%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU326+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 14:36:17 EDT 2022
% Result : Theorem 0.19s 0.49s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of clauses : 29 ( 13 unt; 1 nHn; 29 RR)
% Number of literals : 48 ( 0 equ; 25 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(17,axiom,
element(skc4,powerset(powerset(skc3))),
file('SEU326+1.p',unknown),
[] ).
cnf(29,axiom,
( skP0(skc3,skc4)
| equal(empty_set,skc4) ),
file('SEU326+1.p',unknown),
[] ).
cnf(34,axiom,
( ~ skP0(u,v)
| ~ equal(v,empty_set) ),
file('SEU326+1.p',unknown),
[] ).
cnf(38,axiom,
( ~ equal(complements_of_subsets(skc3,skc4),empty_set)
| skP0(skc3,skc4) ),
file('SEU326+1.p',unknown),
[] ).
cnf(39,axiom,
( ~ skP0(u,v)
| equal(complements_of_subsets(u,v),empty_set) ),
file('SEU326+1.p',unknown),
[] ).
cnf(74,axiom,
( ~ element(u,powerset(powerset(v)))
| element(complements_of_subsets(v,u),powerset(powerset(v))) ),
file('SEU326+1.p',unknown),
[] ).
cnf(75,axiom,
( ~ element(u,powerset(powerset(v)))
| equal(complements_of_subsets(v,complements_of_subsets(v,u)),u) ),
file('SEU326+1.p',unknown),
[] ).
cnf(76,axiom,
( ~ element(u,powerset(powerset(v)))
| ~ equal(complements_of_subsets(v,u),empty_set)
| equal(u,empty_set) ),
file('SEU326+1.p',unknown),
[] ).
cnf(77,plain,
( ~ equal(complements_of_subsets(skc3,skc4),skc4)
| skP0(skc3,skc4) ),
inference(rew,[status(thm),theory(equality)],[29,38]),
[iquote('0:Rew:29.0,38.0')] ).
cnf(112,plain,
( ~ equal(complements_of_subsets(skc3,skc4),empty_set)
| equal(empty_set,skc4) ),
inference(res,[status(thm),theory(equality)],[17,76]),
[iquote('0:Res:17.0,76.0')] ).
cnf(113,plain,
element(complements_of_subsets(skc3,skc4),powerset(powerset(skc3))),
inference(res,[status(thm),theory(equality)],[17,74]),
[iquote('0:Res:17.0,74.0')] ).
cnf(114,plain,
equal(complements_of_subsets(skc3,complements_of_subsets(skc3,skc4)),skc4),
inference(res,[status(thm),theory(equality)],[17,75]),
[iquote('0:Res:17.0,75.0')] ).
cnf(116,plain,
equal(empty_set,skc4),
inference(spt,[spt(split,[position(s1)])],[29]),
[iquote('1:Spt:29.1')] ).
cnf(117,plain,
( ~ element(u,powerset(powerset(v)))
| ~ equal(complements_of_subsets(v,u),empty_set)
| equal(u,skc4) ),
inference(rew,[status(thm),theory(equality)],[116,76]),
[iquote('1:Rew:116.0,76.2')] ).
cnf(125,plain,
( ~ skP0(u,v)
| ~ equal(v,skc4) ),
inference(rew,[status(thm),theory(equality)],[116,34]),
[iquote('1:Rew:116.0,34.1')] ).
cnf(127,plain,
( ~ element(u,powerset(powerset(v)))
| ~ equal(complements_of_subsets(v,u),skc4)
| equal(u,skc4) ),
inference(rew,[status(thm),theory(equality)],[116,117]),
[iquote('1:Rew:116.0,117.1')] ).
cnf(761,plain,
( ~ equal(complements_of_subsets(skc3,complements_of_subsets(skc3,skc4)),skc4)
| equal(complements_of_subsets(skc3,skc4),skc4) ),
inference(res,[status(thm),theory(equality)],[113,127]),
[iquote('1:Res:113.0,127.0')] ).
cnf(765,plain,
( ~ equal(skc4,skc4)
| equal(complements_of_subsets(skc3,skc4),skc4) ),
inference(rew,[status(thm),theory(equality)],[114,761]),
[iquote('1:Rew:114.0,761.0')] ).
cnf(766,plain,
equal(complements_of_subsets(skc3,skc4),skc4),
inference(obv,[status(thm),theory(equality)],[765]),
[iquote('1:Obv:765.0')] ).
cnf(770,plain,
( ~ equal(skc4,skc4)
| skP0(skc3,skc4) ),
inference(rew,[status(thm),theory(equality)],[766,77]),
[iquote('1:Rew:766.0,77.0')] ).
cnf(804,plain,
skP0(skc3,skc4),
inference(obv,[status(thm),theory(equality)],[770]),
[iquote('1:Obv:770.0')] ).
cnf(806,plain,
~ equal(skc4,skc4),
inference(res,[status(thm),theory(equality)],[804,125]),
[iquote('1:Res:804.0,125.0')] ).
cnf(807,plain,
$false,
inference(obv,[status(thm),theory(equality)],[806]),
[iquote('1:Obv:806.0')] ).
cnf(808,plain,
~ equal(empty_set,skc4),
inference(spt,[spt(split,[position(sa)])],[807,116]),
[iquote('1:Spt:807.0,29.1,116.0')] ).
cnf(809,plain,
skP0(skc3,skc4),
inference(spt,[spt(split,[position(s2)])],[29]),
[iquote('1:Spt:807.0,29.0')] ).
cnf(810,plain,
~ equal(complements_of_subsets(skc3,skc4),empty_set),
inference(mrr,[status(thm)],[112,808]),
[iquote('1:MRR:112.1,808.0')] ).
cnf(1007,plain,
( ~ skP0(skc3,skc4)
| ~ equal(empty_set,empty_set) ),
inference(spl,[status(thm),theory(equality)],[39,810]),
[iquote('1:SpL:39.1,810.0')] ).
cnf(1008,plain,
~ skP0(skc3,skc4),
inference(obv,[status(thm),theory(equality)],[1007]),
[iquote('1:Obv:1007.1')] ).
cnf(1009,plain,
$false,
inference(mrr,[status(thm)],[1008,809]),
[iquote('1:MRR:1008.0,809.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU326+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n026.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 19:21:40 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.49
% 0.19/0.49 SPASS V 3.9
% 0.19/0.49 SPASS beiseite: Proof found.
% 0.19/0.49 % SZS status Theorem
% 0.19/0.49 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.49 SPASS derived 895 clauses, backtracked 171 clauses, performed 1 splits and kept 688 clauses.
% 0.19/0.49 SPASS allocated 98182 KBytes.
% 0.19/0.49 SPASS spent 0:00:00.15 on the problem.
% 0.19/0.49 0:00:00.03 for the input.
% 0.19/0.49 0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.49 0:00:00.01 for inferences.
% 0.19/0.49 0:00:00.00 for the backtracking.
% 0.19/0.49 0:00:00.04 for the reduction.
% 0.19/0.49
% 0.19/0.49
% 0.19/0.49 Here is a proof with depth 2, length 29 :
% 0.19/0.49 % SZS output start Refutation
% See solution above
% 0.19/0.49 Formulae used in the proof : t10_tops_2 dt_k7_setfam_1 involutiveness_k7_setfam_1 t46_setfam_1
% 0.19/0.49
%------------------------------------------------------------------------------