TSTP Solution File: SEU135+2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU135+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.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 14:34:13 EDT 2022
% Result : Theorem 1.07s 1.25s
% Output : Refutation 1.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of clauses : 32 ( 13 unt; 9 nHn; 32 RR)
% Number of literals : 64 ( 0 equ; 29 neg)
% Maximal clause size : 4 ( 2 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(16,axiom,
equal(set_union2(u,v),set_union2(v,u)),
file('SEU135+2.p',unknown),
[] ).
cnf(41,axiom,
~ equal(set_union2(skc5,set_difference(skc4,skc5)),set_union2(skc5,skc4)),
file('SEU135+2.p',unknown),
[] ).
cnf(51,axiom,
( ~ in(u,v)
| ~ equal(w,set_union2(x,v))
| in(u,w) ),
file('SEU135+2.p',unknown),
[] ).
cnf(54,axiom,
( ~ in(u,v)
| ~ equal(v,set_difference(w,x))
| in(u,w) ),
file('SEU135+2.p',unknown),
[] ).
cnf(60,axiom,
( ~ in(u,v)
| ~ equal(v,set_union2(w,x))
| in(u,x)
| in(u,w) ),
file('SEU135+2.p',unknown),
[] ).
cnf(61,axiom,
( ~ in(u,v)
| ~ equal(w,set_difference(v,x))
| in(u,w)
| in(u,x) ),
file('SEU135+2.p',unknown),
[] ).
cnf(67,axiom,
( ~ in(skf9(u,v,w),w)
| ~ in(skf9(u,v,w),v)
| equal(w,set_union2(v,u)) ),
file('SEU135+2.p',unknown),
[] ).
cnf(68,axiom,
( ~ in(skf9(u,v,w),w)
| ~ in(skf9(u,v,w),u)
| equal(w,set_union2(v,u)) ),
file('SEU135+2.p',unknown),
[] ).
cnf(69,axiom,
( equal(u,set_union2(v,w))
| in(skf9(w,v,u),w)
| in(skf9(w,v,u),v)
| in(skf9(w,v,u),u) ),
file('SEU135+2.p',unknown),
[] ).
cnf(73,plain,
~ equal(set_union2(skc5,set_difference(skc4,skc5)),set_union2(skc4,skc5)),
inference(rew,[status(thm),theory(equality)],[16,41]),
[iquote('0:Rew:16.0,41.0')] ).
cnf(85,plain,
( in(skf9(set_difference(skc4,skc5),skc5,set_union2(skc4,skc5)),skc5)
| in(skf9(set_difference(skc4,skc5),skc5,set_union2(skc4,skc5)),set_difference(skc4,skc5))
| in(skf9(set_difference(skc4,skc5),skc5,set_union2(skc4,skc5)),set_union2(skc4,skc5)) ),
inference(res,[status(thm),theory(equality)],[69,73]),
[iquote('0:Res:69.3,73.0')] ).
cnf(86,plain,
( ~ in(skf9(set_difference(skc4,skc5),skc5,set_union2(skc4,skc5)),skc5)
| ~ in(skf9(set_difference(skc4,skc5),skc5,set_union2(skc4,skc5)),set_union2(skc4,skc5)) ),
inference(res,[status(thm),theory(equality)],[67,73]),
[iquote('0:Res:67.2,73.0')] ).
cnf(87,plain,
( ~ in(skf9(set_difference(skc4,skc5),skc5,set_union2(skc4,skc5)),set_union2(skc4,skc5))
| ~ in(skf9(set_difference(skc4,skc5),skc5,set_union2(skc4,skc5)),set_difference(skc4,skc5)) ),
inference(res,[status(thm),theory(equality)],[68,73]),
[iquote('0:Res:68.2,73.0')] ).
cnf(88,plain,
in(skf9(set_difference(skc4,skc5),skc5,set_union2(skc4,skc5)),set_union2(skc4,skc5)),
inference(spt,[spt(split,[position(s1)])],[85]),
[iquote('1:Spt:85.2')] ).
cnf(89,plain,
~ in(skf9(set_difference(skc4,skc5),skc5,set_union2(skc4,skc5)),skc5),
inference(mrr,[status(thm)],[86,88]),
[iquote('1:MRR:86.1,88.0')] ).
cnf(90,plain,
~ in(skf9(set_difference(skc4,skc5),skc5,set_union2(skc4,skc5)),set_difference(skc4,skc5)),
inference(mrr,[status(thm)],[87,88]),
[iquote('1:MRR:87.0,88.0')] ).
cnf(417,plain,
( ~ in(u,set_difference(v,w))
| in(u,v) ),
inference(eqr,[status(thm),theory(equality)],[54]),
[iquote('0:EqR:54.1')] ).
cnf(573,plain,
( ~ in(u,v)
| in(u,set_union2(w,v)) ),
inference(eqr,[status(thm),theory(equality)],[51]),
[iquote('0:EqR:51.1')] ).
cnf(633,plain,
( ~ in(u,v)
| in(u,set_union2(v,w)) ),
inference(spr,[status(thm),theory(equality)],[16,573]),
[iquote('0:SpR:16.0,573.1')] ).
cnf(1444,plain,
( ~ in(u,v)
| in(u,set_difference(v,w))
| in(u,w) ),
inference(eqr,[status(thm),theory(equality)],[61]),
[iquote('0:EqR:61.1')] ).
cnf(1473,plain,
( ~ in(u,set_union2(v,w))
| in(u,w)
| in(u,v) ),
inference(eqr,[status(thm),theory(equality)],[60]),
[iquote('0:EqR:60.1')] ).
cnf(3654,plain,
( in(skf9(set_difference(skc4,skc5),skc5,set_union2(skc4,skc5)),skc5)
| in(skf9(set_difference(skc4,skc5),skc5,set_union2(skc4,skc5)),skc4) ),
inference(res,[status(thm),theory(equality)],[88,1473]),
[iquote('1:Res:88.0,1473.0')] ).
cnf(3729,plain,
in(skf9(set_difference(skc4,skc5),skc5,set_union2(skc4,skc5)),skc4),
inference(mrr,[status(thm)],[3654,89]),
[iquote('1:MRR:3654.0,89.0')] ).
cnf(3851,plain,
( ~ in(skf9(set_difference(skc4,skc5),skc5,set_union2(skc4,skc5)),skc4)
| in(skf9(set_difference(skc4,skc5),skc5,set_union2(skc4,skc5)),skc5) ),
inference(res,[status(thm),theory(equality)],[1444,90]),
[iquote('1:Res:1444.1,90.0')] ).
cnf(3853,plain,
$false,
inference(mrr,[status(thm)],[3851,3729,89]),
[iquote('1:MRR:3851.0,3851.1,3729.0,89.0')] ).
cnf(3854,plain,
~ in(skf9(set_difference(skc4,skc5),skc5,set_union2(skc4,skc5)),set_union2(skc4,skc5)),
inference(spt,[spt(split,[position(sa)])],[3853,88]),
[iquote('1:Spt:3853.0,85.2,88.0')] ).
cnf(3855,plain,
( in(skf9(set_difference(skc4,skc5),skc5,set_union2(skc4,skc5)),skc5)
| in(skf9(set_difference(skc4,skc5),skc5,set_union2(skc4,skc5)),set_difference(skc4,skc5)) ),
inference(spt,[spt(split,[position(s2)])],[85]),
[iquote('1:Spt:3853.0,85.0,85.1')] ).
cnf(3887,plain,
( in(skf9(set_difference(skc4,skc5),skc5,set_union2(skc4,skc5)),skc5)
| in(skf9(set_difference(skc4,skc5),skc5,set_union2(skc4,skc5)),skc4) ),
inference(res,[status(thm),theory(equality)],[3855,417]),
[iquote('1:Res:3855.1,417.0')] ).
cnf(4053,plain,
~ in(skf9(set_difference(skc4,skc5),skc5,set_union2(skc4,skc5)),skc5),
inference(res,[status(thm),theory(equality)],[573,3854]),
[iquote('1:Res:573.1,3854.0')] ).
cnf(4054,plain,
~ in(skf9(set_difference(skc4,skc5),skc5,set_union2(skc4,skc5)),skc4),
inference(res,[status(thm),theory(equality)],[633,3854]),
[iquote('1:Res:633.1,3854.0')] ).
cnf(4059,plain,
in(skf9(set_difference(skc4,skc5),skc5,set_union2(skc4,skc5)),skc4),
inference(mrr,[status(thm)],[3887,4053]),
[iquote('1:MRR:3887.0,4053.0')] ).
cnf(4064,plain,
$false,
inference(mrr,[status(thm)],[4054,4059]),
[iquote('1:MRR:4054.0,4059.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SEU135+2 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n008.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 : Sun Jun 19 23:53:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.07/1.25
% 1.07/1.25 SPASS V 3.9
% 1.07/1.25 SPASS beiseite: Proof found.
% 1.07/1.25 % SZS status Theorem
% 1.07/1.25 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.07/1.25 SPASS derived 3521 clauses, backtracked 5 clauses, performed 1 splits and kept 1484 clauses.
% 1.07/1.25 SPASS allocated 100736 KBytes.
% 1.07/1.25 SPASS spent 0:00:00.90 on the problem.
% 1.07/1.25 0:00:00.03 for the input.
% 1.07/1.25 0:00:00.05 for the FLOTTER CNF translation.
% 1.07/1.25 0:00:00.04 for inferences.
% 1.07/1.25 0:00:00.00 for the backtracking.
% 1.07/1.25 0:00:00.75 for the reduction.
% 1.07/1.25
% 1.07/1.25
% 1.07/1.25 Here is a proof with depth 3, length 32 :
% 1.07/1.25 % SZS output start Refutation
% See solution above
% 1.07/1.25 Formulae used in the proof : commutativity_k2_xboole_0 t39_xboole_1 d2_xboole_0 d4_xboole_0
% 1.07/1.25
%------------------------------------------------------------------------------