%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET230-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 05:25:10 EDT 2022
% Result : Unsatisfiable 1.23s 1.43s
% Output : Refutation 1.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of clauses : 23 ( 6 unt; 4 nHn; 23 RR)
% Number of literals : 45 ( 0 equ; 21 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(cross_product(w__dfg,w__dfg),cross_product(u__dfg,u__dfg)),
file('SET230-6.p',unknown),
[] ).
cnf(2,axiom,
~ equal(w__dfg,u__dfg),
file('SET230-6.p',unknown),
[] ).
cnf(4,axiom,
( subclass(u,v)
| member(not_subclass_element(u,v),u) ),
file('SET230-6.p',unknown),
[] ).
cnf(5,axiom,
( ~ member(not_subclass_element(u,v),v)
| subclass(u,v) ),
file('SET230-6.p',unknown),
[] ).
cnf(9,axiom,
( ~ subclass(u,v)
| ~ subclass(v,u)
| equal(v,u) ),
file('SET230-6.p',unknown),
[] ).
cnf(16,axiom,
( ~ member(ordered_pair(u,v),cross_product(w,x))
| member(u,w) ),
file('SET230-6.p',unknown),
[] ).
cnf(17,axiom,
( ~ member(ordered_pair(u,v),cross_product(w,x))
| member(v,x) ),
file('SET230-6.p',unknown),
[] ).
cnf(18,axiom,
( ~ member(u,v)
| ~ member(w,x)
| member(ordered_pair(w,u),cross_product(x,v)) ),
file('SET230-6.p',unknown),
[] ).
cnf(118,plain,
( ~ subclass(u__dfg,w__dfg)
| ~ subclass(w__dfg,u__dfg) ),
inference(res,[status(thm),theory(equality)],[9,2]),
[iquote('0:Res:9.2,2.0')] ).
cnf(412,plain,
( ~ member(ordered_pair(u,v),cross_product(u__dfg,u__dfg))
| member(v,w__dfg) ),
inference(spl,[status(thm),theory(equality)],[1,17]),
[iquote('0:SpL:1.0,17.0')] ).
cnf(874,plain,
( ~ member(u,w__dfg)
| ~ member(v,w__dfg)
| member(ordered_pair(v,u),cross_product(u__dfg,u__dfg)) ),
inference(spr,[status(thm),theory(equality)],[1,18]),
[iquote('0:SpR:1.0,18.2')] ).
cnf(1264,plain,
( ~ member(u,u__dfg)
| ~ member(v,u__dfg)
| member(u,w__dfg) ),
inference(res,[status(thm),theory(equality)],[18,412]),
[iquote('0:Res:18.2,412.0')] ).
cnf(1265,plain,
( ~ member(u,u__dfg)
| member(u,w__dfg) ),
inference(con,[status(thm)],[1264]),
[iquote('0:Con:1264.1')] ).
cnf(1271,plain,
( ~ member(not_subclass_element(u,w__dfg),u__dfg)
| subclass(u,w__dfg) ),
inference(res,[status(thm),theory(equality)],[1265,5]),
[iquote('0:Res:1265.1,5.0')] ).
cnf(1280,plain,
( subclass(u__dfg,w__dfg)
| subclass(u__dfg,w__dfg) ),
inference(res,[status(thm),theory(equality)],[4,1271]),
[iquote('0:Res:4.1,1271.0')] ).
cnf(1281,plain,
subclass(u__dfg,w__dfg),
inference(obv,[status(thm),theory(equality)],[1280]),
[iquote('0:Obv:1280.0')] ).
cnf(1282,plain,
~ subclass(w__dfg,u__dfg),
inference(mrr,[status(thm)],[118,1281]),
[iquote('0:MRR:118.0,1281.0')] ).
cnf(5228,plain,
( ~ member(u,w__dfg)
| ~ member(v,w__dfg)
| member(v,u__dfg) ),
inference(res,[status(thm),theory(equality)],[874,16]),
[iquote('0:Res:874.2,16.0')] ).
cnf(5232,plain,
( ~ member(u,w__dfg)
| member(u,u__dfg) ),
inference(con,[status(thm)],[5228]),
[iquote('0:Con:5228.0')] ).
cnf(5236,plain,
( subclass(w__dfg,u)
| member(not_subclass_element(w__dfg,u),u__dfg) ),
inference(res,[status(thm),theory(equality)],[4,5232]),
[iquote('0:Res:4.1,5232.0')] ).
cnf(5271,plain,
( subclass(w__dfg,u__dfg)
| subclass(w__dfg,u__dfg) ),
inference(res,[status(thm),theory(equality)],[5236,5]),
[iquote('0:Res:5236.1,5.0')] ).
cnf(5273,plain,
subclass(w__dfg,u__dfg),
inference(obv,[status(thm),theory(equality)],[5271]),
[iquote('0:Obv:5271.0')] ).
cnf(5274,plain,
$false,
inference(mrr,[status(thm)],[5273,1282]),
[iquote('0:MRR:5273.0,1282.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SET230-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n025.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sat Jul 9 22:20:31 EDT 2022
% 0.14/0.34 % CPUTime :
% 1.23/1.43
% 1.23/1.43 SPASS V 3.9
% 1.23/1.43 SPASS beiseite: Proof found.
% 1.23/1.43 % SZS status Theorem
% 1.23/1.43 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.23/1.43 SPASS derived 4452 clauses, backtracked 209 clauses, performed 3 splits and kept 2696 clauses.
% 1.23/1.43 SPASS allocated 80546 KBytes.
% 1.23/1.43 SPASS spent 0:00:01.04 on the problem.
% 1.23/1.43 0:00:00.04 for the input.
% 1.23/1.43 0:00:00.00 for the FLOTTER CNF translation.
% 1.23/1.43 0:00:00.06 for inferences.
% 1.23/1.43 0:00:00.02 for the backtracking.
% 1.23/1.43 0:00:00.87 for the reduction.
% 1.23/1.43
% 1.23/1.43
% 1.23/1.43 Here is a proof with depth 4, length 23 :
% 1.23/1.43 % SZS output start Refutation
% See solution above
% 1.23/1.43 Formulae used in the proof : prove_corollary_to_cross_product_cancellation_1 prove_corollary_to_cross_product_cancellation_2 not_subclass_members1 not_subclass_members2 subclass_implies_equal cartesian_product1 cartesian_product2 cartesian_product3
% 1.23/1.43
%------------------------------------------------------------------------------