TSTP Solution File: GEO084-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GEO084-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 : Sat Jul 16 06:22:11 EDT 2022
% Result : Unsatisfiable 43.83s 44.06s
% Output : Refutation 43.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of clauses : 32 ( 6 unt; 14 nHn; 32 RR)
% Number of literals : 73 ( 0 equ; 22 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 : 10 ( 10 usr; 7 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
part_of(sk14,sk16),
file('GEO084-1.p',unknown),
[] ).
cnf(2,axiom,
part_of(sk15,sk16),
file('GEO084-1.p',unknown),
[] ).
cnf(4,axiom,
~ part_of(sum__dfg(sk14,sk15),sk16),
file('GEO084-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ incident_c(u,v)
| ~ part_of(v,w)
| incident_c(u,w) ),
file('GEO084-1.p',unknown),
[] ).
cnf(6,axiom,
( part_of(u,v)
| incident_c(ax0_sk1(u,v),u) ),
file('GEO084-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ incident_c(ax0_sk1(u,v),v)
| part_of(u,v) ),
file('GEO084-1.p',unknown),
[] ).
cnf(8,axiom,
( ~ incident_c(u,v)
| ~ equal(v,sum__dfg(w,x))
| incident_c(u,x)
| incident_c(u,w) ),
file('GEO084-1.p',unknown),
[] ).
cnf(10,axiom,
( ~ incident_c(u,v)
| ~ equal(w,sum__dfg(x,v))
| incident_c(u,w) ),
file('GEO084-1.p',unknown),
[] ).
cnf(11,axiom,
( equal(u,sum__dfg(v,w))
| incident_c(ax0_sk2(w,v,u),w)
| incident_c(ax0_sk2(w,v,u),v)
| incident_c(ax0_sk2(w,v,u),u) ),
file('GEO084-1.p',unknown),
[] ).
cnf(15,axiom,
( ~ incident_c(ax0_sk2(u,v,w),w)
| ~ incident_c(ax0_sk2(u,v,w),v)
| equal(w,sum__dfg(v,u)) ),
file('GEO084-1.p',unknown),
[] ).
cnf(54,plain,
( ~ incident_c(u,sk15)
| incident_c(u,sk16) ),
inference(res,[status(thm),theory(equality)],[2,5]),
[iquote('0:Res:2.0,5.0')] ).
cnf(61,plain,
( ~ incident_c(u,sk14)
| incident_c(u,sk16) ),
inference(res,[status(thm),theory(equality)],[1,5]),
[iquote('0:Res:1.0,5.0')] ).
cnf(271,plain,
( ~ incident_c(ax0_sk1(u,sk16),sk14)
| part_of(u,sk16) ),
inference(res,[status(thm),theory(equality)],[61,7]),
[iquote('0:Res:61.1,7.0')] ).
cnf(400,plain,
( ~ incident_c(u,v)
| incident_c(u,sum__dfg(w,v)) ),
inference(eqr,[status(thm),theory(equality)],[10]),
[iquote('0:EqR:10.1')] ).
cnf(404,plain,
( ~ incident_c(ax0_sk1(u,sum__dfg(v,w)),w)
| part_of(u,sum__dfg(v,w)) ),
inference(res,[status(thm),theory(equality)],[400,7]),
[iquote('0:Res:400.1,7.0')] ).
cnf(477,plain,
( ~ incident_c(u,sum__dfg(v,w))
| incident_c(u,w)
| incident_c(u,v) ),
inference(eqr,[status(thm),theory(equality)],[8]),
[iquote('0:EqR:8.1')] ).
cnf(571,plain,
( part_of(sum__dfg(u,v),w)
| incident_c(ax0_sk1(sum__dfg(u,v),w),v)
| incident_c(ax0_sk1(sum__dfg(u,v),w),u) ),
inference(res,[status(thm),theory(equality)],[6,477]),
[iquote('0:Res:6.1,477.0')] ).
cnf(649,plain,
( equal(sum__dfg(u,v),u)
| incident_c(ax0_sk2(v,u,u),v)
| incident_c(ax0_sk2(v,u,u),u) ),
inference(fac,[status(thm)],[11]),
[iquote('0:Fac:11.2,11.3')] ).
cnf(1477,plain,
( ~ incident_c(ax0_sk2(u,v,v),v)
| equal(sum__dfg(v,u),v)
| incident_c(ax0_sk2(u,v,v),u)
| equal(sum__dfg(v,u),v) ),
inference(res,[status(thm),theory(equality)],[649,15]),
[iquote('0:Res:649.2,15.0')] ).
cnf(1481,plain,
( ~ incident_c(ax0_sk2(u,v,v),v)
| incident_c(ax0_sk2(u,v,v),u)
| equal(sum__dfg(v,u),v) ),
inference(obv,[status(thm),theory(equality)],[1477]),
[iquote('0:Obv:1477.1')] ).
cnf(1482,plain,
( incident_c(ax0_sk2(u,v,v),u)
| equal(sum__dfg(v,u),v) ),
inference(mrr,[status(thm)],[1481,649]),
[iquote('0:MRR:1481.0,649.2')] ).
cnf(2277,plain,
( equal(sum__dfg(u,sk15),u)
| incident_c(ax0_sk2(sk15,u,u),sk16) ),
inference(res,[status(thm),theory(equality)],[1482,54]),
[iquote('0:Res:1482.0,54.0')] ).
cnf(2290,plain,
( ~ incident_c(ax0_sk2(sk15,sk16,sk16),sk16)
| equal(sum__dfg(sk16,sk15),sk16)
| equal(sum__dfg(sk16,sk15),sk16) ),
inference(res,[status(thm),theory(equality)],[2277,15]),
[iquote('0:Res:2277.1,15.0')] ).
cnf(2292,plain,
( ~ incident_c(ax0_sk2(sk15,sk16,sk16),sk16)
| equal(sum__dfg(sk16,sk15),sk16) ),
inference(obv,[status(thm),theory(equality)],[2290]),
[iquote('0:Obv:2290.1')] ).
cnf(2293,plain,
equal(sum__dfg(sk16,sk15),sk16),
inference(mrr,[status(thm)],[2292,2277]),
[iquote('0:MRR:2292.0,2277.1')] ).
cnf(3683,plain,
( ~ incident_c(ax0_sk1(u,sk16),sk15)
| part_of(u,sum__dfg(sk16,sk15)) ),
inference(spl,[status(thm),theory(equality)],[2293,404]),
[iquote('0:SpL:2293.0,404.0')] ).
cnf(3702,plain,
( ~ incident_c(ax0_sk1(u,sk16),sk15)
| part_of(u,sk16) ),
inference(rew,[status(thm),theory(equality)],[2293,3683]),
[iquote('0:Rew:2293.0,3683.1')] ).
cnf(7601,plain,
( part_of(sum__dfg(u,sk15),sk16)
| incident_c(ax0_sk1(sum__dfg(u,sk15),sk16),u)
| part_of(sum__dfg(u,sk15),sk16) ),
inference(res,[status(thm),theory(equality)],[571,3702]),
[iquote('0:Res:571.1,3702.0')] ).
cnf(7638,plain,
( incident_c(ax0_sk1(sum__dfg(u,sk15),sk16),u)
| part_of(sum__dfg(u,sk15),sk16) ),
inference(obv,[status(thm),theory(equality)],[7601]),
[iquote('0:Obv:7601.0')] ).
cnf(32004,plain,
( part_of(sum__dfg(sk14,sk15),sk16)
| part_of(sum__dfg(sk14,sk15),sk16) ),
inference(res,[status(thm),theory(equality)],[7638,271]),
[iquote('0:Res:7638.0,271.0')] ).
cnf(32017,plain,
part_of(sum__dfg(sk14,sk15),sk16),
inference(obv,[status(thm),theory(equality)],[32004]),
[iquote('0:Obv:32004.0')] ).
cnf(32018,plain,
$false,
inference(mrr,[status(thm)],[32017,4]),
[iquote('0:MRR:32017.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GEO084-1 : TPTP v8.1.0. Released v2.4.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.11/0.33 % Computer : n017.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Fri Jun 17 21:52:12 EDT 2022
% 0.11/0.33 % CPUTime :
% 43.83/44.06
% 43.83/44.06 SPASS V 3.9
% 43.83/44.06 SPASS beiseite: Proof found.
% 43.83/44.06 % SZS status Theorem
% 43.83/44.06 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 43.83/44.06 SPASS derived 28908 clauses, backtracked 158 clauses, performed 34 splits and kept 11974 clauses.
% 43.83/44.06 SPASS allocated 104396 KBytes.
% 43.83/44.06 SPASS spent 0:0:43.18 on the problem.
% 43.83/44.06 0:00:00.04 for the input.
% 43.83/44.06 0:00:00.00 for the FLOTTER CNF translation.
% 43.83/44.06 0:00:00.42 for inferences.
% 43.83/44.06 0:00:01.80 for the backtracking.
% 43.83/44.06 0:0:40.71 for the reduction.
% 43.83/44.06
% 43.83/44.06
% 43.83/44.06 Here is a proof with depth 7, length 32 :
% 43.83/44.06 % SZS output start Refutation
% See solution above
% 43.83/44.06 Formulae used in the proof : corollary_2_6_2_67 corollary_2_6_2_68 corollary_2_6_2_70 part_of_defn_1 part_of_defn_2 part_of_defn_3 sum_defn_4 sum_defn_6 sum_defn_7 sum_defn_11
% 43.83/44.06
%------------------------------------------------------------------------------