TSTP Solution File: SEU138+2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU138+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n013.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 1.46s 1.65s
% Output : Refutation 1.46s
% 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(17,axiom,
equal(set_intersection2(u,v),set_intersection2(v,u)),
file('SEU138+2.p',unknown),
[] ).
cnf(43,axiom,
~ equal(set_difference(skc5,set_difference(skc5,skc4)),set_intersection2(skc5,skc4)),
file('SEU138+2.p',unknown),
[] ).
cnf(56,axiom,
( ~ in(u,v)
| ~ equal(v,set_intersection2(w,x))
| in(u,x) ),
file('SEU138+2.p',unknown),
[] ).
cnf(61,axiom,
( ~ in(u,v)
| ~ in(u,w)
| ~ equal(v,set_difference(x,w)) ),
file('SEU138+2.p',unknown),
[] ).
cnf(64,axiom,
( ~ in(u,v)
| ~ equal(w,set_difference(v,x))
| in(u,w)
| in(u,x) ),
file('SEU138+2.p',unknown),
[] ).
cnf(65,axiom,
( ~ in(u,v)
| ~ in(u,w)
| ~ equal(x,set_intersection2(w,v))
| in(u,x) ),
file('SEU138+2.p',unknown),
[] ).
cnf(68,axiom,
( equal(u,set_difference(v,w))
| in(skf12(w,v,u),u)
| in(skf12(w,v,u),v) ),
file('SEU138+2.p',unknown),
[] ).
cnf(69,axiom,
( ~ in(skf12(u,v,w),u)
| equal(w,set_difference(v,u))
| in(skf12(u,v,w),w) ),
file('SEU138+2.p',unknown),
[] ).
cnf(73,axiom,
( ~ in(skf12(u,v,w),v)
| ~ in(skf12(u,v,w),w)
| equal(w,set_difference(v,u))
| in(skf12(u,v,w),u) ),
file('SEU138+2.p',unknown),
[] ).
cnf(76,plain,
~ equal(set_difference(skc5,set_difference(skc5,skc4)),set_intersection2(skc4,skc5)),
inference(rew,[status(thm),theory(equality)],[17,43]),
[iquote('0:Rew:17.0,43.0')] ).
cnf(89,plain,
( ~ in(skf12(set_difference(skc5,skc4),skc5,set_intersection2(skc4,skc5)),skc5)
| ~ in(skf12(set_difference(skc5,skc4),skc5,set_intersection2(skc4,skc5)),set_intersection2(skc4,skc5))
| in(skf12(set_difference(skc5,skc4),skc5,set_intersection2(skc4,skc5)),set_difference(skc5,skc4)) ),
inference(res,[status(thm),theory(equality)],[73,76]),
[iquote('0:Res:73.3,76.0')] ).
cnf(90,plain,
( ~ in(skf12(set_difference(skc5,skc4),skc5,set_intersection2(skc4,skc5)),set_difference(skc5,skc4))
| in(skf12(set_difference(skc5,skc4),skc5,set_intersection2(skc4,skc5)),set_intersection2(skc4,skc5)) ),
inference(res,[status(thm),theory(equality)],[69,76]),
[iquote('0:Res:69.2,76.0')] ).
cnf(91,plain,
( in(skf12(set_difference(skc5,skc4),skc5,set_intersection2(skc4,skc5)),skc5)
| in(skf12(set_difference(skc5,skc4),skc5,set_intersection2(skc4,skc5)),set_intersection2(skc4,skc5)) ),
inference(res,[status(thm),theory(equality)],[68,76]),
[iquote('0:Res:68.2,76.0')] ).
cnf(92,plain,
in(skf12(set_difference(skc5,skc4),skc5,set_intersection2(skc4,skc5)),set_intersection2(skc4,skc5)),
inference(spt,[spt(split,[position(s1)])],[91]),
[iquote('1:Spt:91.1')] ).
cnf(93,plain,
( ~ in(skf12(set_difference(skc5,skc4),skc5,set_intersection2(skc4,skc5)),skc5)
| in(skf12(set_difference(skc5,skc4),skc5,set_intersection2(skc4,skc5)),set_difference(skc5,skc4)) ),
inference(mrr,[status(thm)],[89,92]),
[iquote('1:MRR:89.1,92.0')] ).
cnf(874,plain,
( ~ in(u,set_intersection2(v,w))
| in(u,w) ),
inference(eqr,[status(thm),theory(equality)],[56]),
[iquote('0:EqR:56.1')] ).
cnf(911,plain,
( ~ in(u,set_intersection2(v,w))
| in(u,v) ),
inference(spl,[status(thm),theory(equality)],[17,874]),
[iquote('0:SpL:17.0,874.0')] ).
cnf(916,plain,
in(skf12(set_difference(skc5,skc4),skc5,set_intersection2(skc4,skc5)),skc5),
inference(res,[status(thm),theory(equality)],[92,874]),
[iquote('1:Res:92.0,874.0')] ).
cnf(926,plain,
in(skf12(set_difference(skc5,skc4),skc5,set_intersection2(skc4,skc5)),set_difference(skc5,skc4)),
inference(mrr,[status(thm)],[93,916]),
[iquote('1:MRR:93.0,916.0')] ).
cnf(987,plain,
in(skf12(set_difference(skc5,skc4),skc5,set_intersection2(skc4,skc5)),skc4),
inference(res,[status(thm),theory(equality)],[92,911]),
[iquote('1:Res:92.0,911.0')] ).
cnf(1444,plain,
( ~ in(u,set_difference(v,w))
| ~ in(u,w) ),
inference(eqr,[status(thm),theory(equality)],[61]),
[iquote('0:EqR:61.2')] ).
cnf(1920,plain,
( ~ in(u,v)
| in(u,set_difference(v,w))
| in(u,w) ),
inference(eqr,[status(thm),theory(equality)],[64]),
[iquote('0:EqR:64.1')] ).
cnf(2077,plain,
( ~ in(u,v)
| ~ in(u,w)
| in(u,set_intersection2(w,v)) ),
inference(eqr,[status(thm),theory(equality)],[65]),
[iquote('0:EqR:65.2')] ).
cnf(5271,plain,
~ in(skf12(set_difference(skc5,skc4),skc5,set_intersection2(skc4,skc5)),skc4),
inference(res,[status(thm),theory(equality)],[926,1444]),
[iquote('1:Res:926.0,1444.0')] ).
cnf(5273,plain,
$false,
inference(mrr,[status(thm)],[5271,987]),
[iquote('1:MRR:5271.0,987.0')] ).
cnf(5277,plain,
~ in(skf12(set_difference(skc5,skc4),skc5,set_intersection2(skc4,skc5)),set_intersection2(skc4,skc5)),
inference(spt,[spt(split,[position(sa)])],[5273,92]),
[iquote('1:Spt:5273.0,91.1,92.0')] ).
cnf(5278,plain,
in(skf12(set_difference(skc5,skc4),skc5,set_intersection2(skc4,skc5)),skc5),
inference(spt,[spt(split,[position(s2)])],[91]),
[iquote('1:Spt:5273.0,91.0')] ).
cnf(5291,plain,
~ in(skf12(set_difference(skc5,skc4),skc5,set_intersection2(skc4,skc5)),set_difference(skc5,skc4)),
inference(mrr,[status(thm)],[90,5277]),
[iquote('1:MRR:90.1,5277.0')] ).
cnf(6408,plain,
( ~ in(skf12(set_difference(skc5,skc4),skc5,set_intersection2(skc4,skc5)),skc5)
| in(skf12(set_difference(skc5,skc4),skc5,set_intersection2(skc4,skc5)),skc4) ),
inference(res,[status(thm),theory(equality)],[1920,5291]),
[iquote('1:Res:1920.1,5291.0')] ).
cnf(6409,plain,
in(skf12(set_difference(skc5,skc4),skc5,set_intersection2(skc4,skc5)),skc4),
inference(mrr,[status(thm)],[6408,5278]),
[iquote('1:MRR:6408.0,5278.0')] ).
cnf(7460,plain,
( ~ in(skf12(set_difference(skc5,skc4),skc5,set_intersection2(skc4,skc5)),skc5)
| ~ in(skf12(set_difference(skc5,skc4),skc5,set_intersection2(skc4,skc5)),skc4) ),
inference(res,[status(thm),theory(equality)],[2077,5277]),
[iquote('1:Res:2077.2,5277.0')] ).
cnf(7468,plain,
$false,
inference(mrr,[status(thm)],[7460,5278,6409]),
[iquote('1:MRR:7460.0,7460.1,5278.0,6409.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU138+2 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jun 19 23:51:14 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.46/1.65
% 1.46/1.65 SPASS V 3.9
% 1.46/1.65 SPASS beiseite: Proof found.
% 1.46/1.65 % SZS status Theorem
% 1.46/1.65 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.46/1.65 SPASS derived 6204 clauses, backtracked 26 clauses, performed 1 splits and kept 2176 clauses.
% 1.46/1.65 SPASS allocated 102659 KBytes.
% 1.46/1.65 SPASS spent 0:00:01.27 on the problem.
% 1.46/1.65 0:00:00.03 for the input.
% 1.46/1.65 0:00:00.07 for the FLOTTER CNF translation.
% 1.46/1.65 0:00:00.06 for inferences.
% 1.46/1.65 0:00:00.01 for the backtracking.
% 1.46/1.65 0:00:01.06 for the reduction.
% 1.46/1.65
% 1.46/1.65
% 1.46/1.65 Here is a proof with depth 3, length 32 :
% 1.46/1.65 % SZS output start Refutation
% See solution above
% 1.46/1.65 Formulae used in the proof : commutativity_k3_xboole_0 t48_xboole_1 d3_xboole_0 d4_xboole_0
% 1.46/1.65
%------------------------------------------------------------------------------