%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET072-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 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 05:23:34 EDT 2022
% Result : Unsatisfiable 0.18s 0.43s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of clauses : 11 ( 9 unt; 0 nHn; 11 RR)
% Number of literals : 14 ( 0 equ; 7 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 : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(17,axiom,
equal(unordered_pair(u,v),unordered_pair(v,u)),
file('SET072-7.p',unknown),
[] ).
cnf(23,axiom,
( ~ equal(unordered_pair(u,v),unordered_pair(u,w))
| ~ member(ordered_pair(v,w),cross_product(universal_class,universal_class))
| equal(v,w) ),
file('SET072-7.p',unknown),
[] ).
cnf(24,axiom,
equal(unordered_pair(y__dfg,z__dfg),unordered_pair(x__dfg,z__dfg)),
file('SET072-7.p',unknown),
[] ).
cnf(25,axiom,
member(ordered_pair(x__dfg,y__dfg),cross_product(universal_class,universal_class)),
file('SET072-7.p',unknown),
[] ).
cnf(26,axiom,
~ equal(y__dfg,x__dfg),
file('SET072-7.p',unknown),
[] ).
cnf(118,plain,
equal(unordered_pair(z__dfg,y__dfg),unordered_pair(x__dfg,z__dfg)),
inference(rew,[status(thm),theory(equality)],[17,24]),
[iquote('0:Rew:17.0,24.0')] ).
cnf(144,plain,
( ~ equal(unordered_pair(u,y__dfg),unordered_pair(u,x__dfg))
| equal(y__dfg,x__dfg) ),
inference(res,[status(thm),theory(equality)],[25,23]),
[iquote('0:Res:25.0,23.1')] ).
cnf(157,plain,
~ equal(unordered_pair(u,y__dfg),unordered_pair(u,x__dfg)),
inference(mrr,[status(thm)],[144,26]),
[iquote('0:MRR:144.1,26.0')] ).
cnf(207,plain,
~ equal(unordered_pair(z__dfg,x__dfg),unordered_pair(x__dfg,z__dfg)),
inference(spl,[status(thm),theory(equality)],[118,157]),
[iquote('0:SpL:118.0,157.0')] ).
cnf(210,plain,
~ equal(unordered_pair(x__dfg,z__dfg),unordered_pair(x__dfg,z__dfg)),
inference(rew,[status(thm),theory(equality)],[17,207]),
[iquote('0:Rew:17.0,207.0')] ).
cnf(211,plain,
$false,
inference(obv,[status(thm),theory(equality)],[210]),
[iquote('0:Obv:210.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET072-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n026.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jul 10 18:40:26 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.18/0.43
% 0.18/0.43 SPASS V 3.9
% 0.18/0.43 SPASS beiseite: Proof found.
% 0.18/0.43 % SZS status Theorem
% 0.18/0.43 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.43 SPASS derived 71 clauses, backtracked 0 clauses, performed 0 splits and kept 148 clauses.
% 0.18/0.43 SPASS allocated 75842 KBytes.
% 0.18/0.43 SPASS spent 0:00:00.08 on the problem.
% 0.18/0.43 0:00:00.04 for the input.
% 0.18/0.43 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.43 0:00:00.00 for inferences.
% 0.18/0.43 0:00:00.00 for the backtracking.
% 0.18/0.43 0:00:00.01 for the reduction.
% 0.18/0.43
% 0.18/0.43
% 0.18/0.43 Here is a proof with depth 2, length 11 :
% 0.18/0.43 % SZS output start Refutation
% See solution above
% 0.18/0.43 Formulae used in the proof : commutativity_of_unordered_pair left_cancellation prove_right_cancellation_1 prove_right_cancellation_2 prove_right_cancellation_3
% 0.18/0.43
%------------------------------------------------------------------------------