%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU141+1 : 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 14:34:16 EDT 2022
% Result : Theorem 0.19s 0.59s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of clauses : 39 ( 10 unt; 13 nHn; 39 RR)
% Number of literals : 82 ( 0 equ; 39 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(10,axiom,
equal(set_intersection2(u,v),set_intersection2(v,u)),
file('SEU141+1.p',unknown),
[] ).
cnf(15,axiom,
( disjoint(skc4,skc5)
| equal(set_difference(skc4,skc5),skc4) ),
file('SEU141+1.p',unknown),
[] ).
cnf(19,axiom,
( ~ disjoint(u,v)
| equal(set_intersection2(u,v),empty_set) ),
file('SEU141+1.p',unknown),
[] ).
cnf(22,axiom,
( ~ disjoint(skc4,skc5)
| ~ equal(set_difference(skc4,skc5),skc4) ),
file('SEU141+1.p',unknown),
[] ).
cnf(23,axiom,
( disjoint(u,v)
| in(skf7(v,u),set_intersection2(u,v)) ),
file('SEU141+1.p',unknown),
[] ).
cnf(24,axiom,
( ~ in(u,set_intersection2(v,w))
| ~ disjoint(v,w) ),
file('SEU141+1.p',unknown),
[] ).
cnf(28,axiom,
( ~ in(u,v)
| ~ equal(v,set_intersection2(w,x))
| in(u,x) ),
file('SEU141+1.p',unknown),
[] ).
cnf(30,axiom,
( ~ in(u,v)
| ~ in(u,w)
| ~ equal(v,set_difference(x,w)) ),
file('SEU141+1.p',unknown),
[] ).
cnf(32,axiom,
( ~ in(u,v)
| ~ in(u,w)
| ~ equal(x,set_intersection2(w,v))
| in(u,x) ),
file('SEU141+1.p',unknown),
[] ).
cnf(35,axiom,
( equal(u,set_difference(v,w))
| in(skf6(w,v,u),u)
| in(skf6(w,v,u),v) ),
file('SEU141+1.p',unknown),
[] ).
cnf(37,axiom,
( ~ in(skf6(u,v,w),v)
| ~ in(skf6(u,v,w),w)
| equal(w,set_difference(v,u))
| in(skf6(u,v,w),u) ),
file('SEU141+1.p',unknown),
[] ).
cnf(39,plain,
( ~ disjoint(u,v)
| ~ in(w,empty_set) ),
inference(rew,[status(thm),theory(equality)],[19,24]),
[iquote('0:Rew:19.1,24.0')] ).
cnf(63,plain,
disjoint(skc4,skc5),
inference(spt,[spt(split,[position(s1)])],[15]),
[iquote('1:Spt:15.0')] ).
cnf(64,plain,
~ equal(set_difference(skc4,skc5),skc4),
inference(mrr,[status(thm)],[22,63]),
[iquote('1:MRR:22.0,63.0')] ).
cnf(67,plain,
~ in(u,empty_set),
inference(res,[status(thm),theory(equality)],[63,39]),
[iquote('1:Res:63.0,39.0')] ).
cnf(108,plain,
( disjoint(u,v)
| in(skf7(v,u),set_intersection2(v,u)) ),
inference(spr,[status(thm),theory(equality)],[10,23]),
[iquote('0:SpR:10.0,23.1')] ).
cnf(178,plain,
( ~ in(u,set_intersection2(v,w))
| in(u,w) ),
inference(eqr,[status(thm),theory(equality)],[28]),
[iquote('0:EqR:28.1')] ).
cnf(195,plain,
( disjoint(u,v)
| in(skf7(v,u),v) ),
inference(res,[status(thm),theory(equality)],[23,178]),
[iquote('0:Res:23.1,178.0')] ).
cnf(196,plain,
( disjoint(u,v)
| in(skf7(v,u),u) ),
inference(res,[status(thm),theory(equality)],[108,178]),
[iquote('0:Res:108.1,178.0')] ).
cnf(239,plain,
( ~ in(u,set_difference(v,w))
| ~ in(u,w) ),
inference(eqr,[status(thm),theory(equality)],[30]),
[iquote('0:EqR:30.2')] ).
cnf(274,plain,
( ~ in(u,v)
| ~ in(u,w)
| in(u,set_intersection2(w,v)) ),
inference(eqr,[status(thm),theory(equality)],[32]),
[iquote('0:EqR:32.2')] ).
cnf(312,plain,
( equal(set_difference(u,v),u)
| in(skf6(v,u,u),u) ),
inference(fac,[status(thm)],[35]),
[iquote('0:Fac:35.1,35.2')] ).
cnf(639,plain,
( ~ in(skf6(u,v,v),v)
| equal(set_difference(v,u),v)
| equal(set_difference(v,u),v)
| in(skf6(u,v,v),u) ),
inference(res,[status(thm),theory(equality)],[312,37]),
[iquote('0:Res:312.1,37.0')] ).
cnf(643,plain,
( ~ in(skf6(u,v,v),v)
| equal(set_difference(v,u),v)
| in(skf6(u,v,v),u) ),
inference(obv,[status(thm),theory(equality)],[639]),
[iquote('0:Obv:639.1')] ).
cnf(644,plain,
( equal(set_difference(u,v),u)
| in(skf6(v,u,u),v) ),
inference(mrr,[status(thm)],[643,312]),
[iquote('0:MRR:643.0,312.1')] ).
cnf(933,plain,
( ~ disjoint(u,v)
| ~ in(w,v)
| ~ in(w,u)
| in(w,empty_set) ),
inference(spr,[status(thm),theory(equality)],[19,274]),
[iquote('0:SpR:19.1,274.2')] ).
cnf(954,plain,
( ~ disjoint(u,v)
| ~ in(w,v)
| ~ in(w,u) ),
inference(mrr,[status(thm)],[933,67]),
[iquote('1:MRR:933.3,67.0')] ).
cnf(1117,plain,
( ~ in(u,skc5)
| ~ in(u,skc4) ),
inference(res,[status(thm),theory(equality)],[63,954]),
[iquote('1:Res:63.0,954.0')] ).
cnf(1143,plain,
( ~ in(skf6(skc5,u,u),skc4)
| equal(set_difference(u,skc5),u) ),
inference(res,[status(thm),theory(equality)],[644,1117]),
[iquote('1:Res:644.1,1117.0')] ).
cnf(1348,plain,
( equal(set_difference(skc4,skc5),skc4)
| equal(set_difference(skc4,skc5),skc4) ),
inference(res,[status(thm),theory(equality)],[312,1143]),
[iquote('1:Res:312.1,1143.0')] ).
cnf(1351,plain,
equal(set_difference(skc4,skc5),skc4),
inference(obv,[status(thm),theory(equality)],[1348]),
[iquote('1:Obv:1348.0')] ).
cnf(1352,plain,
$false,
inference(mrr,[status(thm)],[1351,64]),
[iquote('1:MRR:1351.0,64.0')] ).
cnf(1355,plain,
~ disjoint(skc4,skc5),
inference(spt,[spt(split,[position(sa)])],[1352,63]),
[iquote('1:Spt:1352.0,15.0,63.0')] ).
cnf(1356,plain,
equal(set_difference(skc4,skc5),skc4),
inference(spt,[spt(split,[position(s2)])],[15]),
[iquote('1:Spt:1352.0,15.1')] ).
cnf(1385,plain,
( ~ in(u,skc4)
| ~ in(u,skc5) ),
inference(spl,[status(thm),theory(equality)],[1356,239]),
[iquote('1:SpL:1356.0,239.0')] ).
cnf(1547,plain,
( ~ in(skf7(skc5,u),skc4)
| disjoint(u,skc5) ),
inference(res,[status(thm),theory(equality)],[195,1385]),
[iquote('1:Res:195.1,1385.1')] ).
cnf(1709,plain,
( disjoint(skc4,skc5)
| disjoint(skc4,skc5) ),
inference(res,[status(thm),theory(equality)],[196,1547]),
[iquote('1:Res:196.1,1547.0')] ).
cnf(1710,plain,
disjoint(skc4,skc5),
inference(obv,[status(thm),theory(equality)],[1709]),
[iquote('1:Obv:1709.0')] ).
cnf(1711,plain,
$false,
inference(mrr,[status(thm)],[1710,1355]),
[iquote('1:MRR:1710.0,1355.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU141+1 : 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 04:03:40 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.59
% 0.19/0.59 SPASS V 3.9
% 0.19/0.59 SPASS beiseite: Proof found.
% 0.19/0.59 % SZS status Theorem
% 0.19/0.59 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.59 SPASS derived 1339 clauses, backtracked 86 clauses, performed 1 splits and kept 523 clauses.
% 0.19/0.59 SPASS allocated 98728 KBytes.
% 0.19/0.59 SPASS spent 0:00:00.24 on the problem.
% 0.19/0.59 0:00:00.04 for the input.
% 0.19/0.59 0:00:00.05 for the FLOTTER CNF translation.
% 0.19/0.59 0:00:00.02 for inferences.
% 0.19/0.59 0:00:00.00 for the backtracking.
% 0.19/0.59 0:00:00.11 for the reduction.
% 0.19/0.59
% 0.19/0.59
% 0.19/0.59 Here is a proof with depth 5, length 39 :
% 0.19/0.59 % SZS output start Refutation
% See solution above
% 0.19/0.59 Formulae used in the proof : commutativity_k3_xboole_0 t83_xboole_1 d7_xboole_0 t4_xboole_0 d3_xboole_0 d4_xboole_0
% 0.19/0.59
%------------------------------------------------------------------------------