%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU308+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 14:36:07 EDT 2022
% Result : Theorem 0.19s 0.50s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of clauses : 26 ( 17 unt; 0 nHn; 26 RR)
% Number of literals : 38 ( 0 equ; 17 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
one_sorted_str(skc4),
file('SEU308+1.p',unknown),
[] ).
cnf(16,axiom,
empty(skf4(u)),
file('SEU308+1.p',unknown),
[] ).
cnf(19,axiom,
element(skc5,powerset(the_carrier(skc4))),
file('SEU308+1.p',unknown),
[] ).
cnf(24,axiom,
equal(set_difference(u,empty_set),u),
file('SEU308+1.p',unknown),
[] ).
cnf(27,axiom,
element(skf4(u),powerset(u)),
file('SEU308+1.p',unknown),
[] ).
cnf(34,axiom,
( ~ empty(u)
| equal(u,empty_set) ),
file('SEU308+1.p',unknown),
[] ).
cnf(55,axiom,
( ~ one_sorted_str(u)
| equal(the_carrier(u),cast_as_carrier_subset(u)) ),
file('SEU308+1.p',unknown),
[] ).
cnf(89,axiom,
( ~ element(u,powerset(v))
| element(subset_complement(v,u),powerset(v)) ),
file('SEU308+1.p',unknown),
[] ).
cnf(90,axiom,
~ equal(subset_difference(the_carrier(skc4),cast_as_carrier_subset(skc4),skc5),subset_complement(the_carrier(skc4),skc5)),
file('SEU308+1.p',unknown),
[] ).
cnf(94,axiom,
( ~ element(u,powerset(v))
| equal(set_difference(v,u),subset_complement(v,u)) ),
file('SEU308+1.p',unknown),
[] ).
cnf(96,axiom,
( ~ element(u,powerset(v))
| ~ element(w,powerset(v))
| equal(subset_difference(v,w,u),set_difference(w,u)) ),
file('SEU308+1.p',unknown),
[] ).
cnf(100,plain,
equal(the_carrier(skc4),cast_as_carrier_subset(skc4)),
inference(res,[status(thm),theory(equality)],[1,55]),
[iquote('0:Res:1.0,55.0')] ).
cnf(135,plain,
equal(set_difference(the_carrier(skc4),skc5),subset_complement(the_carrier(skc4),skc5)),
inference(res,[status(thm),theory(equality)],[19,94]),
[iquote('0:Res:19.0,94.0')] ).
cnf(144,plain,
element(skc5,powerset(cast_as_carrier_subset(skc4))),
inference(rew,[status(thm),theory(equality)],[100,19]),
[iquote('0:Rew:100.0,19.0')] ).
cnf(145,plain,
~ equal(subset_difference(cast_as_carrier_subset(skc4),cast_as_carrier_subset(skc4),skc5),subset_complement(cast_as_carrier_subset(skc4),skc5)),
inference(rew,[status(thm),theory(equality)],[100,90]),
[iquote('0:Rew:100.0,90.0')] ).
cnf(149,plain,
equal(set_difference(cast_as_carrier_subset(skc4),skc5),subset_complement(cast_as_carrier_subset(skc4),skc5)),
inference(rew,[status(thm),theory(equality)],[100,135]),
[iquote('0:Rew:100.0,135.0')] ).
cnf(166,plain,
equal(skf4(u),empty_set),
inference(ems,[status(thm)],[34,16]),
[iquote('0:EmS:34.0,16.0')] ).
cnf(169,plain,
element(empty_set,powerset(u)),
inference(rew,[status(thm),theory(equality)],[166,27]),
[iquote('0:Rew:166.0,27.0')] ).
cnf(858,plain,
equal(set_difference(u,empty_set),subset_complement(u,empty_set)),
inference(res,[status(thm),theory(equality)],[169,94]),
[iquote('0:Res:169.0,94.0')] ).
cnf(862,plain,
equal(subset_complement(u,empty_set),u),
inference(rew,[status(thm),theory(equality)],[24,858]),
[iquote('0:Rew:24.0,858.0')] ).
cnf(864,plain,
( ~ element(empty_set,powerset(u))
| element(u,powerset(u)) ),
inference(spr,[status(thm),theory(equality)],[862,89]),
[iquote('0:SpR:862.0,89.1')] ).
cnf(867,plain,
element(u,powerset(u)),
inference(mrr,[status(thm)],[864,169]),
[iquote('0:MRR:864.0,169.0')] ).
cnf(999,plain,
( ~ element(skc5,powerset(cast_as_carrier_subset(skc4)))
| ~ element(cast_as_carrier_subset(skc4),powerset(cast_as_carrier_subset(skc4)))
| ~ equal(set_difference(cast_as_carrier_subset(skc4),skc5),subset_complement(cast_as_carrier_subset(skc4),skc5)) ),
inference(spl,[status(thm),theory(equality)],[96,145]),
[iquote('0:SpL:96.2,145.0')] ).
cnf(1000,plain,
( ~ element(skc5,powerset(cast_as_carrier_subset(skc4)))
| ~ element(cast_as_carrier_subset(skc4),powerset(cast_as_carrier_subset(skc4)))
| ~ equal(subset_complement(cast_as_carrier_subset(skc4),skc5),subset_complement(cast_as_carrier_subset(skc4),skc5)) ),
inference(rew,[status(thm),theory(equality)],[149,999]),
[iquote('0:Rew:149.0,999.2')] ).
cnf(1001,plain,
( ~ element(skc5,powerset(cast_as_carrier_subset(skc4)))
| ~ element(cast_as_carrier_subset(skc4),powerset(cast_as_carrier_subset(skc4))) ),
inference(obv,[status(thm),theory(equality)],[1000]),
[iquote('0:Obv:1000.2')] ).
cnf(1002,plain,
$false,
inference(mrr,[status(thm)],[1001,144,867]),
[iquote('0:MRR:1001.0,1001.1,144.0,867.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU308+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n029.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 01:44:59 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.50
% 0.19/0.50 SPASS V 3.9
% 0.19/0.50 SPASS beiseite: Proof found.
% 0.19/0.50 % SZS status Theorem
% 0.19/0.50 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.50 SPASS derived 877 clauses, backtracked 0 clauses, performed 0 splits and kept 553 clauses.
% 0.19/0.50 SPASS allocated 98204 KBytes.
% 0.19/0.50 SPASS spent 0:00:00.15 on the problem.
% 0.19/0.50 0:00:00.03 for the input.
% 0.19/0.50 0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.50 0:00:00.01 for inferences.
% 0.19/0.50 0:00:00.00 for the backtracking.
% 0.19/0.50 0:00:00.04 for the reduction.
% 0.19/0.50
% 0.19/0.50
% 0.19/0.50 Here is a proof with depth 2, length 26 :
% 0.19/0.50 % SZS output start Refutation
% See solution above
% 0.19/0.50 Formulae used in the proof : t17_pre_topc rc2_subset_1 t3_boole t6_boole d3_pre_topc dt_k3_subset_1 d5_subset_1 redefinition_k6_subset_1
% 0.19/0.50
%------------------------------------------------------------------------------