%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU120+2 : TPTP v8.1.0. Released v3.3.0.
% 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 14:34:04 EDT 2022
% Result : Theorem 0.19s 0.46s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of clauses : 20 ( 7 unt; 4 nHn; 20 RR)
% Number of literals : 34 ( 0 equ; 14 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
disjoint(skc10,skc9),
file('SEU120+2.p',unknown),
[] ).
cnf(6,axiom,
equal(set_intersection2(u,v),set_intersection2(v,u)),
file('SEU120+2.p',unknown),
[] ).
cnf(7,axiom,
( equal(u,empty_set)
| in(skf3(u),u) ),
file('SEU120+2.p',unknown),
[] ).
cnf(9,axiom,
( skP0(skc7,skc8)
| in(skc11,set_intersection2(skc10,skc9)) ),
file('SEU120+2.p',unknown),
[] ).
cnf(10,axiom,
( ~ skP0(u,v)
| ~ disjoint(v,u) ),
file('SEU120+2.p',unknown),
[] ).
cnf(12,axiom,
( ~ in(u,v)
| ~ equal(v,empty_set) ),
file('SEU120+2.p',unknown),
[] ).
cnf(15,axiom,
( ~ disjoint(u,v)
| equal(set_intersection2(u,v),empty_set) ),
file('SEU120+2.p',unknown),
[] ).
cnf(16,axiom,
( ~ equal(set_intersection2(u,v),empty_set)
| disjoint(u,v) ),
file('SEU120+2.p',unknown),
[] ).
cnf(17,axiom,
( ~ skP0(u,v)
| ~ in(w,set_intersection2(v,u)) ),
file('SEU120+2.p',unknown),
[] ).
cnf(25,plain,
( skP0(skc7,skc8)
| in(skc11,set_intersection2(skc9,skc10)) ),
inference(rew,[status(thm),theory(equality)],[6,9]),
[iquote('0:Rew:6.0,9.1')] ).
cnf(26,plain,
equal(set_intersection2(skc10,skc9),empty_set),
inference(res,[status(thm),theory(equality)],[3,15]),
[iquote('0:Res:3.0,15.0')] ).
cnf(31,plain,
equal(set_intersection2(skc9,skc10),empty_set),
inference(rew,[status(thm),theory(equality)],[6,26]),
[iquote('0:Rew:6.0,26.0')] ).
cnf(32,plain,
( in(skc11,empty_set)
| skP0(skc7,skc8) ),
inference(rew,[status(thm),theory(equality)],[31,25]),
[iquote('0:Rew:31.0,25.1')] ).
cnf(47,plain,
( ~ equal(empty_set,empty_set)
| skP0(skc7,skc8) ),
inference(res,[status(thm),theory(equality)],[32,12]),
[iquote('0:Res:32.0,12.0')] ).
cnf(49,plain,
skP0(skc7,skc8),
inference(obv,[status(thm),theory(equality)],[47]),
[iquote('0:Obv:47.0')] ).
cnf(114,plain,
( ~ skP0(u,v)
| equal(set_intersection2(v,u),empty_set) ),
inference(res,[status(thm),theory(equality)],[7,17]),
[iquote('0:Res:7.1,17.1')] ).
cnf(144,plain,
( ~ skP0(u,v)
| ~ equal(empty_set,empty_set)
| disjoint(v,u) ),
inference(spl,[status(thm),theory(equality)],[114,16]),
[iquote('0:SpL:114.1,16.0')] ).
cnf(147,plain,
( ~ skP0(u,v)
| disjoint(v,u) ),
inference(obv,[status(thm),theory(equality)],[144]),
[iquote('0:Obv:144.1')] ).
cnf(148,plain,
~ skP0(u,v),
inference(mrr,[status(thm)],[147,10]),
[iquote('0:MRR:147.1,10.1')] ).
cnf(149,plain,
$false,
inference(unc,[status(thm)],[148,49]),
[iquote('0:UnC:148.0,49.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU120+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jun 19 13:26:10 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.19/0.46
% 0.19/0.46 SPASS V 3.9
% 0.19/0.46 SPASS beiseite: Proof found.
% 0.19/0.46 % SZS status Theorem
% 0.19/0.46 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.46 SPASS derived 107 clauses, backtracked 1 clauses, performed 1 splits and kept 68 clauses.
% 0.19/0.46 SPASS allocated 85392 KBytes.
% 0.19/0.46 SPASS spent 0:00:00.10 on the problem.
% 0.19/0.46 0:00:00.04 for the input.
% 0.19/0.46 0:00:00.04 for the FLOTTER CNF translation.
% 0.19/0.46 0:00:00.00 for inferences.
% 0.19/0.46 0:00:00.00 for the backtracking.
% 0.19/0.46 0:00:00.00 for the reduction.
% 0.19/0.46
% 0.19/0.46
% 0.19/0.46 Here is a proof with depth 2, length 20 :
% 0.19/0.46 % SZS output start Refutation
% See solution above
% 0.19/0.46 Formulae used in the proof : t4_xboole_0 idempotence_k3_xboole_0 d7_xboole_0 symmetry_r1_xboole_0 commutativity_k3_xboole_0 d1_xboole_0
% 0.19/0.46
%------------------------------------------------------------------------------