TSTP Solution File: SEU159+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU159+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 14:34:29 EDT 2022
% Result : Theorem 0.37s 0.54s
% Output : Refutation 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of clauses : 39 ( 10 unt; 11 nHn; 39 RR)
% Number of literals : 85 ( 0 equ; 41 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(2,axiom,
equal(unordered_pair(u,v),unordered_pair(v,u)),
file('SEU159+1.p',unknown),
[] ).
cnf(3,axiom,
( in(skc3,skc5)
| subset(unordered_pair(skc3,skc4),skc5) ),
file('SEU159+1.p',unknown),
[] ).
cnf(4,axiom,
( in(skc4,skc5)
| subset(unordered_pair(skc3,skc4),skc5) ),
file('SEU159+1.p',unknown),
[] ).
cnf(6,axiom,
( subset(u,v)
| in(skf3(v,u),u) ),
file('SEU159+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ in(skf3(u,v),u)
| subset(w,u) ),
file('SEU159+1.p',unknown),
[] ).
cnf(8,axiom,
( ~ in(u,v)
| ~ subset(v,w)
| in(u,w) ),
file('SEU159+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ equal(u,v)
| ~ equal(w,unordered_pair(x,v))
| in(u,w) ),
file('SEU159+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ in(skc4,skc5)
| ~ in(skc3,skc5)
| ~ subset(unordered_pair(skc3,skc4),skc5) ),
file('SEU159+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ in(u,v)
| ~ equal(v,unordered_pair(w,x))
| equal(u,x)
| equal(u,w) ),
file('SEU159+1.p',unknown),
[] ).
cnf(16,plain,
subset(unordered_pair(skc3,skc4),skc5),
inference(spt,[spt(split,[position(s1)])],[4]),
[iquote('1:Spt:4.1')] ).
cnf(17,plain,
( ~ in(skc4,skc5)
| ~ in(skc3,skc5) ),
inference(mrr,[status(thm)],[11,16]),
[iquote('1:MRR:11.2,16.0')] ).
cnf(30,plain,
( ~ equal(u,v)
| in(u,unordered_pair(w,v)) ),
inference(eqr,[status(thm),theory(equality)],[10]),
[iquote('0:EqR:10.1')] ).
cnf(33,plain,
( ~ equal(u,v)
| in(u,unordered_pair(v,w)) ),
inference(spr,[status(thm),theory(equality)],[2,30]),
[iquote('0:SpR:2.0,30.1')] ).
cnf(35,plain,
( ~ equal(u,v)
| ~ subset(unordered_pair(w,v),x)
| in(u,x) ),
inference(res,[status(thm),theory(equality)],[30,8]),
[iquote('0:Res:30.1,8.0')] ).
cnf(40,plain,
( ~ equal(u,v)
| ~ subset(unordered_pair(v,w),x)
| in(u,x) ),
inference(res,[status(thm),theory(equality)],[33,8]),
[iquote('0:Res:33.1,8.0')] ).
cnf(69,plain,
( ~ in(u,unordered_pair(v,w))
| equal(u,w)
| equal(u,v) ),
inference(eqr,[status(thm),theory(equality)],[12]),
[iquote('0:EqR:12.1')] ).
cnf(86,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)],[6,69]),
[iquote('0:Res:6.1,69.0')] ).
cnf(94,plain,
( ~ equal(u,skc4)
| in(u,skc5) ),
inference(res,[status(thm),theory(equality)],[16,35]),
[iquote('1:Res:16.0,35.1')] ).
cnf(96,plain,
( ~ equal(skc4,skc4)
| ~ in(skc3,skc5) ),
inference(res,[status(thm),theory(equality)],[94,17]),
[iquote('1:Res:94.1,17.0')] ).
cnf(103,plain,
~ in(skc3,skc5),
inference(obv,[status(thm),theory(equality)],[96]),
[iquote('1:Obv:96.0')] ).
cnf(131,plain,
( ~ equal(u,skc3)
| in(u,skc5) ),
inference(res,[status(thm),theory(equality)],[16,40]),
[iquote('1:Res:16.0,40.1')] ).
cnf(149,plain,
~ equal(skc3,skc3),
inference(res,[status(thm),theory(equality)],[131,103]),
[iquote('1:Res:131.1,103.0')] ).
cnf(150,plain,
$false,
inference(obv,[status(thm),theory(equality)],[149]),
[iquote('1:Obv:149.0')] ).
cnf(151,plain,
~ subset(unordered_pair(skc3,skc4),skc5),
inference(spt,[spt(split,[position(sa)])],[150,16]),
[iquote('1:Spt:150.0,4.1,16.0')] ).
cnf(152,plain,
in(skc4,skc5),
inference(spt,[spt(split,[position(s2)])],[4]),
[iquote('1:Spt:150.0,4.0')] ).
cnf(153,plain,
in(skc3,skc5),
inference(mrr,[status(thm)],[3,151]),
[iquote('1:MRR:3.1,151.0')] ).
cnf(170,plain,
( subset(unordered_pair(u,u),v)
| equal(skf3(v,unordered_pair(u,u)),u) ),
inference(fac,[status(thm)],[86]),
[iquote('0:Fac:86.1,86.2')] ).
cnf(186,plain,
( ~ in(u,v)
| subset(unordered_pair(w,u),v)
| equal(skf3(v,unordered_pair(w,u)),w)
| subset(x,v) ),
inference(spl,[status(thm),theory(equality)],[86,7]),
[iquote('0:SpL:86.1,7.0')] ).
cnf(202,plain,
( ~ in(u,v)
| subset(unordered_pair(w,u),v)
| equal(skf3(v,unordered_pair(w,u)),w) ),
inference(con,[status(thm)],[186]),
[iquote('0:Con:186.3')] ).
cnf(235,plain,
( ~ in(u,v)
| subset(unordered_pair(u,u),v)
| subset(w,v) ),
inference(spl,[status(thm),theory(equality)],[170,7]),
[iquote('0:SpL:170.1,7.0')] ).
cnf(241,plain,
( ~ in(u,v)
| subset(unordered_pair(u,u),v) ),
inference(con,[status(thm)],[235]),
[iquote('0:Con:235.2')] ).
cnf(253,plain,
( ~ in(u,v)
| ~ equal(w,u)
| in(w,v) ),
inference(res,[status(thm),theory(equality)],[241,35]),
[iquote('0:Res:241.1,35.1')] ).
cnf(315,plain,
( ~ equal(u,skc3)
| in(u,skc5) ),
inference(res,[status(thm),theory(equality)],[153,253]),
[iquote('1:Res:153.0,253.0')] ).
cnf(330,plain,
( ~ equal(skf3(skc5,u),skc3)
| subset(v,skc5) ),
inference(res,[status(thm),theory(equality)],[315,7]),
[iquote('1:Res:315.1,7.0')] ).
cnf(710,plain,
( ~ in(u,skc5)
| ~ equal(v,skc3)
| subset(unordered_pair(v,u),skc5)
| subset(w,skc5) ),
inference(spl,[status(thm),theory(equality)],[202,330]),
[iquote('1:SpL:202.2,330.0')] ).
cnf(719,plain,
( ~ in(u,skc5)
| ~ equal(v,skc3)
| subset(unordered_pair(v,u),skc5) ),
inference(con,[status(thm)],[710]),
[iquote('1:Con:710.3')] ).
cnf(745,plain,
( ~ in(skc4,skc5)
| ~ equal(skc3,skc3) ),
inference(res,[status(thm),theory(equality)],[719,151]),
[iquote('1:Res:719.2,151.0')] ).
cnf(749,plain,
~ in(skc4,skc5),
inference(obv,[status(thm),theory(equality)],[745]),
[iquote('1:Obv:745.1')] ).
cnf(750,plain,
$false,
inference(mrr,[status(thm)],[749,152]),
[iquote('1:MRR:749.0,152.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU159+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jun 18 22:55:17 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.37/0.54
% 0.37/0.54 SPASS V 3.9
% 0.37/0.54 SPASS beiseite: Proof found.
% 0.37/0.54 % SZS status Theorem
% 0.37/0.54 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.37/0.54 SPASS derived 554 clauses, backtracked 4 clauses, performed 1 splits and kept 250 clauses.
% 0.37/0.54 SPASS allocated 85842 KBytes.
% 0.37/0.54 SPASS spent 0:00:00.20 on the problem.
% 0.37/0.54 0:00:00.03 for the input.
% 0.37/0.54 0:00:00.03 for the FLOTTER CNF translation.
% 0.37/0.54 0:00:00.01 for inferences.
% 0.37/0.54 0:00:00.00 for the backtracking.
% 0.37/0.54 0:00:00.09 for the reduction.
% 0.37/0.54
% 0.37/0.54
% 0.37/0.54 Here is a proof with depth 9, length 39 :
% 0.37/0.54 % SZS output start Refutation
% See solution above
% 0.37/0.54 Formulae used in the proof : commutativity_k2_tarski t38_zfmisc_1 d3_tarski d2_tarski
% 0.37/0.54
%------------------------------------------------------------------------------