TSTP Solution File: SEU136+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU136+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n010.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 14:34:14 EDT 2022
% Result : Theorem 0.35s 0.53s
% Output : Refutation 0.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of clauses : 34 ( 15 unt; 9 nHn; 34 RR)
% Number of literals : 67 ( 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_union2(u,v),set_union2(v,u)),
file('SEU136+1.p',unknown),
[] ).
cnf(20,axiom,
~ equal(set_difference(set_union2(skc5,skc4),skc4),set_difference(skc5,skc4)),
file('SEU136+1.p',unknown),
[] ).
cnf(24,axiom,
( ~ in(u,v)
| ~ equal(w,set_union2(x,v))
| in(u,w) ),
file('SEU136+1.p',unknown),
[] ).
cnf(25,axiom,
( ~ in(u,v)
| ~ equal(v,set_difference(w,x))
| in(u,w) ),
file('SEU136+1.p',unknown),
[] ).
cnf(26,axiom,
( ~ in(u,v)
| ~ in(u,w)
| ~ equal(v,set_difference(x,w)) ),
file('SEU136+1.p',unknown),
[] ).
cnf(27,axiom,
( ~ in(u,v)
| ~ equal(v,set_union2(w,x))
| in(u,x)
| in(u,w) ),
file('SEU136+1.p',unknown),
[] ).
cnf(28,axiom,
( ~ in(u,v)
| ~ equal(w,set_difference(v,x))
| in(u,w)
| in(u,x) ),
file('SEU136+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('SEU136+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('SEU136+1.p',unknown),
[] ).
cnf(34,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('SEU136+1.p',unknown),
[] ).
cnf(35,plain,
~ equal(set_difference(set_union2(skc4,skc5),skc4),set_difference(skc5,skc4)),
inference(rew,[status(thm),theory(equality)],[10,20]),
[iquote('0:Rew:10.0,20.0')] ).
cnf(43,plain,
( ~ in(skf5(skc4,set_union2(skc4,skc5),set_difference(skc5,skc4)),set_union2(skc4,skc5))
| ~ in(skf5(skc4,set_union2(skc4,skc5),set_difference(skc5,skc4)),set_difference(skc5,skc4))
| in(skf5(skc4,set_union2(skc4,skc5),set_difference(skc5,skc4)),skc4) ),
inference(res,[status(thm),theory(equality)],[34,35]),
[iquote('0:Res:34.3,35.0')] ).
cnf(44,plain,
( ~ in(skf5(skc4,set_union2(skc4,skc5),set_difference(skc5,skc4)),skc4)
| in(skf5(skc4,set_union2(skc4,skc5),set_difference(skc5,skc4)),set_difference(skc5,skc4)) ),
inference(res,[status(thm),theory(equality)],[30,35]),
[iquote('0:Res:30.2,35.0')] ).
cnf(45,plain,
( in(skf5(skc4,set_union2(skc4,skc5),set_difference(skc5,skc4)),set_difference(skc5,skc4))
| in(skf5(skc4,set_union2(skc4,skc5),set_difference(skc5,skc4)),set_union2(skc4,skc5)) ),
inference(res,[status(thm),theory(equality)],[29,35]),
[iquote('0:Res:29.2,35.0')] ).
cnf(46,plain,
in(skf5(skc4,set_union2(skc4,skc5),set_difference(skc5,skc4)),set_difference(skc5,skc4)),
inference(spt,[spt(split,[position(s1)])],[45]),
[iquote('1:Spt:45.0')] ).
cnf(47,plain,
( ~ in(skf5(skc4,set_union2(skc4,skc5),set_difference(skc5,skc4)),set_union2(skc4,skc5))
| in(skf5(skc4,set_union2(skc4,skc5),set_difference(skc5,skc4)),skc4) ),
inference(mrr,[status(thm)],[43,46]),
[iquote('1:MRR:43.1,46.0')] ).
cnf(98,plain,
( ~ in(u,set_difference(v,w))
| in(u,v) ),
inference(eqr,[status(thm),theory(equality)],[25]),
[iquote('0:EqR:25.1')] ).
cnf(103,plain,
in(skf5(skc4,set_union2(skc4,skc5),set_difference(skc5,skc4)),skc5),
inference(res,[status(thm),theory(equality)],[46,98]),
[iquote('1:Res:46.0,98.0')] ).
cnf(108,plain,
( ~ in(u,v)
| in(u,set_union2(w,v)) ),
inference(eqr,[status(thm),theory(equality)],[24]),
[iquote('0:EqR:24.1')] ).
cnf(155,plain,
( ~ in(u,set_difference(v,w))
| ~ in(u,w) ),
inference(eqr,[status(thm),theory(equality)],[26]),
[iquote('0:EqR:26.2')] ).
cnf(167,plain,
( ~ in(u,v)
| in(u,set_difference(v,w))
| in(u,w) ),
inference(eqr,[status(thm),theory(equality)],[28]),
[iquote('0:EqR:28.1')] ).
cnf(187,plain,
( ~ in(u,set_union2(v,w))
| in(u,w)
| in(u,v) ),
inference(eqr,[status(thm),theory(equality)],[27]),
[iquote('0:EqR:27.1')] ).
cnf(210,plain,
~ in(skf5(skc4,set_union2(skc4,skc5),set_difference(skc5,skc4)),skc4),
inference(res,[status(thm),theory(equality)],[46,155]),
[iquote('1:Res:46.0,155.0')] ).
cnf(214,plain,
~ in(skf5(skc4,set_union2(skc4,skc5),set_difference(skc5,skc4)),set_union2(skc4,skc5)),
inference(mrr,[status(thm)],[47,210]),
[iquote('1:MRR:47.1,210.0')] ).
cnf(567,plain,
~ in(skf5(skc4,set_union2(skc4,skc5),set_difference(skc5,skc4)),skc5),
inference(res,[status(thm),theory(equality)],[108,214]),
[iquote('1:Res:108.1,214.0')] ).
cnf(569,plain,
$false,
inference(mrr,[status(thm)],[567,103]),
[iquote('1:MRR:567.0,103.0')] ).
cnf(570,plain,
~ in(skf5(skc4,set_union2(skc4,skc5),set_difference(skc5,skc4)),set_difference(skc5,skc4)),
inference(spt,[spt(split,[position(sa)])],[569,46]),
[iquote('1:Spt:569.0,45.0,46.0')] ).
cnf(571,plain,
in(skf5(skc4,set_union2(skc4,skc5),set_difference(skc5,skc4)),set_union2(skc4,skc5)),
inference(spt,[spt(split,[position(s2)])],[45]),
[iquote('1:Spt:569.0,45.1')] ).
cnf(572,plain,
~ in(skf5(skc4,set_union2(skc4,skc5),set_difference(skc5,skc4)),skc4),
inference(mrr,[status(thm)],[44,155]),
[iquote('0:MRR:44.1,155.0')] ).
cnf(582,plain,
( in(skf5(skc4,set_union2(skc4,skc5),set_difference(skc5,skc4)),skc5)
| in(skf5(skc4,set_union2(skc4,skc5),set_difference(skc5,skc4)),skc4) ),
inference(res,[status(thm),theory(equality)],[571,187]),
[iquote('1:Res:571.0,187.0')] ).
cnf(584,plain,
in(skf5(skc4,set_union2(skc4,skc5),set_difference(skc5,skc4)),skc5),
inference(mrr,[status(thm)],[582,572]),
[iquote('1:MRR:582.1,572.0')] ).
cnf(603,plain,
( ~ in(skf5(skc4,set_union2(skc4,skc5),set_difference(skc5,skc4)),skc5)
| in(skf5(skc4,set_union2(skc4,skc5),set_difference(skc5,skc4)),skc4) ),
inference(res,[status(thm),theory(equality)],[167,570]),
[iquote('1:Res:167.1,570.0')] ).
cnf(607,plain,
in(skf5(skc4,set_union2(skc4,skc5),set_difference(skc5,skc4)),skc4),
inference(mrr,[status(thm)],[603,584]),
[iquote('1:MRR:603.0,584.0')] ).
cnf(608,plain,
$false,
inference(mrr,[status(thm)],[607,572]),
[iquote('1:MRR:607.0,572.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU136+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.14 % Command : run_spass %d %s
% 0.14/0.36 % Computer : n010.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Mon Jun 20 02:04:37 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.35/0.53
% 0.35/0.53 SPASS V 3.9
% 0.35/0.53 SPASS beiseite: Proof found.
% 0.35/0.53 % SZS status Theorem
% 0.35/0.53 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.35/0.53 SPASS derived 506 clauses, backtracked 7 clauses, performed 1 splits and kept 274 clauses.
% 0.35/0.53 SPASS allocated 98134 KBytes.
% 0.35/0.53 SPASS spent 0:00:00.16 on the problem.
% 0.35/0.53 0:00:00.03 for the input.
% 0.35/0.53 0:00:00.05 for the FLOTTER CNF translation.
% 0.35/0.53 0:00:00.01 for inferences.
% 0.35/0.53 0:00:00.00 for the backtracking.
% 0.35/0.53 0:00:00.05 for the reduction.
% 0.35/0.53
% 0.35/0.53
% 0.35/0.53 Here is a proof with depth 3, length 34 :
% 0.35/0.53 % SZS output start Refutation
% See solution above
% 0.35/0.53 Formulae used in the proof : commutativity_k2_xboole_0 t40_xboole_1 d2_xboole_0 d4_xboole_0
% 0.35/0.53
%------------------------------------------------------------------------------