TSTP Solution File: SEU138+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU138+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 14:34:15 EDT 2022
% Result : Theorem 0.41s 0.59s
% Output : Refutation 0.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of clauses : 32 ( 14 unt; 6 nHn; 32 RR)
% Number of literals : 63 ( 0 equ; 32 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(10,axiom,
equal(set_intersection2(u,v),set_intersection2(v,u)),
file('SEU138+1.p',unknown),
[] ).
cnf(18,axiom,
~ equal(set_difference(skc5,set_difference(skc5,skc4)),set_intersection2(skc5,skc4)),
file('SEU138+1.p',unknown),
[] ).
cnf(22,axiom,
( ~ in(u,v)
| ~ equal(v,set_intersection2(w,x))
| in(u,x) ),
file('SEU138+1.p',unknown),
[] ).
cnf(24,axiom,
( ~ in(u,v)
| ~ in(u,w)
| ~ equal(v,set_difference(x,w)) ),
file('SEU138+1.p',unknown),
[] ).
cnf(25,axiom,
( ~ in(u,v)
| ~ equal(w,set_difference(v,x))
| in(u,w)
| in(u,x) ),
file('SEU138+1.p',unknown),
[] ).
cnf(26,axiom,
( ~ in(u,v)
| ~ in(u,w)
| ~ equal(x,set_intersection2(w,v))
| in(u,x) ),
file('SEU138+1.p',unknown),
[] ).
cnf(29,axiom,
( equal(u,set_difference(v,w))
| in(skf5(w,v,u),u)
| in(skf5(w,v,u),v) ),
file('SEU138+1.p',unknown),
[] ).
cnf(30,axiom,
( ~ in(skf5(u,v,w),u)
| equal(w,set_difference(v,u))
| in(skf5(u,v,w),w) ),
file('SEU138+1.p',unknown),
[] ).
cnf(31,axiom,
( ~ in(skf5(u,v,w),v)
| ~ in(skf5(u,v,w),w)
| equal(w,set_difference(v,u))
| in(skf5(u,v,w),u) ),
file('SEU138+1.p',unknown),
[] ).
cnf(33,plain,
~ equal(set_difference(skc5,set_difference(skc5,skc4)),set_intersection2(skc4,skc5)),
inference(rew,[status(thm),theory(equality)],[10,18]),
[iquote('0:Rew:10.0,18.0')] ).
cnf(41,plain,
( ~ in(skf5(set_difference(skc5,skc4),skc5,set_intersection2(skc4,skc5)),skc5)
| ~ in(skf5(set_difference(skc5,skc4),skc5,set_intersection2(skc4,skc5)),set_intersection2(skc4,skc5))
| in(skf5(set_difference(skc5,skc4),skc5,set_intersection2(skc4,skc5)),set_difference(skc5,skc4)) ),
inference(res,[status(thm),theory(equality)],[31,33]),
[iquote('0:Res:31.3,33.0')] ).
cnf(42,plain,
( ~ in(skf5(set_difference(skc5,skc4),skc5,set_intersection2(skc4,skc5)),set_difference(skc5,skc4))
| in(skf5(set_difference(skc5,skc4),skc5,set_intersection2(skc4,skc5)),set_intersection2(skc4,skc5)) ),
inference(res,[status(thm),theory(equality)],[30,33]),
[iquote('0:Res:30.2,33.0')] ).
cnf(43,plain,
( in(skf5(set_difference(skc5,skc4),skc5,set_intersection2(skc4,skc5)),skc5)
| in(skf5(set_difference(skc5,skc4),skc5,set_intersection2(skc4,skc5)),set_intersection2(skc4,skc5)) ),
inference(res,[status(thm),theory(equality)],[29,33]),
[iquote('0:Res:29.2,33.0')] ).
cnf(44,plain,
in(skf5(set_difference(skc5,skc4),skc5,set_intersection2(skc4,skc5)),set_intersection2(skc4,skc5)),
inference(spt,[spt(split,[position(s1)])],[43]),
[iquote('1:Spt:43.1')] ).
cnf(45,plain,
( ~ in(skf5(set_difference(skc5,skc4),skc5,set_intersection2(skc4,skc5)),skc5)
| in(skf5(set_difference(skc5,skc4),skc5,set_intersection2(skc4,skc5)),set_difference(skc5,skc4)) ),
inference(mrr,[status(thm)],[41,44]),
[iquote('1:MRR:41.1,44.0')] ).
cnf(117,plain,
( ~ in(u,set_intersection2(v,w))
| in(u,w) ),
inference(eqr,[status(thm),theory(equality)],[22]),
[iquote('0:EqR:22.1')] ).
cnf(143,plain,
( ~ in(u,set_intersection2(v,w))
| in(u,v) ),
inference(spl,[status(thm),theory(equality)],[10,117]),
[iquote('0:SpL:10.0,117.0')] ).
cnf(146,plain,
in(skf5(set_difference(skc5,skc4),skc5,set_intersection2(skc4,skc5)),skc5),
inference(res,[status(thm),theory(equality)],[44,117]),
[iquote('1:Res:44.0,117.0')] ).
cnf(150,plain,
in(skf5(set_difference(skc5,skc4),skc5,set_intersection2(skc4,skc5)),set_difference(skc5,skc4)),
inference(mrr,[status(thm)],[45,146]),
[iquote('1:MRR:45.0,146.0')] ).
cnf(180,plain,
( ~ in(u,set_difference(v,w))
| ~ in(u,w) ),
inference(eqr,[status(thm),theory(equality)],[24]),
[iquote('0:EqR:24.2')] ).
cnf(207,plain,
( ~ in(u,v)
| in(u,set_difference(v,w))
| in(u,w) ),
inference(eqr,[status(thm),theory(equality)],[25]),
[iquote('0:EqR:25.1')] ).
cnf(249,plain,
in(skf5(set_difference(skc5,skc4),skc5,set_intersection2(skc4,skc5)),skc4),
inference(res,[status(thm),theory(equality)],[44,143]),
[iquote('1:Res:44.0,143.0')] ).
cnf(253,plain,
( ~ in(u,v)
| ~ in(u,w)
| in(u,set_intersection2(w,v)) ),
inference(eqr,[status(thm),theory(equality)],[26]),
[iquote('0:EqR:26.2')] ).
cnf(764,plain,
~ in(skf5(set_difference(skc5,skc4),skc5,set_intersection2(skc4,skc5)),skc4),
inference(res,[status(thm),theory(equality)],[150,180]),
[iquote('1:Res:150.0,180.0')] ).
cnf(767,plain,
$false,
inference(mrr,[status(thm)],[764,249]),
[iquote('1:MRR:764.0,249.0')] ).
cnf(768,plain,
~ in(skf5(set_difference(skc5,skc4),skc5,set_intersection2(skc4,skc5)),set_intersection2(skc4,skc5)),
inference(spt,[spt(split,[position(sa)])],[767,44]),
[iquote('1:Spt:767.0,43.1,44.0')] ).
cnf(769,plain,
in(skf5(set_difference(skc5,skc4),skc5,set_intersection2(skc4,skc5)),skc5),
inference(spt,[spt(split,[position(s2)])],[43]),
[iquote('1:Spt:767.0,43.0')] ).
cnf(777,plain,
~ in(skf5(set_difference(skc5,skc4),skc5,set_intersection2(skc4,skc5)),set_difference(skc5,skc4)),
inference(mrr,[status(thm)],[42,768]),
[iquote('1:MRR:42.1,768.0')] ).
cnf(1060,plain,
( ~ in(skf5(set_difference(skc5,skc4),skc5,set_intersection2(skc4,skc5)),skc5)
| in(skf5(set_difference(skc5,skc4),skc5,set_intersection2(skc4,skc5)),skc4) ),
inference(res,[status(thm),theory(equality)],[207,777]),
[iquote('1:Res:207.1,777.0')] ).
cnf(1061,plain,
in(skf5(set_difference(skc5,skc4),skc5,set_intersection2(skc4,skc5)),skc4),
inference(mrr,[status(thm)],[1060,769]),
[iquote('1:MRR:1060.0,769.0')] ).
cnf(1126,plain,
( ~ in(skf5(set_difference(skc5,skc4),skc5,set_intersection2(skc4,skc5)),skc5)
| ~ in(skf5(set_difference(skc5,skc4),skc5,set_intersection2(skc4,skc5)),skc4) ),
inference(res,[status(thm),theory(equality)],[253,768]),
[iquote('1:Res:253.2,768.0')] ).
cnf(1131,plain,
$false,
inference(mrr,[status(thm)],[1126,769,1061]),
[iquote('1:MRR:1126.0,1126.1,769.0,1061.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SEU138+1 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.15 % Command : run_spass %d %s
% 0.14/0.37 % Computer : n020.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 600
% 0.14/0.37 % DateTime : Sun Jun 19 07:32:03 EDT 2022
% 0.14/0.37 % CPUTime :
% 0.41/0.59
% 0.41/0.59 SPASS V 3.9
% 0.41/0.59 SPASS beiseite: Proof found.
% 0.41/0.59 % SZS status Theorem
% 0.41/0.59 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.41/0.59 SPASS derived 923 clauses, backtracked 12 clauses, performed 1 splits and kept 405 clauses.
% 0.41/0.59 SPASS allocated 98383 KBytes.
% 0.41/0.59 SPASS spent 0:00:00.20 on the problem.
% 0.41/0.59 0:00:00.03 for the input.
% 0.41/0.59 0:00:00.05 for the FLOTTER CNF translation.
% 0.41/0.59 0:00:00.01 for inferences.
% 0.41/0.59 0:00:00.00 for the backtracking.
% 0.41/0.59 0:00:00.08 for the reduction.
% 0.41/0.59
% 0.41/0.59
% 0.41/0.59 Here is a proof with depth 3, length 32 :
% 0.41/0.59 % SZS output start Refutation
% See solution above
% 0.41/0.59 Formulae used in the proof : commutativity_k3_xboole_0 t48_xboole_1 d3_xboole_0 d4_xboole_0
% 0.41/0.59
%------------------------------------------------------------------------------