TSTP Solution File: SEU197+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU197+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 14:34:54 EDT 2022
% Result : Theorem 7.67s 7.91s
% Output : Refutation 7.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of clauses : 62 ( 11 unt; 12 nHn; 62 RR)
% Number of literals : 188 ( 0 equ; 115 neg)
% Maximal clause size : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
relation(skc7),
file('SEU197+1.p',unknown),
[] ).
cnf(20,axiom,
( ~ relation(u)
| relation(relation_rng_restriction(v,u)) ),
file('SEU197+1.p',unknown),
[] ).
cnf(24,axiom,
( in(skc9,skc8)
| in(skc9,relation_rng(relation_rng_restriction(skc8,skc7))) ),
file('SEU197+1.p',unknown),
[] ).
cnf(28,axiom,
( in(skc9,relation_rng(skc7))
| in(skc9,relation_rng(relation_rng_restriction(skc8,skc7))) ),
file('SEU197+1.p',unknown),
[] ).
cnf(31,axiom,
( ~ in(skc9,skc8)
| ~ in(skc9,relation_rng(skc7))
| ~ in(skc9,relation_rng(relation_rng_restriction(skc8,skc7))) ),
file('SEU197+1.p',unknown),
[] ).
cnf(32,axiom,
( ~ relation(u)
| ~ equal(v,relation_rng(u))
| ~ in(ordered_pair(w,x),u)
| in(x,v) ),
file('SEU197+1.p',unknown),
[] ).
cnf(33,axiom,
( ~ relation(u)
| ~ in(v,w)
| ~ equal(w,relation_rng(u))
| in(ordered_pair(skf8(u,v),v),u) ),
file('SEU197+1.p',unknown),
[] ).
cnf(35,axiom,
( ~ relation(u)
| ~ relation(v)
| ~ equal(v,relation_rng_restriction(w,u))
| ~ in(ordered_pair(x,y),v)
| in(y,w) ),
file('SEU197+1.p',unknown),
[] ).
cnf(36,axiom,
( ~ relation(u)
| ~ relation(v)
| ~ equal(v,relation_rng_restriction(w,u))
| ~ in(ordered_pair(x,y),v)
| in(ordered_pair(x,y),u) ),
file('SEU197+1.p',unknown),
[] ).
cnf(37,axiom,
( ~ relation(u)
| ~ relation(v)
| ~ in(w,x)
| ~ equal(v,relation_rng_restriction(x,u))
| ~ in(ordered_pair(y,w),u)
| in(ordered_pair(y,w),v) ),
file('SEU197+1.p',unknown),
[] ).
cnf(38,axiom,
( ~ relation(u)
| ~ relation(v)
| equal(v,relation_rng_restriction(w,u))
| in(ordered_pair(skf6(u,w,v),skf7(u,w,v)),v)
| in(skf7(u,w,v),w) ),
file('SEU197+1.p',unknown),
[] ).
cnf(39,axiom,
( ~ in(ordered_pair(skf6(u,v,w),skf7(u,v,w)),u)
| ~ in(ordered_pair(skf6(u,v,w),skf7(u,v,w)),w)
| ~ in(skf7(u,v,w),v) ),
file('SEU197+1.p',unknown),
[] ).
cnf(40,axiom,
( ~ relation(u)
| ~ relation(v)
| equal(v,relation_rng_restriction(w,u))
| in(ordered_pair(skf6(u,w,v),skf7(u,w,v)),v)
| in(ordered_pair(skf6(u,w,v),skf7(u,w,v)),u) ),
file('SEU197+1.p',unknown),
[] ).
cnf(48,plain,
( ~ in(u,v)
| ~ equal(v,relation_rng(skc7))
| in(ordered_pair(skf8(skc7,u),u),skc7) ),
inference(res,[status(thm),theory(equality)],[1,33]),
[iquote('0:Res:1.0,33.0')] ).
cnf(49,plain,
( ~ equal(u,relation_rng(skc7))
| ~ in(ordered_pair(v,w),skc7)
| in(w,u) ),
inference(res,[status(thm),theory(equality)],[1,32]),
[iquote('0:Res:1.0,32.0')] ).
cnf(51,plain,
relation(relation_rng_restriction(u,skc7)),
inference(res,[status(thm),theory(equality)],[1,20]),
[iquote('0:Res:1.0,20.0')] ).
cnf(54,plain,
( ~ relation(u)
| ~ in(v,w)
| ~ equal(u,relation_rng_restriction(w,skc7))
| ~ in(ordered_pair(x,v),skc7)
| in(ordered_pair(x,v),u) ),
inference(res,[status(thm),theory(equality)],[1,37]),
[iquote('0:Res:1.0,37.1')] ).
cnf(55,plain,
( ~ relation(u)
| ~ equal(u,relation_rng_restriction(v,skc7))
| ~ in(ordered_pair(w,x),u)
| in(ordered_pair(w,x),skc7) ),
inference(res,[status(thm),theory(equality)],[1,36]),
[iquote('0:Res:1.0,36.1')] ).
cnf(56,plain,
( ~ relation(u)
| ~ equal(u,relation_rng_restriction(v,skc7))
| ~ in(ordered_pair(w,x),u)
| in(x,v) ),
inference(res,[status(thm),theory(equality)],[1,35]),
[iquote('0:Res:1.0,35.1')] ).
cnf(69,plain,
in(skc9,relation_rng(relation_rng_restriction(skc8,skc7))),
inference(spt,[spt(split,[position(s1)])],[24]),
[iquote('1:Spt:24.1')] ).
cnf(70,plain,
( ~ in(skc9,skc8)
| ~ in(skc9,relation_rng(skc7)) ),
inference(mrr,[status(thm)],[31,69]),
[iquote('1:MRR:31.2,69.0')] ).
cnf(191,plain,
( ~ relation(u)
| ~ in(v,relation_rng(u))
| in(ordered_pair(skf8(u,v),v),u) ),
inference(eqr,[status(thm),theory(equality)],[33]),
[iquote('0:EqR:33.2')] ).
cnf(214,plain,
( ~ relation(u)
| ~ relation(relation_rng_restriction(v,u))
| ~ in(ordered_pair(w,x),relation_rng_restriction(v,u))
| in(x,v) ),
inference(eqr,[status(thm),theory(equality)],[35]),
[iquote('0:EqR:35.2')] ).
cnf(215,plain,
( ~ relation(u)
| ~ in(ordered_pair(v,w),relation_rng_restriction(x,u))
| in(w,x) ),
inference(ssi,[status(thm)],[214,20]),
[iquote('0:SSi:214.1,20.1')] ).
cnf(265,plain,
( ~ relation(u)
| ~ relation(v)
| ~ relation(v)
| ~ equal(w,relation_rng(v))
| equal(v,relation_rng_restriction(x,u))
| in(skf7(u,x,v),x)
| in(skf7(u,x,v),w) ),
inference(res,[status(thm),theory(equality)],[38,32]),
[iquote('0:Res:38.3,32.2')] ).
cnf(273,plain,
( ~ relation(u)
| ~ relation(v)
| ~ equal(w,relation_rng(v))
| equal(v,relation_rng_restriction(x,u))
| in(skf7(u,x,v),x)
| in(skf7(u,x,v),w) ),
inference(obv,[status(thm),theory(equality)],[265]),
[iquote('0:Obv:265.1')] ).
cnf(342,plain,
( ~ relation(u)
| ~ relation(u)
| equal(relation_rng_restriction(v,u),u)
| in(ordered_pair(skf6(u,v,u),skf7(u,v,u)),u) ),
inference(fac,[status(thm)],[40]),
[iquote('0:Fac:40.3,40.4')] ).
cnf(362,plain,
( ~ relation(u)
| equal(relation_rng_restriction(v,u),u)
| in(ordered_pair(skf6(u,v,u),skf7(u,v,u)),u) ),
inference(obv,[status(thm),theory(equality)],[342]),
[iquote('0:Obv:342.0')] ).
cnf(412,plain,
( ~ in(u,relation_rng(skc7))
| in(ordered_pair(skf8(skc7,u),u),skc7) ),
inference(eqr,[status(thm),theory(equality)],[48]),
[iquote('0:EqR:48.1')] ).
cnf(665,plain,
( ~ relation(relation_rng_restriction(u,skc7))
| ~ in(ordered_pair(v,w),relation_rng_restriction(u,skc7))
| in(w,u) ),
inference(eqr,[status(thm),theory(equality)],[56]),
[iquote('0:EqR:56.1')] ).
cnf(668,plain,
( ~ in(ordered_pair(u,v),relation_rng_restriction(w,skc7))
| in(v,w) ),
inference(ssi,[status(thm)],[665,51]),
[iquote('0:SSi:665.0,51.0')] ).
cnf(674,plain,
( ~ relation(relation_rng_restriction(u,skc7))
| ~ in(v,relation_rng(relation_rng_restriction(u,skc7)))
| in(v,u) ),
inference(res,[status(thm),theory(equality)],[191,668]),
[iquote('0:Res:191.2,668.0')] ).
cnf(679,plain,
( ~ in(u,relation_rng(relation_rng_restriction(v,skc7)))
| in(u,v) ),
inference(ssi,[status(thm)],[674,51]),
[iquote('0:SSi:674.0,51.0')] ).
cnf(689,plain,
in(skc9,skc8),
inference(res,[status(thm),theory(equality)],[69,679]),
[iquote('1:Res:69.0,679.0')] ).
cnf(701,plain,
~ in(skc9,relation_rng(skc7)),
inference(mrr,[status(thm)],[70,689]),
[iquote('1:MRR:70.0,689.0')] ).
cnf(760,plain,
( ~ relation(u)
| ~ in(ordered_pair(skf6(u,v,u),skf7(u,v,u)),u)
| ~ in(skf7(u,v,u),v)
| equal(relation_rng_restriction(v,u),u) ),
inference(res,[status(thm),theory(equality)],[362,39]),
[iquote('0:Res:362.2,39.0')] ).
cnf(768,plain,
( ~ relation(u)
| ~ in(skf7(u,v,u),v)
| equal(relation_rng_restriction(v,u),u) ),
inference(mrr,[status(thm)],[760,362]),
[iquote('0:MRR:760.1,362.2')] ).
cnf(828,plain,
( ~ relation(relation_rng_restriction(u,skc7))
| ~ in(ordered_pair(v,w),relation_rng_restriction(u,skc7))
| in(ordered_pair(v,w),skc7) ),
inference(eqr,[status(thm),theory(equality)],[55]),
[iquote('0:EqR:55.1')] ).
cnf(832,plain,
( ~ in(ordered_pair(u,v),relation_rng_restriction(w,skc7))
| in(ordered_pair(u,v),skc7) ),
inference(ssi,[status(thm)],[828,51]),
[iquote('0:SSi:828.0,51.0')] ).
cnf(1273,plain,
( ~ relation(relation_rng_restriction(u,skc7))
| ~ in(v,relation_rng(relation_rng_restriction(u,skc7)))
| in(ordered_pair(skf8(relation_rng_restriction(u,skc7),v),v),skc7) ),
inference(res,[status(thm),theory(equality)],[191,832]),
[iquote('0:Res:191.2,832.0')] ).
cnf(1282,plain,
( ~ in(u,relation_rng(relation_rng_restriction(v,skc7)))
| in(ordered_pair(skf8(relation_rng_restriction(v,skc7),u),u),skc7) ),
inference(ssi,[status(thm)],[1273,51]),
[iquote('0:SSi:1273.0,51.0')] ).
cnf(1488,plain,
( ~ relation(relation_rng_restriction(u,skc7))
| ~ in(v,u)
| ~ in(ordered_pair(w,v),skc7)
| in(ordered_pair(w,v),relation_rng_restriction(u,skc7)) ),
inference(eqr,[status(thm),theory(equality)],[54]),
[iquote('0:EqR:54.2')] ).
cnf(1495,plain,
( ~ in(u,v)
| ~ in(ordered_pair(w,u),skc7)
| in(ordered_pair(w,u),relation_rng_restriction(v,skc7)) ),
inference(ssi,[status(thm)],[1488,51]),
[iquote('0:SSi:1488.0,51.0')] ).
cnf(1805,plain,
( ~ relation(u)
| ~ relation(v)
| equal(v,relation_rng_restriction(w,u))
| in(skf7(u,w,v),w)
| in(skf7(u,w,v),relation_rng(v)) ),
inference(eqr,[status(thm),theory(equality)],[273]),
[iquote('0:EqR:273.2')] ).
cnf(2225,plain,
( ~ in(u,relation_rng(relation_rng_restriction(v,skc7)))
| ~ equal(w,relation_rng(skc7))
| in(u,w) ),
inference(res,[status(thm),theory(equality)],[1282,49]),
[iquote('0:Res:1282.1,49.1')] ).
cnf(2269,plain,
( ~ equal(u,relation_rng(skc7))
| in(skc9,u) ),
inference(res,[status(thm),theory(equality)],[69,2225]),
[iquote('1:Res:69.0,2225.0')] ).
cnf(2316,plain,
~ equal(relation_rng(skc7),relation_rng(skc7)),
inference(res,[status(thm),theory(equality)],[2269,701]),
[iquote('1:Res:2269.1,701.0')] ).
cnf(2341,plain,
$false,
inference(obv,[status(thm),theory(equality)],[2316]),
[iquote('1:Obv:2316.0')] ).
cnf(2343,plain,
~ in(skc9,relation_rng(relation_rng_restriction(skc8,skc7))),
inference(spt,[spt(split,[position(sa)])],[2341,69]),
[iquote('1:Spt:2341.0,24.1,69.0')] ).
cnf(2344,plain,
in(skc9,skc8),
inference(spt,[spt(split,[position(s2)])],[24]),
[iquote('1:Spt:2341.0,24.0')] ).
cnf(2349,plain,
in(skc9,relation_rng(skc7)),
inference(mrr,[status(thm)],[28,2343]),
[iquote('1:MRR:28.1,2343.0')] ).
cnf(5769,plain,
( ~ relation(u)
| ~ relation(u)
| ~ relation(u)
| equal(relation_rng_restriction(v,u),u)
| in(skf7(u,v,u),relation_rng(u))
| equal(relation_rng_restriction(v,u),u) ),
inference(res,[status(thm),theory(equality)],[1805,768]),
[iquote('0:Res:1805.3,768.1')] ).
cnf(5793,plain,
( ~ relation(u)
| in(skf7(u,v,u),relation_rng(u))
| equal(relation_rng_restriction(v,u),u) ),
inference(obv,[status(thm),theory(equality)],[5769]),
[iquote('0:Obv:5769.3')] ).
cnf(6438,plain,
( ~ relation(u)
| ~ relation(u)
| equal(relation_rng_restriction(relation_rng(u),u),u)
| equal(relation_rng_restriction(relation_rng(u),u),u) ),
inference(res,[status(thm),theory(equality)],[5793,768]),
[iquote('0:Res:5793.1,768.1')] ).
cnf(6444,plain,
( ~ relation(u)
| equal(relation_rng_restriction(relation_rng(u),u),u) ),
inference(obv,[status(thm),theory(equality)],[6438]),
[iquote('0:Obv:6438.2')] ).
cnf(6529,plain,
( ~ relation(u)
| ~ relation(u)
| ~ in(ordered_pair(v,w),u)
| in(w,relation_rng(u)) ),
inference(spl,[status(thm),theory(equality)],[6444,215]),
[iquote('0:SpL:6444.1,215.1')] ).
cnf(6544,plain,
( ~ relation(u)
| ~ in(ordered_pair(v,w),u)
| in(w,relation_rng(u)) ),
inference(obv,[status(thm),theory(equality)],[6529]),
[iquote('0:Obv:6529.0')] ).
cnf(6807,plain,
( ~ relation(relation_rng_restriction(u,skc7))
| ~ in(v,u)
| ~ in(ordered_pair(w,v),skc7)
| in(v,relation_rng(relation_rng_restriction(u,skc7))) ),
inference(res,[status(thm),theory(equality)],[1495,6544]),
[iquote('0:Res:1495.2,6544.1')] ).
cnf(6820,plain,
( ~ in(u,v)
| ~ in(ordered_pair(w,u),skc7)
| in(u,relation_rng(relation_rng_restriction(v,skc7))) ),
inference(ssi,[status(thm)],[6807,51]),
[iquote('0:SSi:6807.0,51.0')] ).
cnf(9975,plain,
( ~ in(u,relation_rng(skc7))
| ~ in(u,v)
| in(u,relation_rng(relation_rng_restriction(v,skc7))) ),
inference(res,[status(thm),theory(equality)],[412,6820]),
[iquote('0:Res:412.1,6820.1')] ).
cnf(10075,plain,
( ~ in(skc9,relation_rng(skc7))
| ~ in(skc9,skc8) ),
inference(res,[status(thm),theory(equality)],[9975,2343]),
[iquote('1:Res:9975.2,2343.0')] ).
cnf(10076,plain,
$false,
inference(mrr,[status(thm)],[10075,2349,2344]),
[iquote('1:MRR:10075.0,10075.1,2349.0,2344.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU197+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n007.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun Jun 19 04:27:28 EDT 2022
% 0.13/0.35 % CPUTime :
% 7.67/7.91
% 7.67/7.91 SPASS V 3.9
% 7.67/7.91 SPASS beiseite: Proof found.
% 7.67/7.91 % SZS status Theorem
% 7.67/7.91 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.67/7.91 SPASS derived 7477 clauses, backtracked 136 clauses, performed 2 splits and kept 3003 clauses.
% 7.67/7.91 SPASS allocated 107935 KBytes.
% 7.67/7.91 SPASS spent 0:00:07.35 on the problem.
% 7.67/7.91 0:00:00.04 for the input.
% 7.67/7.91 0:00:00.05 for the FLOTTER CNF translation.
% 7.67/7.91 0:00:00.20 for inferences.
% 7.67/7.91 0:00:00.25 for the backtracking.
% 7.67/7.91 0:00:06.75 for the reduction.
% 7.67/7.91
% 7.67/7.91
% 7.67/7.91 Here is a proof with depth 8, length 62 :
% 7.67/7.91 % SZS output start Refutation
% See solution above
% 7.67/7.91 Formulae used in the proof : t115_relat_1 dt_k8_relat_1 d5_relat_1 antisymmetry_r2_hidden d12_relat_1
% 7.67/7.91
%------------------------------------------------------------------------------