TSTP Solution File: SET907+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET907+1 : TPTP v8.1.0. Released v3.2.0.
% 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 05:29:42 EDT 2022
% Result : Theorem 0.17s 0.43s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of clauses : 14 ( 9 unt; 0 nHn; 14 RR)
% Number of literals : 20 ( 0 equ; 10 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
in(skc7,skc5),
file('SET907+1.p',unknown),
[] ).
cnf(3,axiom,
in(skc6,skc5),
file('SET907+1.p',unknown),
[] ).
cnf(7,axiom,
equal(unordered_pair(u,v),unordered_pair(v,u)),
file('SET907+1.p',unknown),
[] ).
cnf(8,axiom,
equal(set_union2(u,v),set_union2(v,u)),
file('SET907+1.p',unknown),
[] ).
cnf(11,axiom,
~ equal(set_union2(unordered_pair(skc7,skc6),skc5),skc5),
file('SET907+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ subset(u,v)
| equal(set_union2(u,v),v) ),
file('SET907+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ in(u,v)
| ~ in(w,v)
| subset(unordered_pair(u,w),v) ),
file('SET907+1.p',unknown),
[] ).
cnf(17,plain,
~ equal(set_union2(skc5,unordered_pair(skc6,skc7)),skc5),
inference(rew,[status(thm),theory(equality)],[8,11,7]),
[iquote('0:Rew:8.0,11.0,7.0,11.0')] ).
cnf(21,plain,
( ~ in(u,skc5)
| subset(unordered_pair(skc6,u),skc5) ),
inference(res,[status(thm),theory(equality)],[3,16]),
[iquote('0:Res:3.0,16.1')] ).
cnf(28,plain,
subset(unordered_pair(skc6,skc7),skc5),
inference(res,[status(thm),theory(equality)],[2,21]),
[iquote('0:Res:2.0,21.0')] ).
cnf(64,plain,
( ~ subset(u,v)
| equal(set_union2(v,u),v) ),
inference(spr,[status(thm),theory(equality)],[13,8]),
[iquote('0:SpR:13.1,8.0')] ).
cnf(123,plain,
( ~ subset(unordered_pair(skc6,skc7),skc5)
| ~ equal(skc5,skc5) ),
inference(spl,[status(thm),theory(equality)],[64,17]),
[iquote('0:SpL:64.1,17.0')] ).
cnf(124,plain,
~ subset(unordered_pair(skc6,skc7),skc5),
inference(obv,[status(thm),theory(equality)],[123]),
[iquote('0:Obv:123.1')] ).
cnf(125,plain,
$false,
inference(mrr,[status(thm)],[124,28]),
[iquote('0:MRR:124.0,28.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET907+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.11/0.32 % Computer : n018.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Sat Jul 9 21:51:57 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.17/0.43
% 0.17/0.43 SPASS V 3.9
% 0.17/0.43 SPASS beiseite: Proof found.
% 0.17/0.43 % SZS status Theorem
% 0.17/0.43 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 SPASS derived 104 clauses, backtracked 0 clauses, performed 0 splits and kept 41 clauses.
% 0.17/0.43 SPASS allocated 85131 KBytes.
% 0.17/0.43 SPASS spent 0:00:00.09 on the problem.
% 0.17/0.43 0:00:00.04 for the input.
% 0.17/0.43 0:00:00.03 for the FLOTTER CNF translation.
% 0.17/0.43 0:00:00.00 for inferences.
% 0.17/0.43 0:00:00.00 for the backtracking.
% 0.17/0.43 0:00:00.00 for the reduction.
% 0.17/0.43
% 0.17/0.43
% 0.17/0.43 Here is a proof with depth 2, length 14 :
% 0.17/0.43 % SZS output start Refutation
% See solution above
% 0.17/0.43 Formulae used in the proof : t48_zfmisc_1 commutativity_k2_tarski commutativity_k2_xboole_0 t12_xboole_1 t38_zfmisc_1
% 0.17/0.43
%------------------------------------------------------------------------------