%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU417+1 : TPTP v8.1.0. Released v3.4.0.
% 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 : Tue Jul 19 14:37:10 EDT 2022
% Result : Theorem 5.38s 5.57s
% Output : Refutation 5.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of clauses : 35 ( 18 unt; 0 nHn; 35 RR)
% Number of literals : 71 ( 0 equ; 41 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(16,axiom,
m1_subset_1(skc8,k1_zfmisc_1(k1_zfmisc_1(skc6))),
file('SEU417+1.p',unknown),
[] ).
cnf(17,axiom,
m1_subset_1(skc7,k1_zfmisc_1(k1_zfmisc_1(skc6))),
file('SEU417+1.p',unknown),
[] ).
cnf(27,axiom,
equal(k2_xboole_0(u,v),k2_xboole_0(v,u)),
file('SEU417+1.p',unknown),
[] ).
cnf(28,axiom,
equal(k3_xboole_0(u,v),k3_xboole_0(v,u)),
file('SEU417+1.p',unknown),
[] ).
cnf(30,axiom,
r1_tarski(k3_xboole_0(u,v),k2_xboole_0(u,w)),
file('SEU417+1.p',unknown),
[] ).
cnf(45,axiom,
~ r1_tarski(k5_subset_1(skc6,k8_setfam_1(skc6,skc7),k8_setfam_1(skc6,skc8)),k8_setfam_1(skc6,k1_relset_2(skc6,skc7,skc8))),
file('SEU417+1.p',unknown),
[] ).
cnf(46,axiom,
( ~ m1_subset_1(u,k1_zfmisc_1(v))
| ~ m1_subset_1(w,k1_zfmisc_1(v))
| m1_subset_1(k4_subset_1(v,u,w),k1_zfmisc_1(v)) ),
file('SEU417+1.p',unknown),
[] ).
cnf(47,axiom,
( ~ m1_subset_1(u,k1_zfmisc_1(v))
| ~ m1_subset_1(w,k1_zfmisc_1(v))
| m1_subset_1(k5_subset_1(v,u,w),k1_zfmisc_1(v)) ),
file('SEU417+1.p',unknown),
[] ).
cnf(48,axiom,
( ~ m1_subset_1(u,k1_zfmisc_1(v))
| ~ m1_subset_1(w,k1_zfmisc_1(v))
| equal(k4_subset_1(v,w,u),k2_xboole_0(w,u)) ),
file('SEU417+1.p',unknown),
[] ).
cnf(49,axiom,
( ~ m1_subset_1(u,k1_zfmisc_1(v))
| ~ m1_subset_1(w,k1_zfmisc_1(v))
| equal(k5_subset_1(v,w,u),k3_xboole_0(w,u)) ),
file('SEU417+1.p',unknown),
[] ).
cnf(52,axiom,
( ~ m1_subset_1(u,k1_zfmisc_1(k1_zfmisc_1(v)))
| ~ m1_subset_1(w,k1_zfmisc_1(k1_zfmisc_1(v)))
| equal(k1_relset_2(v,w,u),k3_xboole_0(w,u)) ),
file('SEU417+1.p',unknown),
[] ).
cnf(55,axiom,
( ~ r1_tarski(u,v)
| ~ m1_subset_1(v,k1_zfmisc_1(k1_zfmisc_1(w)))
| ~ m1_subset_1(u,k1_zfmisc_1(k1_zfmisc_1(w)))
| r1_tarski(k8_setfam_1(w,v),k8_setfam_1(w,u)) ),
file('SEU417+1.p',unknown),
[] ).
cnf(56,axiom,
( ~ m1_subset_1(u,k1_zfmisc_1(k1_zfmisc_1(v)))
| ~ m1_subset_1(w,k1_zfmisc_1(k1_zfmisc_1(v)))
| ~ m1_subset_1(x,k1_zfmisc_1(k1_zfmisc_1(v)))
| ~ equal(u,k4_subset_1(k1_zfmisc_1(v),w,x))
| equal(k8_setfam_1(v,u),k5_subset_1(v,k8_setfam_1(v,w),k8_setfam_1(v,x))) ),
file('SEU417+1.p',unknown),
[] ).
cnf(57,plain,
( ~ m1_subset_1(u,k1_zfmisc_1(v))
| ~ m1_subset_1(w,k1_zfmisc_1(v))
| m1_subset_1(k3_xboole_0(w,u),k1_zfmisc_1(v)) ),
inference(rew,[status(thm),theory(equality)],[49,47]),
[iquote('0:Rew:49.2,47.2')] ).
cnf(58,plain,
( ~ m1_subset_1(u,k1_zfmisc_1(v))
| ~ m1_subset_1(w,k1_zfmisc_1(v))
| m1_subset_1(k2_xboole_0(w,u),k1_zfmisc_1(v)) ),
inference(rew,[status(thm),theory(equality)],[48,46]),
[iquote('0:Rew:48.2,46.2')] ).
cnf(63,plain,
( ~ m1_subset_1(u,k1_zfmisc_1(k1_zfmisc_1(v)))
| ~ m1_subset_1(w,k1_zfmisc_1(k1_zfmisc_1(v)))
| ~ m1_subset_1(x,k1_zfmisc_1(k1_zfmisc_1(v)))
| ~ equal(x,k2_xboole_0(w,u))
| equal(k8_setfam_1(v,x),k5_subset_1(v,k8_setfam_1(v,w),k8_setfam_1(v,u))) ),
inference(rew,[status(thm),theory(equality)],[48,56]),
[iquote('0:Rew:48.2,56.3')] ).
cnf(65,plain,
( ~ m1_subset_1(u,k1_zfmisc_1(k1_zfmisc_1(skc6)))
| ~ m1_subset_1(v,k1_zfmisc_1(k1_zfmisc_1(skc6)))
| ~ equal(v,k2_xboole_0(skc7,u))
| equal(k8_setfam_1(skc6,v),k5_subset_1(skc6,k8_setfam_1(skc6,skc7),k8_setfam_1(skc6,u))) ),
inference(res,[status(thm),theory(equality)],[17,63]),
[iquote('0:Res:17.0,63.1')] ).
cnf(76,plain,
( ~ m1_subset_1(u,k1_zfmisc_1(k1_zfmisc_1(skc6)))
| m1_subset_1(k2_xboole_0(u,skc7),k1_zfmisc_1(k1_zfmisc_1(skc6))) ),
inference(res,[status(thm),theory(equality)],[17,58]),
[iquote('0:Res:17.0,58.1')] ).
cnf(78,plain,
( ~ m1_subset_1(u,k1_zfmisc_1(k1_zfmisc_1(skc6)))
| m1_subset_1(k3_xboole_0(u,skc7),k1_zfmisc_1(k1_zfmisc_1(skc6))) ),
inference(res,[status(thm),theory(equality)],[17,57]),
[iquote('0:Res:17.0,57.1')] ).
cnf(84,plain,
( ~ m1_subset_1(u,k1_zfmisc_1(k1_zfmisc_1(skc6)))
| equal(k1_relset_2(skc6,skc7,u),k3_xboole_0(skc7,u)) ),
inference(res,[status(thm),theory(equality)],[17,52]),
[iquote('0:Res:17.0,52.0')] ).
cnf(113,plain,
( ~ m1_subset_1(u,k1_zfmisc_1(k1_zfmisc_1(skc6)))
| ~ equal(u,k2_xboole_0(skc7,skc8))
| equal(k8_setfam_1(skc6,u),k5_subset_1(skc6,k8_setfam_1(skc6,skc7),k8_setfam_1(skc6,skc8))) ),
inference(res,[status(thm),theory(equality)],[16,65]),
[iquote('0:Res:16.0,65.1')] ).
cnf(139,plain,
equal(k1_relset_2(skc6,skc7,skc8),k3_xboole_0(skc7,skc8)),
inference(res,[status(thm),theory(equality)],[16,84]),
[iquote('0:Res:16.0,84.0')] ).
cnf(145,plain,
m1_subset_1(k3_xboole_0(skc8,skc7),k1_zfmisc_1(k1_zfmisc_1(skc6))),
inference(res,[status(thm),theory(equality)],[16,78]),
[iquote('0:Res:16.0,78.0')] ).
cnf(146,plain,
m1_subset_1(k2_xboole_0(skc8,skc7),k1_zfmisc_1(k1_zfmisc_1(skc6))),
inference(res,[status(thm),theory(equality)],[16,76]),
[iquote('0:Res:16.0,76.0')] ).
cnf(153,plain,
m1_subset_1(k3_xboole_0(skc7,skc8),k1_zfmisc_1(k1_zfmisc_1(skc6))),
inference(rew,[status(thm),theory(equality)],[28,145]),
[iquote('0:Rew:28.0,145.0')] ).
cnf(154,plain,
m1_subset_1(k2_xboole_0(skc7,skc8),k1_zfmisc_1(k1_zfmisc_1(skc6))),
inference(rew,[status(thm),theory(equality)],[27,146]),
[iquote('0:Rew:27.0,146.0')] ).
cnf(157,plain,
~ r1_tarski(k5_subset_1(skc6,k8_setfam_1(skc6,skc7),k8_setfam_1(skc6,skc8)),k8_setfam_1(skc6,k3_xboole_0(skc7,skc8))),
inference(rew,[status(thm),theory(equality)],[139,45]),
[iquote('0:Rew:139.0,45.0')] ).
cnf(221,plain,
r1_tarski(k3_xboole_0(u,v),k2_xboole_0(w,u)),
inference(spr,[status(thm),theory(equality)],[27,30]),
[iquote('0:SpR:27.0,30.0')] ).
cnf(270,plain,
r1_tarski(k3_xboole_0(u,v),k2_xboole_0(w,v)),
inference(spr,[status(thm),theory(equality)],[28,221]),
[iquote('0:SpR:28.0,221.0')] ).
cnf(18499,plain,
( ~ equal(k2_xboole_0(skc7,skc8),k2_xboole_0(skc7,skc8))
| equal(k5_subset_1(skc6,k8_setfam_1(skc6,skc7),k8_setfam_1(skc6,skc8)),k8_setfam_1(skc6,k2_xboole_0(skc7,skc8))) ),
inference(res,[status(thm),theory(equality)],[154,113]),
[iquote('0:Res:154.0,113.0')] ).
cnf(18500,plain,
equal(k5_subset_1(skc6,k8_setfam_1(skc6,skc7),k8_setfam_1(skc6,skc8)),k8_setfam_1(skc6,k2_xboole_0(skc7,skc8))),
inference(obv,[status(thm),theory(equality)],[18499]),
[iquote('0:Obv:18499.0')] ).
cnf(18607,plain,
~ r1_tarski(k8_setfam_1(skc6,k2_xboole_0(skc7,skc8)),k8_setfam_1(skc6,k3_xboole_0(skc7,skc8))),
inference(rew,[status(thm),theory(equality)],[18500,157]),
[iquote('0:Rew:18500.0,157.0')] ).
cnf(18669,plain,
( ~ r1_tarski(k3_xboole_0(skc7,skc8),k2_xboole_0(skc7,skc8))
| ~ m1_subset_1(k2_xboole_0(skc7,skc8),k1_zfmisc_1(k1_zfmisc_1(skc6)))
| ~ m1_subset_1(k3_xboole_0(skc7,skc8),k1_zfmisc_1(k1_zfmisc_1(skc6))) ),
inference(res,[status(thm),theory(equality)],[55,18607]),
[iquote('0:Res:55.3,18607.0')] ).
cnf(18670,plain,
~ m1_subset_1(k3_xboole_0(skc7,skc8),k1_zfmisc_1(k1_zfmisc_1(skc6))),
inference(mrr,[status(thm)],[18669,270,154]),
[iquote('0:MRR:18669.0,18669.1,270.0,154.0')] ).
cnf(18671,plain,
$false,
inference(mrr,[status(thm)],[18670,153]),
[iquote('0:MRR:18670.0,153.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU417+1 : TPTP v8.1.0. Released v3.4.0.
% 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 : Sun Jun 19 20:52:58 EDT 2022
% 0.11/0.33 % CPUTime :
% 5.38/5.57
% 5.38/5.57 SPASS V 3.9
% 5.38/5.57 SPASS beiseite: Proof found.
% 5.38/5.57 % SZS status Theorem
% 5.38/5.57 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.38/5.57 SPASS derived 15003 clauses, backtracked 1784 clauses, performed 20 splits and kept 6080 clauses.
% 5.38/5.57 SPASS allocated 111441 KBytes.
% 5.38/5.57 SPASS spent 0:00:05.11 on the problem.
% 5.38/5.57 0:00:00.04 for the input.
% 5.38/5.57 0:00:00.03 for the FLOTTER CNF translation.
% 5.38/5.57 0:00:00.23 for inferences.
% 5.38/5.57 0:00:00.14 for the backtracking.
% 5.38/5.57 0:00:04.55 for the reduction.
% 5.38/5.57
% 5.38/5.57
% 5.38/5.57 Here is a proof with depth 3, length 35 :
% 5.38/5.57 % SZS output start Refutation
% See solution above
% 5.38/5.57 Formulae used in the proof : t7_relset_2 commutativity_k2_xboole_0 commutativity_k3_xboole_0 t29_xboole_1 dt_k4_subset_1 dt_k5_subset_1 redefinition_k4_subset_1 redefinition_k5_subset_1 redefinition_k1_relset_2 t59_setfam_1 t8_mssubfam
% 5.38/5.57
%------------------------------------------------------------------------------