TSTP Solution File: SEU077+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU077+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 14:33:51 EDT 2022
% Result : Theorem 123.38s 123.67s
% Output : Refutation 123.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of clauses : 35 ( 10 unt; 1 nHn; 35 RR)
% Number of literals : 116 ( 0 equ; 83 neg)
% Maximal clause size : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
relation(skc11),
file('SEU077+1.p',unknown),
[] ).
cnf(2,axiom,
function(skc11),
file('SEU077+1.p',unknown),
[] ).
cnf(26,axiom,
subset(u,u),
file('SEU077+1.p',unknown),
[] ).
cnf(27,axiom,
~ subset(skc12,skc13),
file('SEU077+1.p',unknown),
[] ).
cnf(28,axiom,
subset(skc12,relation_rng(skc11)),
file('SEU077+1.p',unknown),
[] ).
cnf(35,axiom,
~ in(skf9(u,v),u),
file('SEU077+1.p',unknown),
[] ).
cnf(42,axiom,
subset(relation_inverse_image(skc11,skc12),relation_inverse_image(skc11,skc13)),
file('SEU077+1.p',unknown),
[] ).
cnf(46,axiom,
( subset(u,v)
| in(skf9(v,u),u) ),
file('SEU077+1.p',unknown),
[] ).
cnf(54,axiom,
( ~ in(u,v)
| ~ subset(v,w)
| in(u,w) ),
file('SEU077+1.p',unknown),
[] ).
cnf(60,axiom,
( ~ function(u)
| ~ relation(u)
| ~ in(v,w)
| ~ equal(w,relation_rng(u))
| in(skf10(u,x),relation_dom(u)) ),
file('SEU077+1.p',unknown),
[] ).
cnf(61,axiom,
( ~ function(u)
| ~ relation(u)
| ~ in(v,w)
| ~ equal(w,relation_inverse_image(u,x))
| in(apply(u,v),x) ),
file('SEU077+1.p',unknown),
[] ).
cnf(62,axiom,
( ~ function(u)
| ~ relation(u)
| ~ in(v,w)
| ~ equal(w,relation_rng(u))
| equal(apply(u,skf10(u,v)),v) ),
file('SEU077+1.p',unknown),
[] ).
cnf(68,axiom,
( ~ function(u)
| ~ relation(u)
| ~ in(v,relation_dom(u))
| ~ equal(w,relation_inverse_image(u,x))
| ~ in(apply(u,v),x)
| in(v,w) ),
file('SEU077+1.p',unknown),
[] ).
cnf(92,plain,
( ~ in(u,skc12)
| in(u,relation_rng(skc11)) ),
inference(res,[status(thm),theory(equality)],[28,54]),
[iquote('0:Res:28.0,54.0')] ).
cnf(95,plain,
in(skf9(skc13,skc12),skc12),
inference(res,[status(thm),theory(equality)],[46,27]),
[iquote('0:Res:46.1,27.0')] ).
cnf(96,plain,
( ~ in(u,relation_inverse_image(skc11,skc12))
| in(u,relation_inverse_image(skc11,skc13)) ),
inference(res,[status(thm),theory(equality)],[42,54]),
[iquote('0:Res:42.0,54.0')] ).
cnf(392,plain,
( ~ function(u)
| ~ relation(u)
| ~ in(v,relation_rng(u))
| in(skf10(u,w),relation_dom(u)) ),
inference(eqr,[status(thm),theory(equality)],[60]),
[iquote('0:EqR:60.3')] ).
cnf(443,plain,
( ~ function(u)
| ~ relation(u)
| ~ in(v,relation_inverse_image(u,w))
| in(apply(u,v),w) ),
inference(eqr,[status(thm),theory(equality)],[61]),
[iquote('0:EqR:61.3')] ).
cnf(468,plain,
( ~ function(u)
| ~ relation(u)
| ~ in(v,relation_rng(u))
| equal(apply(u,skf10(u,v)),v) ),
inference(eqr,[status(thm),theory(equality)],[62]),
[iquote('0:EqR:62.3')] ).
cnf(601,plain,
( ~ function(u)
| ~ relation(u)
| ~ in(v,relation_dom(u))
| ~ in(apply(u,v),w)
| in(v,relation_inverse_image(u,w)) ),
inference(eqr,[status(thm),theory(equality)],[68]),
[iquote('0:EqR:68.3')] ).
cnf(632,plain,
( ~ in(u,relation_inverse_image(skc11,skc12))
| ~ subset(relation_inverse_image(skc11,skc13),v)
| in(u,v) ),
inference(res,[status(thm),theory(equality)],[96,54]),
[iquote('0:Res:96.1,54.0')] ).
cnf(1243,plain,
( ~ function(u)
| ~ relation(u)
| ~ function(u)
| ~ relation(u)
| ~ in(v,relation_rng(u))
| ~ in(skf10(u,v),relation_inverse_image(u,w))
| in(v,w) ),
inference(spr,[status(thm),theory(equality)],[468,443]),
[iquote('0:SpR:468.3,443.3')] ).
cnf(1247,plain,
( ~ function(u)
| ~ relation(u)
| ~ in(v,relation_rng(u))
| ~ in(skf10(u,v),relation_inverse_image(u,w))
| in(v,w) ),
inference(obv,[status(thm),theory(equality)],[1243]),
[iquote('0:Obv:1243.1')] ).
cnf(1902,plain,
( ~ function(u)
| ~ relation(u)
| ~ function(u)
| ~ relation(u)
| ~ in(v,relation_rng(u))
| ~ in(skf10(u,v),relation_dom(u))
| ~ in(v,w)
| in(skf10(u,v),relation_inverse_image(u,w)) ),
inference(spl,[status(thm),theory(equality)],[468,601]),
[iquote('0:SpL:468.3,601.3')] ).
cnf(1920,plain,
( ~ function(u)
| ~ relation(u)
| ~ in(v,relation_rng(u))
| ~ in(skf10(u,v),relation_dom(u))
| ~ in(v,w)
| in(skf10(u,v),relation_inverse_image(u,w)) ),
inference(obv,[status(thm),theory(equality)],[1902]),
[iquote('0:Obv:1902.1')] ).
cnf(1921,plain,
( ~ function(u)
| ~ relation(u)
| ~ in(v,relation_rng(u))
| ~ in(v,w)
| in(skf10(u,v),relation_inverse_image(u,w)) ),
inference(mrr,[status(thm)],[1920,392]),
[iquote('0:MRR:1920.3,392.3')] ).
cnf(11457,plain,
( ~ function(skc11)
| ~ relation(skc11)
| ~ in(u,relation_rng(skc11))
| ~ in(u,skc12)
| ~ subset(relation_inverse_image(skc11,skc13),v)
| in(skf10(skc11,u),v) ),
inference(res,[status(thm),theory(equality)],[1921,632]),
[iquote('0:Res:1921.4,632.0')] ).
cnf(11477,plain,
( ~ in(u,relation_rng(skc11))
| ~ in(u,skc12)
| ~ subset(relation_inverse_image(skc11,skc13),v)
| in(skf10(skc11,u),v) ),
inference(ssi,[status(thm)],[11457,1,2]),
[iquote('0:SSi:11457.1,11457.0,1.0,2.0,1.0,2.0')] ).
cnf(11478,plain,
( ~ in(u,skc12)
| ~ subset(relation_inverse_image(skc11,skc13),v)
| in(skf10(skc11,u),v) ),
inference(mrr,[status(thm)],[11477,92]),
[iquote('0:MRR:11477.0,92.1')] ).
cnf(42590,plain,
( ~ in(u,skc12)
| in(skf10(skc11,u),relation_inverse_image(skc11,skc13)) ),
inference(res,[status(thm),theory(equality)],[26,11478]),
[iquote('0:Res:26.0,11478.1')] ).
cnf(43737,plain,
( ~ function(skc11)
| ~ relation(skc11)
| ~ in(u,skc12)
| ~ in(u,relation_rng(skc11))
| in(u,skc13) ),
inference(res,[status(thm),theory(equality)],[42590,1247]),
[iquote('0:Res:42590.1,1247.3')] ).
cnf(43738,plain,
( ~ in(u,skc12)
| ~ in(u,relation_rng(skc11))
| in(u,skc13) ),
inference(ssi,[status(thm)],[43737,1,2]),
[iquote('0:SSi:43737.1,43737.0,1.0,2.0,1.0,2.0')] ).
cnf(43739,plain,
( ~ in(u,skc12)
| in(u,skc13) ),
inference(mrr,[status(thm)],[43738,92]),
[iquote('0:MRR:43738.1,92.1')] ).
cnf(43744,plain,
~ in(skf9(skc13,u),skc12),
inference(res,[status(thm),theory(equality)],[43739,35]),
[iquote('0:Res:43739.1,35.0')] ).
cnf(43763,plain,
$false,
inference(unc,[status(thm)],[43744,95]),
[iquote('0:UnC:43744.0,95.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU077+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % 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 19:33:09 EDT 2022
% 0.13/0.34 % CPUTime :
% 123.38/123.67
% 123.38/123.67 SPASS V 3.9
% 123.38/123.67 SPASS beiseite: Proof found.
% 123.38/123.67 % SZS status Theorem
% 123.38/123.67 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 123.38/123.67 SPASS derived 36331 clauses, backtracked 695 clauses, performed 12 splits and kept 18693 clauses.
% 123.38/123.67 SPASS allocated 141051 KBytes.
% 123.38/123.67 SPASS spent 0:02:00.13 on the problem.
% 123.38/123.67 0:00:00.04 for the input.
% 123.38/123.67 0:00:00.05 for the FLOTTER CNF translation.
% 123.38/123.67 0:00:00.61 for inferences.
% 123.38/123.67 0:00:05.03 for the backtracking.
% 123.38/123.67 0:1:53.83 for the reduction.
% 123.38/123.67
% 123.38/123.67
% 123.38/123.67 Here is a proof with depth 6, length 35 :
% 123.38/123.67 % SZS output start Refutation
% See solution above
% 123.38/123.67 Formulae used in the proof : t158_funct_1 reflexivity_r1_tarski d3_tarski antisymmetry_r2_hidden d5_funct_1 d13_funct_1
% 123.38/123.67
%------------------------------------------------------------------------------