TSTP Solution File: SET945+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET945+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 05:29:59 EDT 2022
% Result : Theorem 91.62s 91.84s
% Output : Refutation 91.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of clauses : 28 ( 5 unt; 7 nHn; 28 RR)
% Number of literals : 60 ( 0 equ; 29 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
~ disjoint(union(skc4),skc5),
file('SET945+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ in(u,skc4)
| disjoint(u,skc5) ),
file('SET945+1.p',unknown),
[] ).
cnf(6,axiom,
equal(set_intersection2(u,v),set_intersection2(v,u)),
file('SET945+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ disjoint(u,v)
| disjoint(v,u) ),
file('SET945+1.p',unknown),
[] ).
cnf(9,axiom,
( disjoint(u,v)
| in(skf10(v,u),set_intersection2(u,v)) ),
file('SET945+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ disjoint(u,v)
| ~ in(w,set_intersection2(u,v)) ),
file('SET945+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ in(u,v)
| ~ equal(v,set_intersection2(w,x))
| in(u,x) ),
file('SET945+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ in(u,v)
| ~ equal(v,union(w))
| in(u,skf6(u,x)) ),
file('SET945+1.p',unknown),
[] ).
cnf(14,axiom,
( ~ in(u,v)
| ~ equal(v,union(w))
| in(skf6(u,w),w) ),
file('SET945+1.p',unknown),
[] ).
cnf(18,axiom,
( ~ in(u,v)
| ~ in(u,w)
| ~ equal(x,set_intersection2(w,v))
| in(u,x) ),
file('SET945+1.p',unknown),
[] ).
cnf(25,plain,
~ disjoint(skc5,union(skc4)),
inference(res,[status(thm),theory(equality)],[7,3]),
[iquote('0:Res:7.1,3.0')] ).
cnf(46,plain,
( disjoint(u,v)
| in(skf10(v,u),set_intersection2(v,u)) ),
inference(spr,[status(thm),theory(equality)],[6,9]),
[iquote('0:SpR:6.0,9.1')] ).
cnf(63,plain,
( ~ in(u,set_intersection2(v,w))
| in(u,w) ),
inference(eqr,[status(thm),theory(equality)],[12]),
[iquote('0:EqR:12.1')] ).
cnf(71,plain,
( disjoint(u,v)
| in(skf10(v,u),v) ),
inference(res,[status(thm),theory(equality)],[9,63]),
[iquote('0:Res:9.1,63.0')] ).
cnf(72,plain,
( disjoint(u,v)
| in(skf10(v,u),u) ),
inference(res,[status(thm),theory(equality)],[46,63]),
[iquote('0:Res:46.1,63.0')] ).
cnf(104,plain,
( ~ in(u,union(v))
| in(skf6(u,v),v) ),
inference(eqr,[status(thm),theory(equality)],[14]),
[iquote('0:EqR:14.1')] ).
cnf(117,plain,
( ~ in(u,union(v))
| in(u,skf6(u,w)) ),
inference(eqr,[status(thm),theory(equality)],[13]),
[iquote('0:EqR:13.1')] ).
cnf(135,plain,
( disjoint(u,union(v))
| in(skf10(union(v),u),skf6(skf10(union(v),u),w)) ),
inference(res,[status(thm),theory(equality)],[71,117]),
[iquote('0:Res:71.1,117.0')] ).
cnf(238,plain,
( ~ in(u,v)
| ~ in(u,w)
| in(u,set_intersection2(w,v)) ),
inference(eqr,[status(thm),theory(equality)],[18]),
[iquote('0:EqR:18.2')] ).
cnf(632,plain,
( ~ in(u,v)
| ~ in(u,w)
| ~ disjoint(w,v) ),
inference(res,[status(thm),theory(equality)],[238,10]),
[iquote('0:Res:238.2,10.1')] ).
cnf(644,plain,
( ~ in(skf10(u,v),w)
| ~ disjoint(w,v)
| disjoint(v,u) ),
inference(res,[status(thm),theory(equality)],[72,632]),
[iquote('0:Res:72.1,632.0')] ).
cnf(55256,plain,
( ~ disjoint(skf6(skf10(union(u),v),w),v)
| disjoint(v,union(u))
| disjoint(v,union(u)) ),
inference(res,[status(thm),theory(equality)],[135,644]),
[iquote('0:Res:135.1,644.0')] ).
cnf(55258,plain,
( ~ disjoint(skf6(skf10(union(u),v),w),v)
| disjoint(v,union(u)) ),
inference(obv,[status(thm),theory(equality)],[55256]),
[iquote('0:Obv:55256.1')] ).
cnf(58695,plain,
( ~ in(skf6(skf10(union(u),skc5),v),skc4)
| disjoint(skc5,union(u)) ),
inference(res,[status(thm),theory(equality)],[5,55258]),
[iquote('0:Res:5.1,55258.0')] ).
cnf(58756,plain,
( ~ in(skf10(union(u),skc5),union(skc4))
| disjoint(skc5,union(u)) ),
inference(res,[status(thm),theory(equality)],[104,58695]),
[iquote('0:Res:104.1,58695.0')] ).
cnf(59492,plain,
( disjoint(skc5,union(skc4))
| disjoint(skc5,union(skc4)) ),
inference(res,[status(thm),theory(equality)],[71,58756]),
[iquote('0:Res:71.1,58756.0')] ).
cnf(59499,plain,
disjoint(skc5,union(skc4)),
inference(obv,[status(thm),theory(equality)],[59492]),
[iquote('0:Obv:59492.0')] ).
cnf(59500,plain,
$false,
inference(mrr,[status(thm)],[59499,25]),
[iquote('0:MRR:59499.0,25.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET945+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n029.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 01:54:31 EDT 2022
% 0.13/0.34 % CPUTime :
% 91.62/91.84
% 91.62/91.84 SPASS V 3.9
% 91.62/91.84 SPASS beiseite: Proof found.
% 91.62/91.84 % SZS status Theorem
% 91.62/91.84 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 91.62/91.84 SPASS derived 44779 clauses, backtracked 0 clauses, performed 0 splits and kept 10370 clauses.
% 91.62/91.84 SPASS allocated 123553 KBytes.
% 91.62/91.84 SPASS spent 0:1:27.41 on the problem.
% 91.62/91.84 0:00:00.03 for the input.
% 91.62/91.84 0:00:00.05 for the FLOTTER CNF translation.
% 91.62/91.84 0:00:00.55 for inferences.
% 91.62/91.84 0:00:00.00 for the backtracking.
% 91.62/91.84 0:1:26.59 for the reduction.
% 91.62/91.84
% 91.62/91.84
% 91.62/91.84 Here is a proof with depth 7, length 28 :
% 91.62/91.84 % SZS output start Refutation
% See solution above
% 91.62/91.84 Formulae used in the proof : t98_zfmisc_1 commutativity_k3_xboole_0 symmetry_r1_xboole_0 t4_xboole_0 d3_xboole_0 d4_tarski
% 91.62/91.84
%------------------------------------------------------------------------------