TSTP Solution File: SEU156+3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU156+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.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 14:34:27 EDT 2022
% Result : Theorem 7.97s 8.16s
% Output : Refutation 8.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU156+3 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n009.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jun 19 01:43:07 EDT 2022
% 0.12/0.34 % CPUTime :
% 7.97/8.16
% 7.97/8.16 SPASS V 3.9
% 7.97/8.16 SPASS beiseite: Proof found.
% 7.97/8.16 % SZS status Theorem
% 7.97/8.16 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.97/8.16 SPASS derived 4223 clauses, backtracked 577 clauses, performed 2 splits and kept 2194 clauses.
% 7.97/8.16 SPASS allocated 91666 KBytes.
% 7.97/8.16 SPASS spent 0:00:07.81 on the problem.
% 7.97/8.16 0:00:00.03 for the input.
% 7.97/8.16 0:00:00.02 for the FLOTTER CNF translation.
% 7.97/8.16 0:00:00.06 for inferences.
% 7.97/8.16 0:00:00.02 for the backtracking.
% 7.97/8.16 0:00:07.64 for the reduction.
% 7.97/8.16
% 7.97/8.16
% 7.97/8.16 Here is a proof with depth 9, length 87 :
% 7.97/8.16 % SZS output start Refutation
% 7.97/8.16 3[0:Inp] || -> subset(u,u)*.
% 7.97/8.16 5[0:Inp] || -> equal(unordered_pair(u,u),singleton(u))**.
% 7.97/8.16 6[0:Inp] || -> equal(ordered_pair(skc8,skc9),ordered_pair(skc6,skc7))**.
% 7.97/8.16 7[0:Inp] || -> equal(unordered_pair(u,v),unordered_pair(v,u))*.
% 7.97/8.16 8[0:Inp] || equal(skc9,skc7)** equal(skc8,skc6) -> .
% 7.97/8.16 9[0:Inp] || subset(singleton(u),singleton(v))* -> equal(u,v).
% 7.97/8.16 10[0:Inp] || -> equal(unordered_pair(unordered_pair(u,v),singleton(u)),ordered_pair(u,v))**.
% 7.97/8.16 12[0:Inp] || equal(singleton(u),unordered_pair(v,w))* -> equal(v,w).
% 7.97/8.16 13[0:Inp] || equal(unordered_pair(u,v),unordered_pair(w,x))* -> equal(u,x) equal(u,w).
% 7.97/8.16 14[0:Rew:7.0,10.0] || -> equal(unordered_pair(singleton(u),unordered_pair(u,v)),ordered_pair(u,v))**.
% 7.97/8.16 25[0:SpR:14.0,14.0] || -> equal(unordered_pair(singleton(singleton(u)),ordered_pair(u,v)),ordered_pair(singleton(u),unordered_pair(u,v)))**.
% 7.97/8.16 27[0:SpR:5.0,14.0] || -> equal(unordered_pair(singleton(u),singleton(u)),ordered_pair(u,u))**.
% 7.97/8.16 28[0:SpR:7.0,14.0] || -> equal(unordered_pair(singleton(u),unordered_pair(v,u)),ordered_pair(u,v))**.
% 7.97/8.16 30[0:Rew:5.0,27.0] || -> equal(ordered_pair(u,u),singleton(singleton(u)))**.
% 7.97/8.16 36[0:SpL:14.0,12.0] || equal(singleton(u),ordered_pair(v,w))*+ -> equal(unordered_pair(v,w),singleton(v))**.
% 7.97/8.16 43[0:SpL:7.0,13.0] || equal(unordered_pair(u,v),unordered_pair(w,x))* -> equal(v,x) equal(v,w).
% 7.97/8.16 45[0:SpL:14.0,13.0] || equal(ordered_pair(u,v),unordered_pair(w,x))* -> equal(singleton(u),x) equal(singleton(u),w).
% 7.97/8.16 53[0:SpR:28.0,14.0] || -> equal(unordered_pair(singleton(singleton(u)),ordered_pair(u,v)),ordered_pair(singleton(u),unordered_pair(v,u)))**.
% 7.97/8.16 65[0:Rew:25.0,53.0] || -> equal(ordered_pair(singleton(u),unordered_pair(u,v)),ordered_pair(singleton(u),unordered_pair(v,u)))*.
% 7.97/8.16 78[0:SpL:6.0,36.0] || equal(singleton(u),ordered_pair(skc6,skc7))* -> equal(unordered_pair(skc8,skc9),singleton(skc8))**.
% 7.97/8.16 110[0:SpR:6.0,25.0] || -> equal(unordered_pair(singleton(singleton(skc8)),ordered_pair(skc6,skc7)),ordered_pair(singleton(skc8),unordered_pair(skc8,skc9)))**.
% 7.97/8.16 144[0:SpL:14.0,43.0] || equal(unordered_pair(u,v),ordered_pair(w,x))*+ -> equal(v,unordered_pair(w,x))* equal(v,singleton(w)).
% 7.97/8.16 201[0:SpL:14.0,45.0] || equal(ordered_pair(u,v),ordered_pair(w,x))*+ -> equal(singleton(u),unordered_pair(w,x))* equal(singleton(u),singleton(w)).
% 7.97/8.16 204[0:SpL:110.0,45.0] || equal(ordered_pair(u,v),ordered_pair(singleton(skc8),unordered_pair(skc8,skc9)))* -> equal(singleton(u),ordered_pair(skc6,skc7)) equal(singleton(u),singleton(singleton(skc8))).
% 7.97/8.16 329[0:SpL:28.0,144.0] || equal(ordered_pair(u,v),ordered_pair(w,x)) -> equal(unordered_pair(v,u),unordered_pair(w,x))* equal(unordered_pair(v,u),singleton(w)).
% 7.97/8.16 579[0:SpL:6.0,201.0] || equal(ordered_pair(u,v),ordered_pair(skc6,skc7))* -> equal(singleton(u),unordered_pair(skc8,skc9))* equal(singleton(u),singleton(skc8)).
% 7.97/8.16 581[0:SpL:65.0,201.0] || equal(ordered_pair(u,v),ordered_pair(singleton(w),unordered_pair(x,w)))* -> equal(singleton(u),unordered_pair(singleton(w),unordered_pair(w,x)))* equal(singleton(u),singleton(singleton(w))).
% 7.97/8.16 582[0:Rew:14.0,581.1] || equal(ordered_pair(u,v),ordered_pair(singleton(w),unordered_pair(x,w)))* -> equal(singleton(u),ordered_pair(w,x)) equal(singleton(u),singleton(singleton(w))).
% 7.97/8.16 584[0:EqR:579.0] || -> equal(unordered_pair(skc8,skc9),singleton(skc6))** equal(singleton(skc8),singleton(skc6)).
% 7.97/8.16 589[1:Spt:584.1] || -> equal(singleton(skc8),singleton(skc6))**.
% 7.97/8.16 689[1:SpL:589.0,9.0] || subset(singleton(skc6),singleton(u))* -> equal(skc8,u).
% 7.97/8.16 705[1:Res:3.0,689.0] || -> equal(skc8,skc6)**.
% 7.97/8.16 706[1:Rew:705.0,6.0] || -> equal(ordered_pair(skc6,skc9),ordered_pair(skc6,skc7))**.
% 7.97/8.16 707[1:Rew:705.0,8.1] || equal(skc9,skc7)** equal(skc6,skc6) -> .
% 7.97/8.16 746[1:Obv:707.1] || equal(skc9,skc7)** -> .
% 7.97/8.16 1371[0:EqF:329.1,329.2] || equal(ordered_pair(u,v),ordered_pair(w,x))*+ equal(unordered_pair(w,x),singleton(w))** -> equal(unordered_pair(v,u),singleton(w))*.
% 7.97/8.16 1380[0:SpR:329.1,7.0] || equal(ordered_pair(u,v),ordered_pair(w,x))+ -> equal(unordered_pair(v,u),singleton(w))* equal(unordered_pair(w,x),unordered_pair(u,v))*.
% 7.97/8.16 1535[1:SpL:706.0,1371.0] || equal(ordered_pair(skc6,skc7),ordered_pair(u,v)) equal(unordered_pair(u,v),singleton(u))** -> equal(unordered_pair(skc9,skc6),singleton(u))*.
% 7.97/8.16 1543[1:Rew:7.0,1535.2] || equal(ordered_pair(skc6,skc7),ordered_pair(u,v)) equal(unordered_pair(u,v),singleton(u))** -> equal(unordered_pair(skc6,skc9),singleton(u))*.
% 7.97/8.16 1774[1:EqR:1543.0] || equal(unordered_pair(skc6,skc7),singleton(skc6)) -> equal(unordered_pair(skc6,skc9),singleton(skc6))**.
% 7.97/8.16 1817[1:SpL:1774.1,12.0] || equal(unordered_pair(skc6,skc7),singleton(skc6))**+ equal(singleton(u),singleton(skc6))* -> equal(skc9,skc6).
% 7.97/8.16 2951[1:SpL:706.0,1380.0] || equal(ordered_pair(u,v),ordered_pair(skc6,skc7)) -> equal(unordered_pair(v,u),singleton(skc6))** equal(unordered_pair(skc6,skc9),unordered_pair(u,v))*.
% 7.97/8.16 3334[1:EqR:2951.0] || -> equal(unordered_pair(skc7,skc6),singleton(skc6))** equal(unordered_pair(skc6,skc9),unordered_pair(skc6,skc7)).
% 7.97/8.16 3341[1:Rew:7.0,3334.0] || -> equal(unordered_pair(skc6,skc7),singleton(skc6)) equal(unordered_pair(skc6,skc9),unordered_pair(skc6,skc7))**.
% 7.97/8.16 3426[2:Spt:3341.0] || -> equal(unordered_pair(skc6,skc7),singleton(skc6))**.
% 7.97/8.16 3439[2:Rew:3426.0,1817.0] || equal(singleton(skc6),singleton(skc6))* equal(singleton(u),singleton(skc6))* -> equal(skc9,skc6).
% 7.97/8.16 3922[2:Obv:3439.0] || equal(singleton(u),singleton(skc6))* -> equal(skc9,skc6).
% 7.97/8.16 4663[2:SpL:3426.0,12.0] || equal(singleton(u),singleton(skc6))* -> equal(skc7,skc6).
% 7.97/8.16 5103[2:EqR:3922.0] || -> equal(skc9,skc6)**.
% 7.97/8.16 5104[2:Rew:5103.0,746.0] || equal(skc7,skc6)** -> .
% 7.97/8.16 5204[2:MRR:4663.1,5104.0] || equal(singleton(u),singleton(skc6))* -> .
% 7.97/8.16 5206[2:Obv:5204.0] || -> .
% 7.97/8.16 5463[2:Spt:5206.0,3341.0,3426.0] || equal(unordered_pair(skc6,skc7),singleton(skc6))** -> .
% 7.97/8.16 5464[2:Spt:5206.0,3341.1] || -> equal(unordered_pair(skc6,skc9),unordered_pair(skc6,skc7))**.
% 7.97/8.16 5796[2:SpR:5464.0,28.0] || -> equal(unordered_pair(singleton(skc9),unordered_pair(skc6,skc7)),ordered_pair(skc9,skc6))**.
% 7.97/8.16 5814[2:SpL:5464.0,43.0] || equal(unordered_pair(skc6,skc7),unordered_pair(u,v))* -> equal(skc9,v) equal(skc9,u).
% 7.97/8.16 5983[2:SpL:5796.0,12.0] || equal(singleton(u),ordered_pair(skc9,skc6))*+ -> equal(unordered_pair(skc6,skc7),singleton(skc9))**.
% 7.97/8.16 6064[2:SpL:5464.0,582.0] || equal(ordered_pair(u,v),ordered_pair(singleton(skc9),unordered_pair(skc6,skc7)))* -> equal(singleton(u),ordered_pair(skc9,skc6)) equal(singleton(u),singleton(singleton(skc9))).
% 7.97/8.16 6069[2:EqR:5814.0] || -> equal(skc9,skc7)** equal(skc9,skc6).
% 7.97/8.16 6100[2:MRR:6069.0,746.0] || -> equal(skc9,skc6)**.
% 7.97/8.16 6104[2:Rew:6100.0,5983.0] || equal(singleton(u),ordered_pair(skc6,skc6))* -> equal(unordered_pair(skc6,skc7),singleton(skc9))**.
% 7.97/8.16 6203[2:Rew:6100.0,6064.1] || equal(ordered_pair(u,v),ordered_pair(singleton(skc9),unordered_pair(skc6,skc7)))* -> equal(singleton(u),ordered_pair(skc6,skc6)) equal(singleton(u),singleton(singleton(skc9))).
% 7.97/8.16 6291[2:Rew:30.0,6104.0] || equal(singleton(u),singleton(singleton(skc6)))* -> equal(unordered_pair(skc6,skc7),singleton(skc9))**.
% 7.97/8.16 6292[2:Rew:6100.0,6291.1] || equal(singleton(u),singleton(singleton(skc6)))* -> equal(unordered_pair(skc6,skc7),singleton(skc6))**.
% 7.97/8.16 6293[2:MRR:6292.1,5463.0] || equal(singleton(u),singleton(singleton(skc6)))* -> .
% 7.97/8.16 6367[2:Rew:30.0,6203.1] || equal(ordered_pair(u,v),ordered_pair(singleton(skc9),unordered_pair(skc6,skc7)))* -> equal(singleton(u),singleton(singleton(skc6))) equal(singleton(u),singleton(singleton(skc9))).
% 7.97/8.16 6368[2:Rew:6100.0,6367.2,6100.0,6367.0] || equal(ordered_pair(u,v),ordered_pair(singleton(skc6),unordered_pair(skc6,skc7)))* -> equal(singleton(u),singleton(singleton(skc6))) equal(singleton(u),singleton(singleton(skc6))).
% 7.97/8.16 6369[2:Obv:6368.1] || equal(ordered_pair(u,v),ordered_pair(singleton(skc6),unordered_pair(skc6,skc7)))* -> equal(singleton(u),singleton(singleton(skc6))).
% 8.02/8.19 6370[2:MRR:6369.1,6293.0] || equal(ordered_pair(u,v),ordered_pair(singleton(skc6),unordered_pair(skc6,skc7)))* -> .
% 8.02/8.19 6371[2:UnC:6370.0,65.0] || -> .
% 8.02/8.19 6617[1:Spt:6371.0,584.1,589.0] || equal(singleton(skc8),singleton(skc6))** -> .
% 8.02/8.19 6618[1:Spt:6371.0,584.0] || -> equal(unordered_pair(skc8,skc9),singleton(skc6))**.
% 8.02/8.19 6619[1:Rew:6618.0,78.1] || equal(singleton(u),ordered_pair(skc6,skc7))* -> equal(singleton(skc8),singleton(skc6)).
% 8.02/8.19 6620[1:MRR:6619.1,6617.0] || equal(singleton(u),ordered_pair(skc6,skc7))* -> .
% 8.02/8.19 6636[1:Rew:6618.0,204.0] || equal(ordered_pair(u,v),ordered_pair(singleton(skc8),singleton(skc6)))* -> equal(singleton(u),ordered_pair(skc6,skc7)) equal(singleton(u),singleton(singleton(skc8))).
% 8.02/8.19 6637[1:MRR:6636.1,6620.0] || equal(ordered_pair(u,v),ordered_pair(singleton(skc8),singleton(skc6)))* -> equal(singleton(u),singleton(singleton(skc8))).
% 8.02/8.19 6677[1:SpR:6618.0,28.0] || -> equal(unordered_pair(singleton(skc9),singleton(skc6)),ordered_pair(skc9,skc8))**.
% 8.02/8.19 6708[1:SpL:6618.0,12.0] || equal(singleton(u),singleton(skc6))* -> equal(skc9,skc8).
% 8.02/8.19 6732[1:Rew:7.0,6677.0] || -> equal(unordered_pair(singleton(skc6),singleton(skc9)),ordered_pair(skc9,skc8))**.
% 8.02/8.19 6855[1:SpL:6732.0,12.0] || equal(singleton(u),ordered_pair(skc9,skc8))* -> equal(singleton(skc9),singleton(skc6)).
% 8.02/8.19 6972[1:EqR:6708.0] || -> equal(skc9,skc8)**.
% 8.02/8.19 6995[1:Rew:6972.0,6855.0] || equal(singleton(u),ordered_pair(skc8,skc8))* -> equal(singleton(skc9),singleton(skc6)).
% 8.02/8.19 7040[1:Rew:30.0,6995.0] || equal(singleton(u),singleton(singleton(skc8)))* -> equal(singleton(skc9),singleton(skc6)).
% 8.02/8.19 7041[1:Rew:6972.0,7040.1] || equal(singleton(u),singleton(singleton(skc8)))* -> equal(singleton(skc8),singleton(skc6)).
% 8.02/8.19 7042[1:MRR:7041.1,6617.0] || equal(singleton(u),singleton(singleton(skc8)))* -> .
% 8.02/8.19 7043[1:MRR:6637.1,7042.0] || equal(ordered_pair(u,v),ordered_pair(singleton(skc8),singleton(skc6)))* -> .
% 8.02/8.19 7044[1:Obv:7043.0] || -> .
% 8.02/8.19 % SZS output end Refutation
% 8.02/8.19 Formulae used in the proof : reflexivity_r1_tarski t69_enumset1 t33_zfmisc_1 commutativity_k2_tarski t6_zfmisc_1 d5_tarski t9_zfmisc_1 t10_zfmisc_1
% 8.02/8.19
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