TSTP Solution File: SEU159+3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU159+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n005.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 14:34:30 EDT 2022
% Result : Theorem 0.20s 0.54s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of clauses : 41 ( 9 unt; 11 nHn; 41 RR)
% Number of literals : 91 ( 0 equ; 44 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
equal(unordered_pair(u,v),unordered_pair(v,u)),
file('SEU159+3.p',unknown),
[] ).
cnf(5,axiom,
( in(skc5,skc7)
| subset(unordered_pair(skc5,skc6),skc7) ),
file('SEU159+3.p',unknown),
[] ).
cnf(6,axiom,
( in(skc6,skc7)
| subset(unordered_pair(skc5,skc6),skc7) ),
file('SEU159+3.p',unknown),
[] ).
cnf(8,axiom,
( subset(u,v)
| in(skf3(v,u),u) ),
file('SEU159+3.p',unknown),
[] ).
cnf(9,axiom,
( ~ in(skf3(u,v),u)
| subset(w,u) ),
file('SEU159+3.p',unknown),
[] ).
cnf(10,axiom,
( ~ in(u,v)
| ~ subset(v,w)
| in(u,w) ),
file('SEU159+3.p',unknown),
[] ).
cnf(12,axiom,
( ~ equal(u,v)
| ~ equal(w,unordered_pair(x,v))
| in(u,w) ),
file('SEU159+3.p',unknown),
[] ).
cnf(13,axiom,
( ~ in(skc6,skc7)
| ~ in(skc5,skc7)
| ~ subset(unordered_pair(skc5,skc6),skc7) ),
file('SEU159+3.p',unknown),
[] ).
cnf(14,axiom,
( ~ in(u,v)
| ~ equal(v,unordered_pair(w,x))
| equal(u,x)
| equal(u,w) ),
file('SEU159+3.p',unknown),
[] ).
cnf(18,plain,
subset(unordered_pair(skc5,skc6),skc7),
inference(spt,[spt(split,[position(s1)])],[6]),
[iquote('1:Spt:6.1')] ).
cnf(19,plain,
( ~ in(skc6,skc7)
| ~ in(skc5,skc7) ),
inference(mrr,[status(thm)],[13,18]),
[iquote('1:MRR:13.2,18.0')] ).
cnf(32,plain,
( ~ equal(u,v)
| in(u,unordered_pair(w,v)) ),
inference(eqr,[status(thm),theory(equality)],[12]),
[iquote('0:EqR:12.1')] ).
cnf(35,plain,
( ~ equal(u,v)
| in(u,unordered_pair(v,w)) ),
inference(spr,[status(thm),theory(equality)],[4,32]),
[iquote('0:SpR:4.0,32.1')] ).
cnf(37,plain,
( ~ equal(u,v)
| ~ subset(unordered_pair(w,v),x)
| in(u,x) ),
inference(res,[status(thm),theory(equality)],[32,10]),
[iquote('0:Res:32.1,10.0')] ).
cnf(42,plain,
( ~ equal(u,v)
| ~ subset(unordered_pair(v,w),x)
| in(u,x) ),
inference(res,[status(thm),theory(equality)],[35,10]),
[iquote('0:Res:35.1,10.0')] ).
cnf(63,plain,
( ~ in(u,unordered_pair(v,w))
| equal(u,w)
| equal(u,v) ),
inference(eqr,[status(thm),theory(equality)],[14]),
[iquote('0:EqR:14.1')] ).
cnf(90,plain,
( subset(unordered_pair(u,v),w)
| equal(skf3(w,unordered_pair(u,v)),v)
| equal(skf3(w,unordered_pair(u,v)),u) ),
inference(res,[status(thm),theory(equality)],[8,63]),
[iquote('0:Res:8.1,63.0')] ).
cnf(96,plain,
( ~ equal(u,skc6)
| in(u,skc7) ),
inference(res,[status(thm),theory(equality)],[18,37]),
[iquote('1:Res:18.0,37.1')] ).
cnf(100,plain,
( ~ equal(skc6,skc6)
| ~ in(skc5,skc7) ),
inference(res,[status(thm),theory(equality)],[96,19]),
[iquote('1:Res:96.1,19.0')] ).
cnf(108,plain,
~ in(skc5,skc7),
inference(obv,[status(thm),theory(equality)],[100]),
[iquote('1:Obv:100.0')] ).
cnf(141,plain,
( ~ equal(u,skc5)
| in(u,skc7) ),
inference(res,[status(thm),theory(equality)],[18,42]),
[iquote('1:Res:18.0,42.1')] ).
cnf(151,plain,
~ equal(skc5,skc5),
inference(res,[status(thm),theory(equality)],[141,108]),
[iquote('1:Res:141.1,108.0')] ).
cnf(152,plain,
$false,
inference(obv,[status(thm),theory(equality)],[151]),
[iquote('1:Obv:151.0')] ).
cnf(153,plain,
~ subset(unordered_pair(skc5,skc6),skc7),
inference(spt,[spt(split,[position(sa)])],[152,18]),
[iquote('1:Spt:152.0,6.1,18.0')] ).
cnf(154,plain,
in(skc6,skc7),
inference(spt,[spt(split,[position(s2)])],[6]),
[iquote('1:Spt:152.0,6.0')] ).
cnf(155,plain,
in(skc5,skc7),
inference(mrr,[status(thm)],[5,153]),
[iquote('1:MRR:5.1,153.0')] ).
cnf(171,plain,
( subset(unordered_pair(u,u),v)
| equal(skf3(v,unordered_pair(u,u)),u) ),
inference(fac,[status(thm)],[90]),
[iquote('0:Fac:90.1,90.2')] ).
cnf(229,plain,
( ~ in(u,v)
| subset(unordered_pair(u,u),v)
| subset(w,v) ),
inference(spl,[status(thm),theory(equality)],[171,9]),
[iquote('0:SpL:171.1,9.0')] ).
cnf(234,plain,
( ~ in(u,v)
| subset(unordered_pair(u,u),v) ),
inference(con,[status(thm)],[229]),
[iquote('0:Con:229.2')] ).
cnf(245,plain,
( ~ in(u,v)
| ~ equal(w,u)
| in(w,v) ),
inference(res,[status(thm),theory(equality)],[234,37]),
[iquote('0:Res:234.1,37.1')] ).
cnf(304,plain,
( ~ equal(u,skc6)
| in(u,skc7) ),
inference(res,[status(thm),theory(equality)],[154,245]),
[iquote('1:Res:154.0,245.0')] ).
cnf(305,plain,
( ~ equal(u,skc5)
| in(u,skc7) ),
inference(res,[status(thm),theory(equality)],[155,245]),
[iquote('1:Res:155.0,245.0')] ).
cnf(309,plain,
( ~ equal(skf3(skc7,u),skc6)
| subset(v,skc7) ),
inference(res,[status(thm),theory(equality)],[304,9]),
[iquote('1:Res:304.1,9.0')] ).
cnf(320,plain,
( ~ equal(skf3(skc7,u),skc5)
| subset(v,skc7) ),
inference(res,[status(thm),theory(equality)],[305,9]),
[iquote('1:Res:305.1,9.0')] ).
cnf(338,plain,
( ~ equal(u,skc6)
| subset(unordered_pair(u,v),skc7)
| equal(skf3(skc7,unordered_pair(u,v)),v)
| subset(w,skc7) ),
inference(spl,[status(thm),theory(equality)],[90,309]),
[iquote('1:SpL:90.2,309.0')] ).
cnf(342,plain,
( ~ equal(u,skc6)
| subset(unordered_pair(u,v),skc7)
| equal(skf3(skc7,unordered_pair(u,v)),v) ),
inference(con,[status(thm)],[338]),
[iquote('1:Con:338.3')] ).
cnf(632,plain,
( ~ equal(u,skc6)
| ~ equal(v,skc5)
| subset(unordered_pair(u,v),skc7)
| subset(w,skc7) ),
inference(spl,[status(thm),theory(equality)],[342,320]),
[iquote('1:SpL:342.2,320.0')] ).
cnf(636,plain,
( ~ equal(u,skc6)
| ~ equal(v,skc5)
| subset(unordered_pair(u,v),skc7) ),
inference(con,[status(thm)],[632]),
[iquote('1:Con:632.3')] ).
cnf(694,plain,
( ~ equal(u,skc6)
| ~ equal(v,skc5)
| subset(unordered_pair(v,u),skc7) ),
inference(spr,[status(thm),theory(equality)],[4,636]),
[iquote('1:SpR:4.0,636.2')] ).
cnf(720,plain,
( ~ equal(skc6,skc6)
| ~ equal(skc5,skc5) ),
inference(res,[status(thm),theory(equality)],[694,153]),
[iquote('1:Res:694.2,153.0')] ).
cnf(725,plain,
$false,
inference(obv,[status(thm),theory(equality)],[720]),
[iquote('1:Obv:720.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU159+3 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n005.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jun 19 00:54:23 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.54
% 0.20/0.54 SPASS V 3.9
% 0.20/0.54 SPASS beiseite: Proof found.
% 0.20/0.54 % SZS status Theorem
% 0.20/0.54 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.54 SPASS derived 543 clauses, backtracked 4 clauses, performed 1 splits and kept 241 clauses.
% 0.20/0.54 SPASS allocated 85815 KBytes.
% 0.20/0.54 SPASS spent 0:00:00.19 on the problem.
% 0.20/0.54 0:00:00.03 for the input.
% 0.20/0.54 0:00:00.03 for the FLOTTER CNF translation.
% 0.20/0.54 0:00:00.01 for inferences.
% 0.20/0.54 0:00:00.00 for the backtracking.
% 0.20/0.54 0:00:00.08 for the reduction.
% 0.20/0.54
% 0.20/0.54
% 0.20/0.54 Here is a proof with depth 11, length 41 :
% 0.20/0.54 % SZS output start Refutation
% See solution above
% 0.20/0.54 Formulae used in the proof : commutativity_k2_tarski t38_zfmisc_1 d3_tarski d2_tarski
% 0.20/0.54
%------------------------------------------------------------------------------