TSTP Solution File: SET914+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET914+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 05:29:45 EDT 2022
% Result : Theorem 0.19s 0.51s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of clauses : 33 ( 8 unt; 3 nHn; 33 RR)
% Number of literals : 66 ( 0 equ; 37 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
in(skc5,skc6),
file('SET914+1.p',unknown),
[] ).
cnf(5,axiom,
disjoint(unordered_pair(skc5,skc7),skc6),
file('SET914+1.p',unknown),
[] ).
cnf(7,axiom,
equal(unordered_pair(u,v),unordered_pair(v,u)),
file('SET914+1.p',unknown),
[] ).
cnf(8,axiom,
equal(set_intersection2(u,v),set_intersection2(v,u)),
file('SET914+1.p',unknown),
[] ).
cnf(9,axiom,
( equal(u,empty_set)
| in(skf3(u),u) ),
file('SET914+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ in(u,v)
| ~ equal(v,empty_set) ),
file('SET914+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ disjoint(u,v)
| equal(set_intersection2(u,v),empty_set) ),
file('SET914+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ equal(u,v)
| ~ equal(w,unordered_pair(x,v))
| in(u,w) ),
file('SET914+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ in(u,v)
| ~ equal(v,set_intersection2(w,x))
| in(u,w) ),
file('SET914+1.p',unknown),
[] ).
cnf(18,axiom,
( ~ in(u,v)
| ~ equal(v,set_intersection2(w,x))
| in(u,x) ),
file('SET914+1.p',unknown),
[] ).
cnf(20,axiom,
( ~ in(u,v)
| ~ in(u,w)
| ~ equal(x,set_intersection2(w,v))
| in(u,x) ),
file('SET914+1.p',unknown),
[] ).
cnf(29,plain,
( ~ equal(u,set_intersection2(skc6,v))
| ~ in(skc5,v)
| in(skc5,u) ),
inference(res,[status(thm),theory(equality)],[3,20]),
[iquote('0:Res:3.0,20.0')] ).
cnf(65,plain,
( ~ disjoint(u,v)
| equal(set_intersection2(v,u),empty_set) ),
inference(spr,[status(thm),theory(equality)],[13,8]),
[iquote('0:SpR:13.1,8.0')] ).
cnf(93,plain,
( ~ equal(u,v)
| in(u,unordered_pair(w,v)) ),
inference(eqr,[status(thm),theory(equality)],[16]),
[iquote('0:EqR:16.1')] ).
cnf(102,plain,
( ~ equal(u,v)
| in(u,unordered_pair(v,w)) ),
inference(spr,[status(thm),theory(equality)],[7,93]),
[iquote('0:SpR:7.0,93.1')] ).
cnf(130,plain,
( ~ in(u,set_intersection2(v,w))
| in(u,w) ),
inference(eqr,[status(thm),theory(equality)],[18]),
[iquote('0:EqR:18.1')] ).
cnf(152,plain,
( ~ in(u,set_intersection2(v,w))
| in(u,v) ),
inference(eqr,[status(thm),theory(equality)],[17]),
[iquote('0:EqR:17.1')] ).
cnf(163,plain,
( equal(set_intersection2(u,v),empty_set)
| in(skf3(set_intersection2(u,v)),v) ),
inference(res,[status(thm),theory(equality)],[9,130]),
[iquote('0:Res:9.1,130.0')] ).
cnf(214,plain,
( ~ equal(u,empty_set)
| equal(set_intersection2(v,u),empty_set) ),
inference(res,[status(thm),theory(equality)],[163,12]),
[iquote('0:Res:163.1,12.0')] ).
cnf(248,plain,
( ~ equal(u,empty_set)
| ~ in(v,empty_set)
| in(v,w) ),
inference(spl,[status(thm),theory(equality)],[214,152]),
[iquote('0:SpL:214.1,152.0')] ).
cnf(253,plain,
( ~ in(u,empty_set)
| in(u,v) ),
inference(aed,[status(thm),theory(equality)],[248]),
[iquote('0:AED:248.0')] ).
cnf(263,plain,
( equal(set_intersection2(u,empty_set),empty_set)
| in(skf3(set_intersection2(u,empty_set)),v) ),
inference(res,[status(thm),theory(equality)],[163,253]),
[iquote('0:Res:163.1,253.0')] ).
cnf(316,plain,
( ~ equal(u,empty_set)
| equal(set_intersection2(v,empty_set),empty_set) ),
inference(res,[status(thm),theory(equality)],[263,12]),
[iquote('0:Res:263.1,12.0')] ).
cnf(323,plain,
equal(set_intersection2(u,empty_set),empty_set),
inference(aed,[status(thm),theory(equality)],[316]),
[iquote('0:AED:316.0')] ).
cnf(606,plain,
( ~ in(skc5,u)
| in(skc5,set_intersection2(skc6,u)) ),
inference(eqr,[status(thm),theory(equality)],[29]),
[iquote('0:EqR:29.0')] ).
cnf(619,plain,
( ~ disjoint(u,skc6)
| ~ in(skc5,u)
| in(skc5,empty_set) ),
inference(spr,[status(thm),theory(equality)],[65,606]),
[iquote('0:SpR:65.1,606.1')] ).
cnf(627,plain,
( ~ in(skc5,u)
| ~ equal(set_intersection2(skc6,u),empty_set) ),
inference(res,[status(thm),theory(equality)],[606,12]),
[iquote('0:Res:606.1,12.0')] ).
cnf(658,plain,
( ~ in(skc5,empty_set)
| ~ equal(empty_set,empty_set) ),
inference(spl,[status(thm),theory(equality)],[323,627]),
[iquote('0:SpL:323.0,627.1')] ).
cnf(659,plain,
~ in(skc5,empty_set),
inference(obv,[status(thm),theory(equality)],[658]),
[iquote('0:Obv:658.1')] ).
cnf(660,plain,
( ~ disjoint(u,skc6)
| ~ in(skc5,u) ),
inference(mrr,[status(thm)],[619,659]),
[iquote('0:MRR:619.2,659.0')] ).
cnf(681,plain,
( ~ equal(skc5,u)
| ~ disjoint(unordered_pair(u,v),skc6) ),
inference(res,[status(thm),theory(equality)],[102,660]),
[iquote('0:Res:102.1,660.1')] ).
cnf(819,plain,
~ equal(skc5,skc5),
inference(res,[status(thm),theory(equality)],[5,681]),
[iquote('0:Res:5.0,681.1')] ).
cnf(822,plain,
$false,
inference(obv,[status(thm),theory(equality)],[819]),
[iquote('0:Obv:819.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET914+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n024.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 Jul 10 15:26:13 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.51
% 0.19/0.51 SPASS V 3.9
% 0.19/0.51 SPASS beiseite: Proof found.
% 0.19/0.51 % SZS status Theorem
% 0.19/0.51 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.51 SPASS derived 716 clauses, backtracked 0 clauses, performed 0 splits and kept 272 clauses.
% 0.19/0.51 SPASS allocated 85673 KBytes.
% 0.19/0.51 SPASS spent 0:00:00.16 on the problem.
% 0.19/0.51 0:00:00.03 for the input.
% 0.19/0.51 0:00:00.04 for the FLOTTER CNF translation.
% 0.19/0.51 0:00:00.01 for inferences.
% 0.19/0.51 0:00:00.00 for the backtracking.
% 0.19/0.51 0:00:00.06 for the reduction.
% 0.19/0.51
% 0.19/0.51
% 0.19/0.51 Here is a proof with depth 7, length 33 :
% 0.19/0.51 % SZS output start Refutation
% See solution above
% 0.19/0.51 Formulae used in the proof : t55_zfmisc_1 commutativity_k2_tarski commutativity_k3_xboole_0 d1_xboole_0 d7_xboole_0 d2_tarski idempotence_k3_xboole_0 d3_xboole_0
% 0.19/0.51
%------------------------------------------------------------------------------