TSTP Solution File: SEU430+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU430+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.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 14:37:23 EDT 2022
% Result : Theorem 0.20s 0.51s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 16
% Syntax : Number of clauses : 49 ( 20 unt; 6 nHn; 49 RR)
% Number of literals : 88 ( 0 equ; 45 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
v1_xboole_0(k1_xboole_0),
file('SEU430+1.p',unknown),
[] ).
cnf(12,axiom,
v1_xboole_0(skf14(u)),
file('SEU430+1.p',unknown),
[] ).
cnf(16,axiom,
m1_subset_1(skc7,k1_zfmisc_1(k1_zfmisc_1(skc6))),
file('SEU430+1.p',unknown),
[] ).
cnf(18,axiom,
r2_hidden(u,skf8(v,u)),
file('SEU430+1.p',unknown),
[] ).
cnf(20,axiom,
m1_subset_1(skf14(u),k1_zfmisc_1(u)),
file('SEU430+1.p',unknown),
[] ).
cnf(22,axiom,
( ~ v1_xboole_0(u)
| equal(u,k1_xboole_0) ),
file('SEU430+1.p',unknown),
[] ).
cnf(23,axiom,
( equal(u,k1_xboole_0)
| r2_hidden(skf7(u),u) ),
file('SEU430+1.p',unknown),
[] ).
cnf(27,axiom,
( ~ r2_hidden(u,v)
| ~ equal(v,k1_xboole_0) ),
file('SEU430+1.p',unknown),
[] ).
cnf(30,axiom,
( ~ equal(k5_setfam_1(skc6,skc7),k1_xboole_0)
| r2_hidden(skc8,skc7) ),
file('SEU430+1.p',unknown),
[] ).
cnf(33,axiom,
( ~ equal(skc8,k1_xboole_0)
| ~ equal(k5_setfam_1(skc6,skc7),k1_xboole_0) ),
file('SEU430+1.p',unknown),
[] ).
cnf(34,axiom,
( ~ r2_hidden(u,skc7)
| equal(k5_setfam_1(skc6,skc7),k1_xboole_0)
| equal(u,k1_xboole_0) ),
file('SEU430+1.p',unknown),
[] ).
cnf(36,axiom,
( ~ m1_subset_1(u,k1_zfmisc_1(k1_zfmisc_1(v)))
| equal(k5_setfam_1(v,u),k3_tarski(u)) ),
file('SEU430+1.p',unknown),
[] ).
cnf(38,axiom,
( ~ v1_xboole_0(u)
| ~ r2_hidden(v,w)
| ~ m1_subset_1(w,k1_zfmisc_1(u)) ),
file('SEU430+1.p',unknown),
[] ).
cnf(39,axiom,
( ~ r2_hidden(u,v)
| ~ equal(v,k3_tarski(w))
| r2_hidden(skf8(w,u),w) ),
file('SEU430+1.p',unknown),
[] ).
cnf(40,axiom,
( equal(u,k3_tarski(v))
| r2_hidden(skf10(v,u),u)
| r2_hidden(skf11(v,w),v) ),
file('SEU430+1.p',unknown),
[] ).
cnf(41,axiom,
( ~ r2_hidden(u,v)
| ~ r2_hidden(w,u)
| ~ equal(x,k3_tarski(v))
| r2_hidden(w,x) ),
file('SEU430+1.p',unknown),
[] ).
cnf(50,plain,
equal(k5_setfam_1(skc6,skc7),k3_tarski(skc7)),
inference(res,[status(thm),theory(equality)],[16,36]),
[iquote('0:Res:16.0,36.0')] ).
cnf(51,plain,
( ~ r2_hidden(u,skc7)
| equal(u,k1_xboole_0)
| equal(k3_tarski(skc7),k1_xboole_0) ),
inference(rew,[status(thm),theory(equality)],[50,34]),
[iquote('0:Rew:50.0,34.1')] ).
cnf(52,plain,
( ~ equal(skc8,k1_xboole_0)
| ~ equal(k3_tarski(skc7),k1_xboole_0) ),
inference(rew,[status(thm),theory(equality)],[50,33]),
[iquote('0:Rew:50.0,33.1')] ).
cnf(53,plain,
( ~ equal(k3_tarski(skc7),k1_xboole_0)
| r2_hidden(skc8,skc7) ),
inference(rew,[status(thm),theory(equality)],[50,30]),
[iquote('0:Rew:50.0,30.0')] ).
cnf(55,plain,
equal(k3_tarski(skc7),k1_xboole_0),
inference(spt,[spt(split,[position(s1)])],[51]),
[iquote('1:Spt:51.2')] ).
cnf(56,plain,
( ~ equal(skc8,k1_xboole_0)
| ~ equal(k1_xboole_0,k1_xboole_0) ),
inference(rew,[status(thm),theory(equality)],[55,52]),
[iquote('1:Rew:55.0,52.1')] ).
cnf(57,plain,
( ~ equal(k1_xboole_0,k1_xboole_0)
| r2_hidden(skc8,skc7) ),
inference(rew,[status(thm),theory(equality)],[55,53]),
[iquote('1:Rew:55.0,53.0')] ).
cnf(60,plain,
r2_hidden(skc8,skc7),
inference(obv,[status(thm),theory(equality)],[57]),
[iquote('1:Obv:57.0')] ).
cnf(61,plain,
~ equal(skc8,k1_xboole_0),
inference(obv,[status(thm),theory(equality)],[56]),
[iquote('1:Obv:56.1')] ).
cnf(64,plain,
equal(skf14(u),k1_xboole_0),
inference(ems,[status(thm)],[22,12]),
[iquote('0:EmS:22.0,12.0')] ).
cnf(70,plain,
m1_subset_1(k1_xboole_0,k1_zfmisc_1(u)),
inference(rew,[status(thm),theory(equality)],[64,20]),
[iquote('0:Rew:64.0,20.0')] ).
cnf(83,plain,
~ equal(skf8(u,v),k1_xboole_0),
inference(res,[status(thm),theory(equality)],[18,27]),
[iquote('0:Res:18.0,27.0')] ).
cnf(137,plain,
( ~ v1_xboole_0(u)
| ~ r2_hidden(v,k1_xboole_0) ),
inference(res,[status(thm),theory(equality)],[70,38]),
[iquote('0:Res:70.0,38.2')] ).
cnf(166,plain,
~ r2_hidden(u,k1_xboole_0),
inference(ems,[status(thm)],[137,4]),
[iquote('0:EmS:137.0,4.0')] ).
cnf(174,plain,
( ~ r2_hidden(u,k3_tarski(v))
| r2_hidden(skf8(v,u),v) ),
inference(eqr,[status(thm),theory(equality)],[39]),
[iquote('0:EqR:39.1')] ).
cnf(198,plain,
( ~ equal(u,k1_xboole_0)
| equal(v,k3_tarski(u))
| r2_hidden(skf10(u,v),v) ),
inference(res,[status(thm),theory(equality)],[40,27]),
[iquote('0:Res:40.2,27.0')] ).
cnf(223,plain,
( ~ r2_hidden(u,v)
| ~ r2_hidden(w,u)
| r2_hidden(w,k3_tarski(v)) ),
inference(eqr,[status(thm),theory(equality)],[41]),
[iquote('0:EqR:41.2')] ).
cnf(350,plain,
( ~ r2_hidden(u,k3_tarski(v))
| ~ equal(v,k1_xboole_0) ),
inference(res,[status(thm),theory(equality)],[174,27]),
[iquote('0:Res:174.1,27.0')] ).
cnf(418,plain,
( ~ equal(u,k1_xboole_0)
| equal(k3_tarski(u),k1_xboole_0) ),
inference(res,[status(thm),theory(equality)],[23,350]),
[iquote('0:Res:23.1,350.0')] ).
cnf(425,plain,
( ~ equal(u,k1_xboole_0)
| equal(v,k1_xboole_0)
| r2_hidden(skf10(u,v),v) ),
inference(rew,[status(thm),theory(equality)],[418,198]),
[iquote('0:Rew:418.1,198.1')] ).
cnf(700,plain,
( ~ r2_hidden(u,skc8)
| r2_hidden(u,k3_tarski(skc7)) ),
inference(res,[status(thm),theory(equality)],[60,223]),
[iquote('1:Res:60.0,223.0')] ).
cnf(713,plain,
( ~ r2_hidden(u,skc8)
| r2_hidden(u,k1_xboole_0) ),
inference(rew,[status(thm),theory(equality)],[55,700]),
[iquote('1:Rew:55.0,700.1')] ).
cnf(714,plain,
~ r2_hidden(u,skc8),
inference(mrr,[status(thm)],[713,166]),
[iquote('1:MRR:713.1,166.0')] ).
cnf(727,plain,
( ~ equal(u,k1_xboole_0)
| equal(skc8,k1_xboole_0) ),
inference(res,[status(thm),theory(equality)],[425,714]),
[iquote('1:Res:425.2,714.0')] ).
cnf(733,plain,
equal(skc8,k1_xboole_0),
inference(aed,[status(thm),theory(equality)],[727]),
[iquote('1:AED:727.0')] ).
cnf(734,plain,
$false,
inference(mrr,[status(thm)],[733,61]),
[iquote('1:MRR:733.0,61.0')] ).
cnf(735,plain,
~ equal(k3_tarski(skc7),k1_xboole_0),
inference(spt,[spt(split,[position(sa)])],[734,55]),
[iquote('1:Spt:734.0,51.2,55.0')] ).
cnf(736,plain,
( ~ r2_hidden(u,skc7)
| equal(u,k1_xboole_0) ),
inference(spt,[spt(split,[position(s2)])],[51]),
[iquote('1:Spt:734.0,51.0,51.1')] ).
cnf(740,plain,
( ~ r2_hidden(u,k3_tarski(skc7))
| equal(skf8(skc7,u),k1_xboole_0) ),
inference(res,[status(thm),theory(equality)],[174,736]),
[iquote('1:Res:174.1,736.0')] ).
cnf(746,plain,
~ r2_hidden(u,k3_tarski(skc7)),
inference(mrr,[status(thm)],[740,83]),
[iquote('1:MRR:740.1,83.0')] ).
cnf(807,plain,
( ~ equal(u,k1_xboole_0)
| equal(k3_tarski(skc7),k1_xboole_0) ),
inference(res,[status(thm),theory(equality)],[425,746]),
[iquote('1:Res:425.2,746.0')] ).
cnf(813,plain,
equal(k3_tarski(skc7),k1_xboole_0),
inference(aed,[status(thm),theory(equality)],[807]),
[iquote('1:AED:807.0')] ).
cnf(814,plain,
$false,
inference(mrr,[status(thm)],[813,735]),
[iquote('1:MRR:813.0,735.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU430+1 : TPTP v8.1.0. Released v3.4.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n011.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 : Mon Jun 20 12:47:54 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.20/0.51
% 0.20/0.51 SPASS V 3.9
% 0.20/0.51 SPASS beiseite: Proof found.
% 0.20/0.51 % SZS status Theorem
% 0.20/0.51 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.51 SPASS derived 625 clauses, backtracked 21 clauses, performed 2 splits and kept 356 clauses.
% 0.20/0.51 SPASS allocated 98204 KBytes.
% 0.20/0.51 SPASS spent 0:00:00.16 on the problem.
% 0.20/0.51 0:00:00.04 for the input.
% 0.20/0.51 0:00:00.04 for the FLOTTER CNF translation.
% 0.20/0.51 0:00:00.01 for inferences.
% 0.20/0.51 0:00:00.00 for the backtracking.
% 0.20/0.51 0:00:00.05 for the reduction.
% 0.20/0.51
% 0.20/0.51
% 0.20/0.51 Here is a proof with depth 3, length 49 :
% 0.20/0.51 % SZS output start Refutation
% See solution above
% 0.20/0.51 Formulae used in the proof : fc4_relat_1 rc2_subset_1 t30_relset_2 d4_tarski reflexivity_r1_tarski t3_subset t2_subset fc1_subset_1 t6_boole d1_xboole_0 redefinition_k5_setfam_1 t5_subset
% 0.20/0.51
%------------------------------------------------------------------------------