknown),
[] ).
cnf(52,axiom,
( ~ member(u,inverse_image2(v,w))
| member(skf66(w,x,y),w) ),
file('SET764+4.p',unknown),
[] ).
cnf(144,plain,
( ~ subset(empty_set,inverse_image2(skc3,empty_set))
| ~ subset(inverse_image2(skc3,empty_set),empty_set) ),
inference(res,[status(thm),theory(equality)],[36,4]),
[iquote('0:Res:36.2,4.0')] ).
cnf(151,plain,
subset(empty_set,u),
inference(res,[status(thm),theory(equality)],[8,2]),
[iquote('0:Res:8.1,2.0')] ).
cnf(154,plain,
~ subset(inverse_image2(skc3,empty_set),empty_set),
inference(mrr,[status(thm)],[144,151]),
[iquote('0:MRR:144.0,151.0')] ).
cnf(485,plain,
( subset(inverse_image2(u,v),w)
| member(skf66(v,x,y),v) ),
inference(res,[status(thm),theory(equality)],[8,52]),
[iquote('0:Res:8.1,52.0')] ).
cnf(2937,plain,
subset(inverse_image2(u,empty_set),v),
inference(res,[status(thm),theory(equality)],[485,2]),
[iquote('0:Res:485.1,2.0')] ).
cnf(2965,plain,
$false,
inference(unc,[status(thm)],[2937,154]),
[iquote('0:UnC:2937.0,154.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : SET764+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.13/0.14 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n029.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 : 600
% 0.13/0.35 % DateTime : Mon Jul 11 02:59:16 EDT 2022
% 0.13/0.35 % CPUTime :
% 2.06/2.27
% 2.06/2.27 SPASS V 3.9
% 2.06/2.27 SPASS beiseite: Proof found.
% 2.06/2.27 % SZS status Theorem
% 2.06/2.27 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.06/2.27 SPASS derived 2814 clauses, backtracked 0 clauses, performed 2 splits and kept 1953 clauses.
% 2.06/2.27 SPASS allocated 91851 KBytes.
% 2.06/2.27 SPASS spent 0:00:01.87 on the problem.
% 2.06/2.27 0:00:00.03 for the input.
% 2.06/2.27 0:00:00.84 for the FLOTTER CNF translation.
% 2.06/2.27 0:00:00.07 for inferences.
% 2.06/2.27 0:00:00.00 for the backtracking.
% 2.06/2.27 0:00:00.86 for the reduction.
% 2.06/2.27
% 2.06/2.27
% 2.06/2.27 Here is a proof with depth 2, length 11 :
% 2.06/2.27 % SZS output start Refutation
% See solution above
% 2.06/2.27 Formulae used in the proof : empty_set thIIa14 subset equal_set inverse_image2
% 2.06/2.27
%------------------------------------------------------------------------------