TSTP Solution File: SEU135+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU135+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 14:34:13 EDT 2022
% Result : Theorem 0.19s 0.52s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of clauses : 33 ( 13 unt; 9 nHn; 33 RR)
% Number of literals : 67 ( 0 equ; 32 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(10,axiom,
equal(set_union2(u,v),set_union2(v,u)),
file('SEU135+1.p',unknown),
[] ).
cnf(20,axiom,
~ equal(set_union2(skc5,set_difference(skc4,skc5)),set_union2(skc5,skc4)),
file('SEU135+1.p',unknown),
[] ).
cnf(23,axiom,
( ~ in(u,v)
| ~ equal(w,set_union2(v,x))
| in(u,w) ),
file('SEU135+1.p',unknown),
[] ).
cnf(24,axiom,
( ~ in(u,v)
| ~ equal(w,set_union2(x,v))
| in(u,w) ),
file('SEU135+1.p',unknown),
[] ).
cnf(25,axiom,
( ~ in(u,v)
| ~ equal(v,set_difference(w,x))
| in(u,w) ),
file('SEU135+1.p',unknown),
[] ).
cnf(27,axiom,
( ~ in(u,v)
| ~ equal(v,set_union2(w,x))
| in(u,x)
| in(u,w) ),
file('SEU135+1.p',unknown),
[] ).
cnf(28,axiom,
( ~ in(u,v)
| ~ equal(w,set_difference(v,x))
| in(u,w)
| in(u,x) ),
file('SEU135+1.p',unknown),
[] ).
cnf(31,axiom,
( ~ in(skf3(u,v,w),w)
| ~ in(skf3(u,v,w),v)
| equal(w,set_union2(v,u)) ),
file('SEU135+1.p',unknown),
[] ).
cnf(32,axiom,
( ~ in(skf3(u,v,w),w)
| ~ in(skf3(u,v,w),u)
| equal(w,set_union2(v,u)) ),
file('SEU135+1.p',unknown),
[] ).
cnf(33,axiom,
( equal(u,set_union2(v,w))
| in(skf3(w,v,u),w)
| in(skf3(w,v,u),v)
| in(skf3(w,v,u),u) ),
file('SEU135+1.p',unknown),
[] ).
cnf(35,plain,
~ equal(set_union2(skc5,set_difference(skc4,skc5)),set_union2(skc4,skc5)),
inference(rew,[status(thm),theory(equality)],[10,20]),
[iquote('0:Rew:10.0,20.0')] ).
cnf(43,plain,
( in(skf3(set_difference(skc4,skc5),skc5,set_union2(skc4,skc5)),skc5)
| in(skf3(set_difference(skc4,skc5),skc5,set_union2(skc4,skc5)),set_difference(skc4,skc5))
| in(skf3(set_difference(skc4,skc5),skc5,set_union2(skc4,skc5)),set_union2(skc4,skc5)) ),
inference(res,[status(thm),theory(equality)],[33,35]),
[iquote('0:Res:33.3,35.0')] ).
cnf(44,plain,
( ~ in(skf3(set_difference(skc4,skc5),skc5,set_union2(skc4,skc5)),skc5)
| ~ in(skf3(set_difference(skc4,skc5),skc5,set_union2(skc4,skc5)),set_union2(skc4,skc5)) ),
inference(res,[status(thm),theory(equality)],[31,35]),
[iquote('0:Res:31.2,35.0')] ).
cnf(45,plain,
( ~ in(skf3(set_difference(skc4,skc5),skc5,set_union2(skc4,skc5)),set_union2(skc4,skc5))
| ~ in(skf3(set_difference(skc4,skc5),skc5,set_union2(skc4,skc5)),set_difference(skc4,skc5)) ),
inference(res,[status(thm),theory(equality)],[32,35]),
[iquote('0:Res:32.2,35.0')] ).
cnf(46,plain,
in(skf3(set_difference(skc4,skc5),skc5,set_union2(skc4,skc5)),set_union2(skc4,skc5)),
inference(spt,[spt(split,[position(s1)])],[43]),
[iquote('1:Spt:43.2')] ).
cnf(47,plain,
~ in(skf3(set_difference(skc4,skc5),skc5,set_union2(skc4,skc5)),skc5),
inference(mrr,[status(thm)],[44,46]),
[iquote('1:MRR:44.1,46.0')] ).
cnf(48,plain,
~ in(skf3(set_difference(skc4,skc5),skc5,set_union2(skc4,skc5)),set_difference(skc4,skc5)),
inference(mrr,[status(thm)],[45,46]),
[iquote('1:MRR:45.0,46.0')] ).
cnf(109,plain,
( ~ in(u,set_difference(v,w))
| in(u,v) ),
inference(eqr,[status(thm),theory(equality)],[25]),
[iquote('0:EqR:25.1')] ).
cnf(136,plain,
( ~ in(u,v)
| in(u,set_union2(w,v)) ),
inference(eqr,[status(thm),theory(equality)],[24]),
[iquote('0:EqR:24.1')] ).
cnf(165,plain,
( ~ in(u,v)
| in(u,set_union2(v,w)) ),
inference(eqr,[status(thm),theory(equality)],[23]),
[iquote('0:EqR:23.1')] ).
cnf(224,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(273,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(574,plain,
( ~ in(skf3(set_difference(skc4,skc5),skc5,set_union2(skc4,skc5)),skc4)
| in(skf3(set_difference(skc4,skc5),skc5,set_union2(skc4,skc5)),skc5) ),
inference(res,[status(thm),theory(equality)],[224,48]),
[iquote('1:Res:224.1,48.0')] ).
cnf(591,plain,
~ in(skf3(set_difference(skc4,skc5),skc5,set_union2(skc4,skc5)),skc4),
inference(mrr,[status(thm)],[574,47]),
[iquote('1:MRR:574.1,47.0')] ).
cnf(604,plain,
( in(skf3(set_difference(skc4,skc5),skc5,set_union2(skc4,skc5)),skc5)
| in(skf3(set_difference(skc4,skc5),skc5,set_union2(skc4,skc5)),skc4) ),
inference(res,[status(thm),theory(equality)],[46,273]),
[iquote('1:Res:46.0,273.0')] ).
cnf(620,plain,
$false,
inference(mrr,[status(thm)],[604,47,591]),
[iquote('1:MRR:604.0,604.1,47.0,591.0')] ).
cnf(621,plain,
~ in(skf3(set_difference(skc4,skc5),skc5,set_union2(skc4,skc5)),set_union2(skc4,skc5)),
inference(spt,[spt(split,[position(sa)])],[620,46]),
[iquote('1:Spt:620.0,43.2,46.0')] ).
cnf(622,plain,
( in(skf3(set_difference(skc4,skc5),skc5,set_union2(skc4,skc5)),skc5)
| in(skf3(set_difference(skc4,skc5),skc5,set_union2(skc4,skc5)),set_difference(skc4,skc5)) ),
inference(spt,[spt(split,[position(s2)])],[43]),
[iquote('1:Spt:620.0,43.0,43.1')] ).
cnf(637,plain,
( in(skf3(set_difference(skc4,skc5),skc5,set_union2(skc4,skc5)),skc5)
| in(skf3(set_difference(skc4,skc5),skc5,set_union2(skc4,skc5)),skc4) ),
inference(res,[status(thm),theory(equality)],[622,109]),
[iquote('1:Res:622.1,109.0')] ).
cnf(661,plain,
~ in(skf3(set_difference(skc4,skc5),skc5,set_union2(skc4,skc5)),skc5),
inference(res,[status(thm),theory(equality)],[136,621]),
[iquote('1:Res:136.1,621.0')] ).
cnf(662,plain,
~ in(skf3(set_difference(skc4,skc5),skc5,set_union2(skc4,skc5)),skc4),
inference(res,[status(thm),theory(equality)],[165,621]),
[iquote('1:Res:165.1,621.0')] ).
cnf(667,plain,
in(skf3(set_difference(skc4,skc5),skc5,set_union2(skc4,skc5)),skc4),
inference(mrr,[status(thm)],[637,661]),
[iquote('1:MRR:637.0,661.0')] ).
cnf(671,plain,
$false,
inference(mrr,[status(thm)],[662,667]),
[iquote('1:MRR:662.0,667.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SEU135+1 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n020.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 20 11:22:48 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.52
% 0.19/0.52 SPASS V 3.9
% 0.19/0.52 SPASS beiseite: Proof found.
% 0.19/0.52 % SZS status Theorem
% 0.19/0.52 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.52 SPASS derived 543 clauses, backtracked 5 clauses, performed 1 splits and kept 277 clauses.
% 0.19/0.52 SPASS allocated 98153 KBytes.
% 0.19/0.52 SPASS spent 0:00:00.16 on the problem.
% 0.19/0.52 0:00:00.03 for the input.
% 0.19/0.52 0:00:00.05 for the FLOTTER CNF translation.
% 0.19/0.52 0:00:00.01 for inferences.
% 0.19/0.52 0:00:00.00 for the backtracking.
% 0.19/0.52 0:00:00.05 for the reduction.
% 0.19/0.52
% 0.19/0.52
% 0.19/0.52 Here is a proof with depth 3, length 33 :
% 0.19/0.52 % SZS output start Refutation
% See solution above
% 0.19/0.52 Formulae used in the proof : commutativity_k2_xboole_0 t39_xboole_1 d2_xboole_0 d4_xboole_0
% 0.19/0.52
%------------------------------------------------------------------------------