%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU101+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 14:33:58 EDT 2022
% Result : Theorem 0.18s 0.48s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 17
% Syntax : Number of clauses : 38 ( 10 unt; 6 nHn; 38 RR)
% Number of literals : 85 ( 0 equ; 52 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(27,axiom,
( ~ preboolean(u)
| cup_closed(u) ),
file('SEU101+1.p',unknown),
[] ).
cnf(28,axiom,
( ~ preboolean(u)
| diff_closed(u) ),
file('SEU101+1.p',unknown),
[] ).
cnf(40,axiom,
( ~ preboolean(skc7)
| in(skc9,skc7) ),
file('SEU101+1.p',unknown),
[] ).
cnf(41,axiom,
( ~ preboolean(skc7)
| in(skc8,skc7) ),
file('SEU101+1.p',unknown),
[] ).
cnf(42,axiom,
( cup_closed(u)
| in(skf11(u),u) ),
file('SEU101+1.p',unknown),
[] ).
cnf(43,axiom,
( cup_closed(u)
| in(skf10(u),u) ),
file('SEU101+1.p',unknown),
[] ).
cnf(44,axiom,
( diff_closed(u)
| in(skf13(u),u) ),
file('SEU101+1.p',unknown),
[] ).
cnf(45,axiom,
( diff_closed(u)
| in(skf12(u),u) ),
file('SEU101+1.p',unknown),
[] ).
cnf(50,axiom,
equal(set_union2(u,v),set_union2(v,u)),
file('SEU101+1.p',unknown),
[] ).
cnf(58,axiom,
( ~ diff_closed(u)
| ~ cup_closed(u)
| preboolean(u) ),
file('SEU101+1.p',unknown),
[] ).
cnf(64,axiom,
( ~ in(set_union2(skf11(u),skf10(u)),u)
| cup_closed(u) ),
file('SEU101+1.p',unknown),
[] ).
cnf(65,axiom,
( ~ in(set_difference(skf13(u),skf12(u)),u)
| diff_closed(u) ),
file('SEU101+1.p',unknown),
[] ).
cnf(69,axiom,
( ~ in(u,skc7)
| ~ in(v,skc7)
| preboolean(skc7)
| in(set_union2(v,u),skc7) ),
file('SEU101+1.p',unknown),
[] ).
cnf(70,axiom,
( ~ in(u,skc7)
| ~ in(v,skc7)
| preboolean(skc7)
| in(set_difference(v,u),skc7) ),
file('SEU101+1.p',unknown),
[] ).
cnf(71,axiom,
( ~ in(set_union2(skc9,skc8),skc7)
| ~ in(set_difference(skc9,skc8),skc7)
| ~ preboolean(skc7) ),
file('SEU101+1.p',unknown),
[] ).
cnf(72,axiom,
( ~ cup_closed(u)
| ~ in(v,u)
| ~ in(w,u)
| in(set_union2(w,v),u) ),
file('SEU101+1.p',unknown),
[] ).
cnf(73,axiom,
( ~ diff_closed(u)
| ~ in(v,u)
| ~ in(w,u)
| in(set_difference(w,v),u) ),
file('SEU101+1.p',unknown),
[] ).
cnf(74,plain,
( ~ in(set_union2(skf10(u),skf11(u)),u)
| cup_closed(u) ),
inference(rew,[status(thm),theory(equality)],[50,64]),
[iquote('0:Rew:50.0,64.0')] ).
cnf(75,plain,
( ~ preboolean(skc7)
| ~ in(set_difference(skc9,skc8),skc7)
| ~ in(set_union2(skc8,skc9),skc7) ),
inference(rew,[status(thm),theory(equality)],[50,71]),
[iquote('0:Rew:50.0,71.0')] ).
cnf(76,plain,
preboolean(skc7),
inference(spt,[spt(split,[position(s1)])],[70]),
[iquote('1:Spt:70.2')] ).
cnf(77,plain,
in(skc8,skc7),
inference(mrr,[status(thm)],[41,76]),
[iquote('1:MRR:41.0,76.0')] ).
cnf(78,plain,
in(skc9,skc7),
inference(mrr,[status(thm)],[40,76]),
[iquote('1:MRR:40.0,76.0')] ).
cnf(79,plain,
( ~ in(set_difference(skc9,skc8),skc7)
| ~ in(set_union2(skc8,skc9),skc7) ),
inference(mrr,[status(thm)],[75,76]),
[iquote('1:MRR:75.0,76.0')] ).
cnf(249,plain,
( ~ diff_closed(skc7)
| ~ in(skc8,skc7)
| ~ in(skc9,skc7)
| ~ in(set_union2(skc8,skc9),skc7) ),
inference(res,[status(thm),theory(equality)],[73,79]),
[iquote('1:Res:73.3,79.0')] ).
cnf(262,plain,
( ~ in(skc8,skc7)
| ~ in(skc9,skc7)
| ~ in(set_union2(skc8,skc9),skc7) ),
inference(ssi,[status(thm)],[249,28,76]),
[iquote('1:SSi:249.0,28.0,76.1')] ).
cnf(263,plain,
~ in(set_union2(skc8,skc9),skc7),
inference(mrr,[status(thm)],[262,77,78]),
[iquote('1:MRR:262.0,262.1,77.0,78.0')] ).
cnf(284,plain,
( ~ cup_closed(skc7)
| ~ in(skc9,skc7)
| ~ in(skc8,skc7) ),
inference(res,[status(thm),theory(equality)],[72,263]),
[iquote('1:Res:72.3,263.0')] ).
cnf(296,plain,
( ~ in(skc9,skc7)
| ~ in(skc8,skc7) ),
inference(ssi,[status(thm)],[284,27,76]),
[iquote('1:SSi:284.0,27.0,76.1')] ).
cnf(297,plain,
$false,
inference(mrr,[status(thm)],[296,78,77]),
[iquote('1:MRR:296.0,296.1,78.0,77.0')] ).
cnf(301,plain,
~ preboolean(skc7),
inference(spt,[spt(split,[position(sa)])],[297,76]),
[iquote('1:Spt:297.0,70.2,76.0')] ).
cnf(302,plain,
( ~ in(u,skc7)
| ~ in(v,skc7)
| in(set_difference(v,u),skc7) ),
inference(spt,[spt(split,[position(s2)])],[70]),
[iquote('1:Spt:297.0,70.0,70.1,70.3')] ).
cnf(303,plain,
( ~ in(u,skc7)
| ~ in(v,skc7)
| in(set_union2(v,u),skc7) ),
inference(mrr,[status(thm)],[69,301]),
[iquote('1:MRR:69.2,301.0')] ).
cnf(307,plain,
( ~ in(skf12(skc7),skc7)
| ~ in(skf13(skc7),skc7)
| diff_closed(skc7) ),
inference(res,[status(thm),theory(equality)],[302,65]),
[iquote('1:Res:302.2,65.0')] ).
cnf(310,plain,
diff_closed(skc7),
inference(mrr,[status(thm)],[307,45,44]),
[iquote('1:MRR:307.0,307.1,45.1,44.1')] ).
cnf(311,plain,
( ~ diff_closed(skc7)
| ~ cup_closed(skc7) ),
inference(res,[status(thm),theory(equality)],[58,301]),
[iquote('1:Res:58.2,301.0')] ).
cnf(312,plain,
~ cup_closed(skc7),
inference(ssi,[status(thm)],[311,310]),
[iquote('1:SSi:311.0,310.0')] ).
cnf(322,plain,
( ~ in(skf11(skc7),skc7)
| ~ in(skf10(skc7),skc7)
| cup_closed(skc7) ),
inference(res,[status(thm),theory(equality)],[303,74]),
[iquote('1:Res:303.2,74.0')] ).
cnf(325,plain,
$false,
inference(mrr,[status(thm)],[322,42,43,312]),
[iquote('1:MRR:322.0,322.1,322.2,42.1,43.1,312.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU101+1 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.13 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n007.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jun 19 22:29:14 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.18/0.48
% 0.18/0.48 SPASS V 3.9
% 0.18/0.48 SPASS beiseite: Proof found.
% 0.18/0.48 % SZS status Theorem
% 0.18/0.48 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.48 SPASS derived 223 clauses, backtracked 6 clauses, performed 1 splits and kept 181 clauses.
% 0.18/0.48 SPASS allocated 98155 KBytes.
% 0.18/0.48 SPASS spent 0:00:00.14 on the problem.
% 0.18/0.48 0:00:00.04 for the input.
% 0.18/0.48 0:00:00.06 for the FLOTTER CNF translation.
% 0.18/0.48 0:00:00.00 for inferences.
% 0.18/0.48 0:00:00.00 for the backtracking.
% 0.18/0.48 0:00:00.01 for the reduction.
% 0.18/0.48
% 0.18/0.48
% 0.18/0.48 Here is a proof with depth 2, length 38 :
% 0.18/0.48 % SZS output start Refutation
% See solution above
% 0.18/0.48 Formulae used in the proof : d4_finsub_1 t10_finsub_1 d1_finsub_1 d3_finsub_1 commutativity_k2_xboole_0
% 0.18/0.48
%------------------------------------------------------------------------------