TSTP Solution File: SET072-6 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET072-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 05:23:34 EDT 2022
% Result : Unsatisfiable 0.13s 0.35s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of clauses : 21 ( 10 unt; 1 nHn; 21 RR)
% Number of literals : 33 ( 0 equ; 14 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(unordered_pair(y__dfg,z__dfg),unordered_pair(x__dfg,z__dfg)),
file('SET072-6.p',unknown),
[] ).
cnf(2,axiom,
member(ordered_pair(x__dfg,y__dfg),cross_product(universal_class,universal_class)),
file('SET072-6.p',unknown),
[] ).
cnf(3,axiom,
~ equal(y__dfg,x__dfg),
file('SET072-6.p',unknown),
[] ).
cnf(11,axiom,
( ~ member(u,unordered_pair(v,w))
| equal(u,w)
| equal(u,v) ),
file('SET072-6.p',unknown),
[] ).
cnf(12,axiom,
( ~ member(u,universal_class)
| member(u,unordered_pair(u,v)) ),
file('SET072-6.p',unknown),
[] ).
cnf(15,axiom,
equal(unordered_pair(u,u),singleton(u)),
file('SET072-6.p',unknown),
[] ).
cnf(17,axiom,
( ~ member(ordered_pair(u,v),cross_product(w,x))
| member(u,w) ),
file('SET072-6.p',unknown),
[] ).
cnf(18,axiom,
( ~ member(ordered_pair(u,v),cross_product(w,x))
| member(v,x) ),
file('SET072-6.p',unknown),
[] ).
cnf(99,plain,
( ~ member(y__dfg,unordered_pair(u,x__dfg))
| equal(y__dfg,u) ),
inference(res,[status(thm),theory(equality)],[11,3]),
[iquote('0:Res:11.2,3.0')] ).
cnf(100,plain,
( ~ member(x__dfg,unordered_pair(y__dfg,u))
| equal(x__dfg,u) ),
inference(res,[status(thm),theory(equality)],[11,3]),
[iquote('0:Res:11.1,3.0')] ).
cnf(105,plain,
member(x__dfg,universal_class),
inference(res,[status(thm),theory(equality)],[2,17]),
[iquote('0:Res:2.0,17.0')] ).
cnf(106,plain,
member(y__dfg,universal_class),
inference(res,[status(thm),theory(equality)],[2,18]),
[iquote('0:Res:2.0,18.0')] ).
cnf(120,plain,
~ member(y__dfg,unordered_pair(x__dfg,x__dfg)),
inference(res,[status(thm),theory(equality)],[99,3]),
[iquote('0:Res:99.1,3.0')] ).
cnf(124,plain,
~ member(y__dfg,singleton(x__dfg)),
inference(rew,[status(thm),theory(equality)],[15,120]),
[iquote('0:Rew:15.0,120.0')] ).
cnf(143,plain,
( ~ member(x__dfg,unordered_pair(x__dfg,z__dfg))
| equal(z__dfg,x__dfg) ),
inference(spl,[status(thm),theory(equality)],[1,100]),
[iquote('0:SpL:1.0,100.0')] ).
cnf(167,plain,
( ~ member(y__dfg,universal_class)
| member(y__dfg,unordered_pair(x__dfg,z__dfg)) ),
inference(spr,[status(thm),theory(equality)],[1,12]),
[iquote('0:SpR:1.0,12.1')] ).
cnf(168,plain,
( ~ member(x__dfg,universal_class)
| equal(z__dfg,x__dfg) ),
inference(res,[status(thm),theory(equality)],[12,143]),
[iquote('0:Res:12.1,143.0')] ).
cnf(171,plain,
equal(z__dfg,x__dfg),
inference(mrr,[status(thm)],[168,105]),
[iquote('0:MRR:168.0,105.0')] ).
cnf(176,plain,
( ~ member(y__dfg,universal_class)
| member(y__dfg,unordered_pair(x__dfg,x__dfg)) ),
inference(rew,[status(thm),theory(equality)],[171,167]),
[iquote('0:Rew:171.0,167.1')] ).
cnf(177,plain,
( ~ member(y__dfg,universal_class)
| member(y__dfg,singleton(x__dfg)) ),
inference(rew,[status(thm),theory(equality)],[15,176]),
[iquote('0:Rew:15.0,176.1')] ).
cnf(178,plain,
$false,
inference(mrr,[status(thm)],[177,106,124]),
[iquote('0:MRR:177.0,177.1,106.0,124.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : SET072-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.00/0.09 % Command : run_spass %d %s
% 0.09/0.28 % Computer : n018.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 600
% 0.09/0.28 % DateTime : Mon Jul 11 06:13:28 EDT 2022
% 0.09/0.28 % CPUTime :
% 0.13/0.35
% 0.13/0.35 SPASS V 3.9
% 0.13/0.35 SPASS beiseite: Proof found.
% 0.13/0.35 % SZS status Theorem
% 0.13/0.35 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35 SPASS derived 62 clauses, backtracked 0 clauses, performed 0 splits and kept 125 clauses.
% 0.13/0.35 SPASS allocated 75821 KBytes.
% 0.13/0.35 SPASS spent 0:00:00.06 on the problem.
% 0.13/0.35 0:00:00.03 for the input.
% 0.13/0.35 0:00:00.00 for the FLOTTER CNF translation.
% 0.13/0.35 0:00:00.00 for inferences.
% 0.13/0.35 0:00:00.00 for the backtracking.
% 0.13/0.35 0:00:00.01 for the reduction.
% 0.13/0.35
% 0.13/0.35
% 0.13/0.35 Here is a proof with depth 3, length 21 :
% 0.13/0.35 % SZS output start Refutation
% See solution above
% 0.13/0.35 Formulae used in the proof : prove_right_cancellation_1 prove_right_cancellation_2 prove_right_cancellation_3 unordered_pair_member unordered_pair2 singleton_set cartesian_product1 cartesian_product2
% 0.13/0.35
%------------------------------------------------------------------------------