%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU008+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n003.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 14:33:31 EDT 2022
% Result : Theorem 0.20s 0.49s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of clauses : 24 ( 12 unt; 0 nHn; 24 RR)
% Number of literals : 64 ( 0 equ; 46 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
relation(skc9),
file('SEU008+1.p',unknown),
[] ).
cnf(2,axiom,
function(skc9),
file('SEU008+1.p',unknown),
[] ).
cnf(18,axiom,
relation(identity_relation(u)),
file('SEU008+1.p',unknown),
[] ).
cnf(19,axiom,
function(identity_relation(u)),
file('SEU008+1.p',unknown),
[] ).
cnf(32,axiom,
in(skc10,set_intersection2(relation_dom(skc9),skc11)),
file('SEU008+1.p',unknown),
[] ).
cnf(37,axiom,
equal(set_intersection2(u,v),set_intersection2(v,u)),
file('SEU008+1.p',unknown),
[] ).
cnf(52,axiom,
~ equal(apply(relation_composition(identity_relation(skc11),skc9),skc10),apply(skc9,skc10)),
file('SEU008+1.p',unknown),
[] ).
cnf(55,axiom,
( ~ in(u,v)
| ~ equal(v,set_intersection2(w,x))
| in(u,w) ),
file('SEU008+1.p',unknown),
[] ).
cnf(57,axiom,
( ~ relation(u)
| ~ function(u)
| ~ equal(u,identity_relation(v))
| equal(relation_dom(u),v) ),
file('SEU008+1.p',unknown),
[] ).
cnf(64,axiom,
( ~ relation(u)
| ~ function(u)
| ~ in(v,w)
| ~ equal(u,identity_relation(w))
| equal(apply(u,v),v) ),
file('SEU008+1.p',unknown),
[] ).
cnf(67,axiom,
( ~ relation(u)
| ~ function(u)
| ~ relation(v)
| ~ function(v)
| ~ in(w,relation_dom(u))
| equal(apply(relation_composition(u,v),w),apply(v,apply(u,w))) ),
file('SEU008+1.p',unknown),
[] ).
cnf(68,plain,
in(skc10,set_intersection2(skc11,relation_dom(skc9))),
inference(rew,[status(thm),theory(equality)],[37,32]),
[iquote('0:Rew:37.0,32.0')] ).
cnf(328,plain,
( ~ in(u,set_intersection2(v,w))
| in(u,v) ),
inference(eqr,[status(thm),theory(equality)],[55]),
[iquote('0:EqR:55.1')] ).
cnf(346,plain,
( ~ relation(identity_relation(u))
| ~ function(identity_relation(u))
| equal(relation_dom(identity_relation(u)),u) ),
inference(eqr,[status(thm),theory(equality)],[57]),
[iquote('0:EqR:57.2')] ).
cnf(347,plain,
equal(relation_dom(identity_relation(u)),u),
inference(ssi,[status(thm)],[346,19,18]),
[iquote('0:SSi:346.1,346.0,19.0,18.0,19.0,18.0')] ).
cnf(499,plain,
( ~ relation(identity_relation(u))
| ~ function(identity_relation(u))
| ~ in(v,u)
| equal(apply(identity_relation(u),v),v) ),
inference(eqr,[status(thm),theory(equality)],[64]),
[iquote('0:EqR:64.3')] ).
cnf(502,plain,
( ~ in(u,v)
| equal(apply(identity_relation(v),u),u) ),
inference(ssi,[status(thm)],[499,19,18]),
[iquote('0:SSi:499.1,499.0,19.0,18.0,19.0,18.0')] ).
cnf(551,plain,
in(skc10,skc11),
inference(res,[status(thm),theory(equality)],[68,328]),
[iquote('0:Res:68.0,328.0')] ).
cnf(568,plain,
( ~ relation(identity_relation(skc11))
| ~ function(identity_relation(skc11))
| ~ relation(skc9)
| ~ function(skc9)
| ~ in(skc10,relation_dom(identity_relation(skc11)))
| ~ equal(apply(skc9,apply(identity_relation(skc11),skc10)),apply(skc9,skc10)) ),
inference(spl,[status(thm),theory(equality)],[67,52]),
[iquote('0:SpL:67.5,52.0')] ).
cnf(572,plain,
( ~ relation(identity_relation(skc11))
| ~ function(identity_relation(skc11))
| ~ relation(skc9)
| ~ function(skc9)
| ~ in(skc10,skc11)
| ~ equal(apply(skc9,apply(identity_relation(skc11),skc10)),apply(skc9,skc10)) ),
inference(rew,[status(thm),theory(equality)],[347,568]),
[iquote('0:Rew:347.0,568.4')] ).
cnf(573,plain,
( ~ relation(identity_relation(skc11))
| ~ function(identity_relation(skc11))
| ~ relation(skc9)
| ~ function(skc9)
| ~ in(skc10,skc11)
| ~ equal(apply(skc9,skc10),apply(skc9,skc10)) ),
inference(rew,[status(thm),theory(equality)],[502,572]),
[iquote('0:Rew:502.1,572.5')] ).
cnf(574,plain,
( ~ relation(identity_relation(skc11))
| ~ function(identity_relation(skc11))
| ~ relation(skc9)
| ~ function(skc9)
| ~ in(skc10,skc11) ),
inference(obv,[status(thm),theory(equality)],[573]),
[iquote('0:Obv:573.5')] ).
cnf(575,plain,
~ in(skc10,skc11),
inference(ssi,[status(thm)],[574,2,1,19,18]),
[iquote('0:SSi:574.3,574.2,574.1,574.0,2.0,1.0,2.0,1.0,19.0,18.0,19.0,18.0')] ).
cnf(576,plain,
$false,
inference(mrr,[status(thm)],[575,551]),
[iquote('0:MRR:575.0,551.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU008+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n003.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jun 20 03:04:44 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.20/0.49
% 0.20/0.49 SPASS V 3.9
% 0.20/0.49 SPASS beiseite: Proof found.
% 0.20/0.49 % SZS status Theorem
% 0.20/0.49 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.49 SPASS derived 427 clauses, backtracked 0 clauses, performed 0 splits and kept 263 clauses.
% 0.20/0.49 SPASS allocated 98080 KBytes.
% 0.20/0.49 SPASS spent 0:00:00.14 on the problem.
% 0.20/0.49 0:00:00.04 for the input.
% 0.20/0.49 0:00:00.04 for the FLOTTER CNF translation.
% 0.20/0.49 0:00:00.00 for inferences.
% 0.20/0.49 0:00:00.00 for the backtracking.
% 0.20/0.49 0:00:00.02 for the reduction.
% 0.20/0.49
% 0.20/0.49
% 0.20/0.49 Here is a proof with depth 2, length 24 :
% 0.20/0.49 % SZS output start Refutation
% See solution above
% 0.20/0.49 Formulae used in the proof : t38_funct_1 fc2_funct_1 commutativity_k3_xboole_0 d3_xboole_0 antisymmetry_r2_hidden t34_funct_1 t23_funct_1
% 0.20/0.49
%------------------------------------------------------------------------------