TSTP Solution File: SEU056+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU056+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n006.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 14:33:45 EDT 2022
% Result : Theorem 0.22s 0.49s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of clauses : 21 ( 14 unt; 0 nHn; 21 RR)
% Number of literals : 31 ( 0 equ; 11 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
relation(skc11),
file('SEU056+1.p',unknown),
[] ).
cnf(2,axiom,
function(skc11),
file('SEU056+1.p',unknown),
[] ).
cnf(3,axiom,
one_to_one(skc11),
file('SEU056+1.p',unknown),
[] ).
cnf(24,axiom,
disjoint(skc13,skc12),
file('SEU056+1.p',unknown),
[] ).
cnf(39,axiom,
equal(set_intersection2(u,v),set_intersection2(v,u)),
file('SEU056+1.p',unknown),
[] ).
cnf(43,axiom,
~ disjoint(relation_image(skc11,skc13),relation_image(skc11,skc12)),
file('SEU056+1.p',unknown),
[] ).
cnf(45,axiom,
( ~ relation(u)
| equal(relation_image(u,empty_set),empty_set) ),
file('SEU056+1.p',unknown),
[] ).
cnf(48,axiom,
( ~ disjoint(u,v)
| equal(set_intersection2(u,v),empty_set) ),
file('SEU056+1.p',unknown),
[] ).
cnf(49,axiom,
( ~ equal(set_intersection2(u,v),empty_set)
| disjoint(u,v) ),
file('SEU056+1.p',unknown),
[] ).
cnf(56,axiom,
( ~ one_to_one(u)
| ~ function(u)
| ~ relation(u)
| equal(relation_image(u,set_intersection2(v,w)),set_intersection2(relation_image(u,v),relation_image(u,w))) ),
file('SEU056+1.p',unknown),
[] ).
cnf(58,plain,
( ~ relation(skc11)
| ~ function(skc11)
| equal(relation_image(skc11,set_intersection2(u,v)),set_intersection2(relation_image(skc11,u),relation_image(skc11,v))) ),
inference(res,[status(thm),theory(equality)],[3,56]),
[iquote('0:Res:3.0,56.2')] ).
cnf(62,plain,
equal(relation_image(skc11,empty_set),empty_set),
inference(res,[status(thm),theory(equality)],[1,45]),
[iquote('0:Res:1.0,45.0')] ).
cnf(64,plain,
equal(set_intersection2(skc13,skc12),empty_set),
inference(res,[status(thm),theory(equality)],[24,48]),
[iquote('0:Res:24.0,48.0')] ).
cnf(68,plain,
equal(set_intersection2(skc12,skc13),empty_set),
inference(rew,[status(thm),theory(equality)],[39,64]),
[iquote('0:Rew:39.0,64.0')] ).
cnf(69,plain,
equal(relation_image(skc11,set_intersection2(u,v)),set_intersection2(relation_image(skc11,u),relation_image(skc11,v))),
inference(mrr,[status(thm)],[58,1,2]),
[iquote('0:MRR:58.0,58.1,1.0,2.0')] ).
cnf(144,plain,
( ~ equal(set_intersection2(u,v),empty_set)
| disjoint(v,u) ),
inference(spl,[status(thm),theory(equality)],[39,49]),
[iquote('0:SpL:39.0,49.0')] ).
cnf(464,plain,
equal(set_intersection2(relation_image(skc11,skc12),relation_image(skc11,skc13)),relation_image(skc11,empty_set)),
inference(spr,[status(thm),theory(equality)],[68,69]),
[iquote('0:SpR:68.0,69.0')] ).
cnf(472,plain,
equal(set_intersection2(relation_image(skc11,skc12),relation_image(skc11,skc13)),empty_set),
inference(rew,[status(thm),theory(equality)],[62,464]),
[iquote('0:Rew:62.0,464.0')] ).
cnf(489,plain,
( ~ equal(empty_set,empty_set)
| disjoint(relation_image(skc11,skc13),relation_image(skc11,skc12)) ),
inference(spl,[status(thm),theory(equality)],[472,144]),
[iquote('0:SpL:472.0,144.0')] ).
cnf(491,plain,
disjoint(relation_image(skc11,skc13),relation_image(skc11,skc12)),
inference(obv,[status(thm),theory(equality)],[489]),
[iquote('0:Obv:489.0')] ).
cnf(492,plain,
$false,
inference(mrr,[status(thm)],[491,43]),
[iquote('0:MRR:491.0,43.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SEU056+1 : TPTP v8.1.0. Released v3.2.0.
% 0.08/0.14 % Command : run_spass %d %s
% 0.15/0.36 % Computer : n006.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Sun Jun 19 20:23:55 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.22/0.49
% 0.22/0.49 SPASS V 3.9
% 0.22/0.49 SPASS beiseite: Proof found.
% 0.22/0.49 % SZS status Theorem
% 0.22/0.49 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.49 SPASS derived 379 clauses, backtracked 0 clauses, performed 0 splits and kept 183 clauses.
% 0.22/0.49 SPASS allocated 97918 KBytes.
% 0.22/0.49 SPASS spent 0:00:00.11 on the problem.
% 0.22/0.49 0:00:00.03 for the input.
% 0.22/0.49 0:00:00.03 for the FLOTTER CNF translation.
% 0.22/0.49 0:00:00.01 for inferences.
% 0.22/0.49 0:00:00.00 for the backtracking.
% 0.22/0.49 0:00:00.02 for the reduction.
% 0.22/0.49
% 0.22/0.49
% 0.22/0.49 Here is a proof with depth 3, length 21 :
% 0.22/0.49 % SZS output start Refutation
% See solution above
% 0.22/0.49 Formulae used in the proof : t125_funct_1 commutativity_k3_xboole_0 t149_relat_1 d7_xboole_0 t121_funct_1
% 0.22/0.49
%------------------------------------------------------------------------------