%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET973+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n016.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 05:30:09 EDT 2022
% Result : Theorem 6.14s 6.31s
% Output : Refutation 6.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 18
% Syntax : Number of clauses : 63 ( 37 unt; 10 nHn; 63 RR)
% Number of literals : 99 ( 0 equ; 30 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 11 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(6,axiom,
equal(set_intersection2(u,u),u),
file('SET973+1.p',unknown),
[] ).
cnf(7,axiom,
subset(set_intersection2(u,v),u),
file('SET973+1.p',unknown),
[] ).
cnf(9,axiom,
equal(set_union2(u,v),set_union2(v,u)),
file('SET973+1.p',unknown),
[] ).
cnf(10,axiom,
equal(set_intersection2(u,v),set_intersection2(v,u)),
file('SET973+1.p',unknown),
[] ).
cnf(16,axiom,
( subset(u,v)
| in(skf10(v,u),u) ),
file('SET973+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ in(skf10(u,v),u)
| subset(w,u) ),
file('SET973+1.p',unknown),
[] ).
cnf(19,axiom,
( ~ subset(u,v)
| ~ subset(v,u)
| equal(v,u) ),
file('SET973+1.p',unknown),
[] ).
cnf(25,axiom,
( ~ subset(u,v)
| subset(set_difference(w,v),set_difference(w,u)) ),
file('SET973+1.p',unknown),
[] ).
cnf(27,axiom,
( ~ in(u,v)
| ~ equal(w,set_union2(x,v))
| in(u,w) ),
file('SET973+1.p',unknown),
[] ).
cnf(28,axiom,
( ~ in(u,v)
| ~ equal(v,set_difference(w,x))
| in(u,w) ),
file('SET973+1.p',unknown),
[] ).
cnf(29,axiom,
equal(cartesian_product2(set_difference(u,v),w),set_difference(cartesian_product2(u,w),cartesian_product2(v,w))),
file('SET973+1.p',unknown),
[] ).
cnf(30,axiom,
equal(cartesian_product2(u,set_difference(v,w)),set_difference(cartesian_product2(u,v),cartesian_product2(u,w))),
file('SET973+1.p',unknown),
[] ).
cnf(31,axiom,
equal(set_difference(u,set_intersection2(v,w)),set_union2(set_difference(u,v),set_difference(u,w))),
file('SET973+1.p',unknown),
[] ).
cnf(34,axiom,
( ~ in(u,v)
| ~ in(u,w)
| ~ equal(v,set_difference(x,w)) ),
file('SET973+1.p',unknown),
[] ).
cnf(37,axiom,
equal(cartesian_product2(set_intersection2(u,v),set_intersection2(w,x)),set_intersection2(cartesian_product2(u,w),cartesian_product2(v,x))),
file('SET973+1.p',unknown),
[] ).
cnf(41,axiom,
( equal(u,set_difference(v,w))
| in(skf11(w,v,u),u)
| in(skf11(w,v,u),v) ),
file('SET973+1.p',unknown),
[] ).
cnf(48,axiom,
~ equal(set_union2(cartesian_product2(set_difference(skc9,skc7),skc8),cartesian_product2(skc9,set_difference(skc8,skc6))),set_difference(cartesian_product2(skc9,skc8),cartesian_product2(skc7,skc6))),
file('SET973+1.p',unknown),
[] ).
cnf(50,axiom,
( ~ in(skf11(u,v,w),v)
| ~ in(skf11(u,v,w),w)
| equal(w,set_difference(v,u))
| in(skf11(u,v,w),u) ),
file('SET973+1.p',unknown),
[] ).
cnf(58,plain,
~ equal(set_union2(set_difference(cartesian_product2(skc9,skc8),cartesian_product2(skc7,skc8)),set_difference(cartesian_product2(skc9,skc8),cartesian_product2(skc9,skc6))),set_difference(cartesian_product2(skc9,skc8),cartesian_product2(skc7,skc6))),
inference(rew,[status(thm),theory(equality)],[29,48,30]),
[iquote('0:Rew:29.0,48.0,30.0,48.0')] ).
cnf(76,plain,
subset(set_intersection2(u,v),v),
inference(spr,[status(thm),theory(equality)],[10,7]),
[iquote('0:SpR:10.0,7.0')] ).
cnf(110,plain,
( ~ subset(u,set_intersection2(u,v))
| equal(set_intersection2(u,v),u) ),
inference(res,[status(thm),theory(equality)],[7,19]),
[iquote('0:Res:7.0,19.0')] ).
cnf(112,plain,
( ~ subset(u,set_intersection2(v,u))
| equal(set_intersection2(v,u),u) ),
inference(res,[status(thm),theory(equality)],[76,19]),
[iquote('0:Res:76.0,19.0')] ).
cnf(126,plain,
( ~ subset(u,set_intersection2(u,v))
| equal(set_intersection2(v,u),u) ),
inference(spl,[status(thm),theory(equality)],[10,112]),
[iquote('0:SpL:10.0,112.0')] ).
cnf(260,plain,
( ~ in(u,set_difference(v,w))
| in(u,v) ),
inference(eqr,[status(thm),theory(equality)],[28]),
[iquote('0:EqR:28.1')] ).
cnf(270,plain,
( subset(set_difference(u,v),w)
| in(skf10(w,set_difference(u,v)),u) ),
inference(res,[status(thm),theory(equality)],[16,260]),
[iquote('0:Res:16.1,260.0')] ).
cnf(311,plain,
( ~ in(u,v)
| in(u,set_union2(w,v)) ),
inference(eqr,[status(thm),theory(equality)],[27]),
[iquote('0:EqR:27.1')] ).
cnf(333,plain,
( ~ in(skf10(set_union2(u,v),w),v)
| subset(x,set_union2(u,v)) ),
inference(res,[status(thm),theory(equality)],[311,17]),
[iquote('0:Res:311.1,17.0')] ).
cnf(441,plain,
( ~ in(u,set_difference(v,w))
| ~ in(u,w) ),
inference(eqr,[status(thm),theory(equality)],[34]),
[iquote('0:EqR:34.2')] ).
cnf(449,plain,
( ~ in(skf10(u,set_difference(v,w)),w)
| subset(set_difference(v,w),u) ),
inference(res,[status(thm),theory(equality)],[16,441]),
[iquote('0:Res:16.1,441.0')] ).
cnf(596,plain,
( subset(set_difference(u,v),set_union2(w,u))
| subset(x,set_union2(w,u)) ),
inference(res,[status(thm),theory(equality)],[270,333]),
[iquote('0:Res:270.1,333.0')] ).
cnf(603,plain,
subset(set_difference(u,v),set_union2(w,u)),
inference(con,[status(thm)],[596]),
[iquote('0:Con:596.1')] ).
cnf(608,plain,
equal(cartesian_product2(set_intersection2(u,v),w),set_intersection2(cartesian_product2(u,w),cartesian_product2(v,w))),
inference(spr,[status(thm),theory(equality)],[6,37]),
[iquote('0:SpR:6.0,37.0')] ).
cnf(609,plain,
equal(cartesian_product2(set_intersection2(u,v),set_intersection2(w,x)),set_intersection2(cartesian_product2(u,x),cartesian_product2(v,w))),
inference(spr,[status(thm),theory(equality)],[10,37]),
[iquote('0:SpR:10.0,37.0')] ).
cnf(611,plain,
equal(cartesian_product2(u,set_intersection2(v,w)),set_intersection2(cartesian_product2(u,v),cartesian_product2(u,w))),
inference(spr,[status(thm),theory(equality)],[6,37]),
[iquote('0:SpR:6.0,37.0')] ).
cnf(619,plain,
equal(set_intersection2(cartesian_product2(u,set_intersection2(v,w)),cartesian_product2(x,set_intersection2(v,w))),set_intersection2(cartesian_product2(u,v),cartesian_product2(x,w))),
inference(rew,[status(thm),theory(equality)],[608,37]),
[iquote('0:Rew:608.0,37.0')] ).
cnf(622,plain,
equal(set_intersection2(set_intersection2(cartesian_product2(u,v),cartesian_product2(u,w)),set_intersection2(cartesian_product2(x,v),cartesian_product2(x,w))),set_intersection2(cartesian_product2(u,w),cartesian_product2(x,v))),
inference(rew,[status(thm),theory(equality)],[611,609,608]),
[iquote('0:Rew:611.0,609.0,611.0,609.0,608.0,609.0')] ).
cnf(626,plain,
equal(set_intersection2(cartesian_product2(u,v),cartesian_product2(w,x)),set_intersection2(cartesian_product2(u,x),cartesian_product2(w,v))),
inference(rew,[status(thm),theory(equality)],[622,619,611]),
[iquote('0:Rew:622.0,619.0,611.0,619.0,611.0,619.0')] ).
cnf(654,plain,
subset(set_difference(u,v),set_union2(u,w)),
inference(spr,[status(thm),theory(equality)],[9,603]),
[iquote('0:SpR:9.0,603.0')] ).
cnf(698,plain,
subset(set_difference(u,set_union2(v,w)),set_difference(u,set_difference(v,x))),
inference(res,[status(thm),theory(equality)],[654,25]),
[iquote('0:Res:654.0,25.0')] ).
cnf(741,plain,
equal(set_difference(u,set_intersection2(cartesian_product2(v,w),cartesian_product2(x,y))),set_union2(set_difference(u,cartesian_product2(v,y)),set_difference(u,cartesian_product2(x,w)))),
inference(spr,[status(thm),theory(equality)],[626,31]),
[iquote('0:SpR:626.0,31.0')] ).
cnf(780,plain,
equal(set_union2(set_difference(u,cartesian_product2(v,w)),set_difference(u,cartesian_product2(x,y))),set_union2(set_difference(u,cartesian_product2(v,y)),set_difference(u,cartesian_product2(x,w)))),
inference(rew,[status(thm),theory(equality)],[31,741]),
[iquote('0:Rew:31.0,741.0')] ).
cnf(911,plain,
( equal(set_difference(u,v),u)
| in(skf11(v,u,u),u) ),
inference(fac,[status(thm)],[41]),
[iquote('0:Fac:41.1,41.2')] ).
cnf(1601,plain,
( ~ in(skf11(u,v,v),v)
| equal(set_difference(v,u),v)
| equal(set_difference(v,u),v)
| in(skf11(u,v,v),u) ),
inference(res,[status(thm),theory(equality)],[911,50]),
[iquote('0:Res:911.1,50.0')] ).
cnf(1603,plain,
( ~ in(skf11(u,v,v),v)
| equal(set_difference(v,u),v)
| in(skf11(u,v,v),u) ),
inference(obv,[status(thm),theory(equality)],[1601]),
[iquote('0:Obv:1601.1')] ).
cnf(1604,plain,
( equal(set_difference(u,v),u)
| in(skf11(v,u,u),v) ),
inference(mrr,[status(thm)],[1603,911]),
[iquote('0:MRR:1603.0,911.1')] ).
cnf(1733,plain,
( subset(set_difference(u,u),v)
| subset(set_difference(u,u),v) ),
inference(res,[status(thm),theory(equality)],[270,449]),
[iquote('0:Res:270.1,449.0')] ).
cnf(1734,plain,
subset(set_difference(u,u),v),
inference(obv,[status(thm),theory(equality)],[1733]),
[iquote('0:Obv:1733.0')] ).
cnf(1743,plain,
equal(set_intersection2(u,set_difference(v,v)),set_difference(v,v)),
inference(res,[status(thm),theory(equality)],[1734,126]),
[iquote('0:Res:1734.0,126.0')] ).
cnf(1744,plain,
equal(set_intersection2(set_difference(u,u),v),set_difference(u,u)),
inference(res,[status(thm),theory(equality)],[1734,110]),
[iquote('0:Res:1734.0,110.0')] ).
cnf(1828,plain,
equal(set_union2(set_difference(u,v),set_difference(u,set_difference(w,w))),set_difference(u,set_difference(w,w))),
inference(spr,[status(thm),theory(equality)],[1743,31]),
[iquote('0:SpR:1743.0,31.0')] ).
cnf(1868,plain,
equal(set_difference(u,u),set_difference(v,v)),
inference(spr,[status(thm),theory(equality)],[1744,1743]),
[iquote('0:SpR:1744.0,1743.0')] ).
cnf(1939,plain,
subset(set_difference(set_difference(u,v),set_union2(u,w)),set_difference(x,x)),
inference(spr,[status(thm),theory(equality)],[1868,698]),
[iquote('0:SpR:1868.0,698.0')] ).
cnf(2040,plain,
( ~ in(u,set_difference(v,v))
| ~ in(u,w) ),
inference(spl,[status(thm),theory(equality)],[1868,441]),
[iquote('0:SpL:1868.0,441.0')] ).
cnf(2064,plain,
~ in(u,set_difference(v,v)),
inference(con,[status(thm)],[2040]),
[iquote('0:Con:2040.1')] ).
cnf(2102,plain,
equal(set_difference(u,set_difference(v,v)),u),
inference(res,[status(thm),theory(equality)],[1604,2064]),
[iquote('0:Res:1604.1,2064.0')] ).
cnf(2112,plain,
equal(set_union2(set_difference(u,v),u),u),
inference(rew,[status(thm),theory(equality)],[2102,1828]),
[iquote('0:Rew:2102.0,1828.0')] ).
cnf(2118,plain,
equal(set_union2(u,set_difference(u,v)),u),
inference(rew,[status(thm),theory(equality)],[9,2112]),
[iquote('0:Rew:9.0,2112.0')] ).
cnf(7758,plain,
( ~ subset(set_difference(u,u),set_difference(set_difference(v,w),set_union2(v,x)))
| equal(set_difference(u,u),set_difference(set_difference(v,w),set_union2(v,x))) ),
inference(res,[status(thm),theory(equality)],[1939,19]),
[iquote('0:Res:1939.0,19.0')] ).
cnf(7777,plain,
equal(set_difference(u,u),set_difference(set_difference(v,w),set_union2(v,x))),
inference(mrr,[status(thm)],[7758,1734]),
[iquote('0:MRR:7758.0,1734.0')] ).
cnf(11336,plain,
equal(set_union2(u,set_difference(set_difference(v,w),set_union2(v,x))),u),
inference(spr,[status(thm),theory(equality)],[7777,2118]),
[iquote('0:SpR:7777.0,2118.0')] ).
cnf(21941,plain,
equal(set_union2(set_difference(cartesian_product2(u,v),cartesian_product2(w,x)),set_difference(set_difference(y,z),set_union2(y,x1))),set_union2(set_difference(cartesian_product2(u,v),cartesian_product2(w,v)),set_difference(cartesian_product2(u,v),cartesian_product2(u,x)))),
inference(spr,[status(thm),theory(equality)],[7777,780]),
[iquote('0:SpR:7777.0,780.0')] ).
cnf(22170,plain,
equal(set_difference(cartesian_product2(u,v),cartesian_product2(w,x)),set_union2(set_difference(cartesian_product2(u,v),cartesian_product2(w,v)),set_difference(cartesian_product2(u,v),cartesian_product2(u,x)))),
inference(rew,[status(thm),theory(equality)],[11336,21941]),
[iquote('0:Rew:11336.0,21941.0')] ).
cnf(22171,plain,
$false,
inference(unc,[status(thm)],[22170,58]),
[iquote('0:UnC:22170.0,58.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET973+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n016.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 Jul 10 00:22:25 EDT 2022
% 0.13/0.34 % CPUTime :
% 6.14/6.31
% 6.14/6.31 SPASS V 3.9
% 6.14/6.31 SPASS beiseite: Proof found.
% 6.14/6.31 % SZS status Theorem
% 6.14/6.31 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.14/6.31 SPASS derived 16248 clauses, backtracked 0 clauses, performed 1 splits and kept 3133 clauses.
% 6.14/6.31 SPASS allocated 101337 KBytes.
% 6.14/6.31 SPASS spent 0:00:05.82 on the problem.
% 6.14/6.31 0:00:00.04 for the input.
% 6.14/6.31 0:00:00.06 for the FLOTTER CNF translation.
% 6.14/6.31 0:00:00.12 for inferences.
% 6.14/6.31 0:00:00.00 for the backtracking.
% 6.14/6.31 0:00:05.55 for the reduction.
% 6.14/6.31
% 6.14/6.31
% 6.14/6.31 Here is a proof with depth 8, length 63 :
% 6.14/6.31 % SZS output start Refutation
% See solution above
% 6.14/6.31 Formulae used in the proof : idempotence_k3_xboole_0 t17_xboole_1 commutativity_k2_xboole_0 commutativity_k3_xboole_0 d3_tarski d10_xboole_0 t34_xboole_1 d2_xboole_0 d4_xboole_0 t125_zfmisc_1 t54_xboole_1 t123_zfmisc_1 t126_zfmisc_1
% 6.14/6.31
%------------------------------------------------------------------------------