%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU136+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 0.88s 1.08s
% Output : Refutation 0.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of clauses : 33 ( 15 unt; 9 nHn; 33 RR)
% Number of literals : 64 ( 0 equ; 30 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(16,axiom,
equal(set_union2(u,v),set_union2(v,u)),
file('SEU136+2.p',unknown),
[] ).
cnf(40,axiom,
equal(set_union2(u,set_difference(v,u)),set_union2(u,v)),
file('SEU136+2.p',unknown),
[] ).
cnf(42,axiom,
~ equal(set_difference(set_union2(skc5,skc4),skc4),set_difference(skc5,skc4)),
file('SEU136+2.p',unknown),
[] ).
cnf(52,axiom,
( ~ in(u,v)
| ~ equal(w,set_union2(x,v))
| in(u,w) ),
file('SEU136+2.p',unknown),
[] ).
cnf(59,axiom,
( ~ in(u,v)
| ~ in(u,w)
| ~ equal(v,set_difference(x,w)) ),
file('SEU136+2.p',unknown),
[] ).
cnf(61,axiom,
( ~ in(u,v)
| ~ equal(v,set_union2(w,x))
| in(u,x)
| in(u,w) ),
file('SEU136+2.p',unknown),
[] ).
cnf(62,axiom,
( ~ in(u,v)
| ~ equal(w,set_difference(v,x))
| in(u,w)
| in(u,x) ),
file('SEU136+2.p',unknown),
[] ).
cnf(66,axiom,
( equal(u,set_difference(v,w))
| in(skf12(w,v,u),u)
| in(skf12(w,v,u),v) ),
file('SEU136+2.p',unknown),
[] ).
cnf(67,axiom,
( ~ in(skf12(u,v,w),u)
| equal(w,set_difference(v,u))
| in(skf12(u,v,w),w) ),
file('SEU136+2.p',unknown),
[] ).
cnf(71,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('SEU136+2.p',unknown),
[] ).
cnf(74,plain,
~ equal(set_difference(set_union2(skc4,skc5),skc4),set_difference(skc5,skc4)),
inference(rew,[status(thm),theory(equality)],[16,42]),
[iquote('0:Rew:16.0,42.0')] ).
cnf(86,plain,
( ~ in(skf12(skc4,set_union2(skc4,skc5),set_difference(skc5,skc4)),set_union2(skc4,skc5))
| ~ in(skf12(skc4,set_union2(skc4,skc5),set_difference(skc5,skc4)),set_difference(skc5,skc4))
| in(skf12(skc4,set_union2(skc4,skc5),set_difference(skc5,skc4)),skc4) ),
inference(res,[status(thm),theory(equality)],[71,74]),
[iquote('0:Res:71.3,74.0')] ).
cnf(87,plain,
( ~ in(skf12(skc4,set_union2(skc4,skc5),set_difference(skc5,skc4)),skc4)
| in(skf12(skc4,set_union2(skc4,skc5),set_difference(skc5,skc4)),set_difference(skc5,skc4)) ),
inference(res,[status(thm),theory(equality)],[67,74]),
[iquote('0:Res:67.2,74.0')] ).
cnf(88,plain,
( in(skf12(skc4,set_union2(skc4,skc5),set_difference(skc5,skc4)),set_difference(skc5,skc4))
| in(skf12(skc4,set_union2(skc4,skc5),set_difference(skc5,skc4)),set_union2(skc4,skc5)) ),
inference(res,[status(thm),theory(equality)],[66,74]),
[iquote('0:Res:66.2,74.0')] ).
cnf(89,plain,
in(skf12(skc4,set_union2(skc4,skc5),set_difference(skc5,skc4)),set_difference(skc5,skc4)),
inference(spt,[spt(split,[position(s1)])],[88]),
[iquote('1:Spt:88.0')] ).
cnf(90,plain,
( ~ in(skf12(skc4,set_union2(skc4,skc5),set_difference(skc5,skc4)),set_union2(skc4,skc5))
| in(skf12(skc4,set_union2(skc4,skc5),set_difference(skc5,skc4)),skc4) ),
inference(mrr,[status(thm)],[86,89]),
[iquote('1:MRR:86.1,89.0')] ).
cnf(609,plain,
( ~ in(u,v)
| in(u,set_union2(w,v)) ),
inference(eqr,[status(thm),theory(equality)],[52]),
[iquote('0:EqR:52.1')] ).
cnf(625,plain,
( ~ in(u,set_difference(v,w))
| in(u,set_union2(w,v)) ),
inference(spr,[status(thm),theory(equality)],[40,609]),
[iquote('0:SpR:40.0,609.1')] ).
cnf(1013,plain,
( ~ in(u,set_difference(v,w))
| ~ in(u,w) ),
inference(eqr,[status(thm),theory(equality)],[59]),
[iquote('0:EqR:59.2')] ).
cnf(1096,plain,
~ in(skf12(skc4,set_union2(skc4,skc5),set_difference(skc5,skc4)),skc4),
inference(res,[status(thm),theory(equality)],[89,1013]),
[iquote('1:Res:89.0,1013.0')] ).
cnf(1116,plain,
~ in(skf12(skc4,set_union2(skc4,skc5),set_difference(skc5,skc4)),set_union2(skc4,skc5)),
inference(mrr,[status(thm)],[90,1096]),
[iquote('1:MRR:90.1,1096.0')] ).
cnf(1256,plain,
( ~ in(u,v)
| in(u,set_difference(v,w))
| in(u,w) ),
inference(eqr,[status(thm),theory(equality)],[62]),
[iquote('0:EqR:62.1')] ).
cnf(1308,plain,
( ~ in(u,set_union2(v,w))
| in(u,w)
| in(u,v) ),
inference(eqr,[status(thm),theory(equality)],[61]),
[iquote('0:EqR:61.1')] ).
cnf(2682,plain,
in(skf12(skc4,set_union2(skc4,skc5),set_difference(skc5,skc4)),set_union2(skc4,skc5)),
inference(res,[status(thm),theory(equality)],[89,625]),
[iquote('1:Res:89.0,625.0')] ).
cnf(2730,plain,
$false,
inference(mrr,[status(thm)],[2682,1116]),
[iquote('1:MRR:2682.0,1116.0')] ).
cnf(2742,plain,
~ in(skf12(skc4,set_union2(skc4,skc5),set_difference(skc5,skc4)),set_difference(skc5,skc4)),
inference(spt,[spt(split,[position(sa)])],[2730,89]),
[iquote('1:Spt:2730.0,88.0,89.0')] ).
cnf(2743,plain,
in(skf12(skc4,set_union2(skc4,skc5),set_difference(skc5,skc4)),set_union2(skc4,skc5)),
inference(spt,[spt(split,[position(s2)])],[88]),
[iquote('1:Spt:2730.0,88.1')] ).
cnf(2753,plain,
~ in(skf12(skc4,set_union2(skc4,skc5),set_difference(skc5,skc4)),skc4),
inference(mrr,[status(thm)],[87,1013]),
[iquote('0:MRR:87.1,1013.0')] ).
cnf(4238,plain,
( ~ in(skf12(skc4,set_union2(skc4,skc5),set_difference(skc5,skc4)),skc5)
| in(skf12(skc4,set_union2(skc4,skc5),set_difference(skc5,skc4)),skc4) ),
inference(res,[status(thm),theory(equality)],[1256,2742]),
[iquote('1:Res:1256.1,2742.0')] ).
cnf(4242,plain,
~ in(skf12(skc4,set_union2(skc4,skc5),set_difference(skc5,skc4)),skc5),
inference(mrr,[status(thm)],[4238,2753]),
[iquote('1:MRR:4238.1,2753.0')] ).
cnf(4349,plain,
( in(skf12(skc4,set_union2(skc4,skc5),set_difference(skc5,skc4)),skc5)
| in(skf12(skc4,set_union2(skc4,skc5),set_difference(skc5,skc4)),skc4) ),
inference(res,[status(thm),theory(equality)],[2743,1308]),
[iquote('1:Res:2743.0,1308.0')] ).
cnf(4353,plain,
in(skf12(skc4,set_union2(skc4,skc5),set_difference(skc5,skc4)),skc5),
inference(mrr,[status(thm)],[4349,2753]),
[iquote('1:MRR:4349.1,2753.0')] ).
cnf(4354,plain,
$false,
inference(mrr,[status(thm)],[4353,4242]),
[iquote('1:MRR:4353.0,4242.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU136+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n028.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 : Sun Jun 19 11:55:15 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.88/1.08
% 0.88/1.08 SPASS V 3.9
% 0.88/1.08 SPASS beiseite: Proof found.
% 0.88/1.08 % SZS status Theorem
% 0.88/1.08 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.88/1.08 SPASS derived 3685 clauses, backtracked 12 clauses, performed 1 splits and kept 1427 clauses.
% 0.88/1.08 SPASS allocated 100696 KBytes.
% 0.88/1.08 SPASS spent 0:00:00.71 on the problem.
% 0.88/1.08 0:00:00.03 for the input.
% 0.88/1.08 0:00:00.07 for the FLOTTER CNF translation.
% 0.88/1.08 0:00:00.04 for inferences.
% 0.88/1.08 0:00:00.00 for the backtracking.
% 0.88/1.08 0:00:00.53 for the reduction.
% 0.88/1.08
% 0.88/1.08
% 0.88/1.08 Here is a proof with depth 3, length 33 :
% 0.88/1.08 % SZS output start Refutation
% See solution above
% 0.88/1.08 Formulae used in the proof : commutativity_k2_xboole_0 t39_xboole_1 t40_xboole_1 d2_xboole_0 d4_xboole_0
% 0.88/1.08
%------------------------------------------------------------------------------