TSTP Solution File: SET831-2 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET831-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n010.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 05:29:01 EDT 2022

% Result   : Unsatisfiable 0.23s 0.55s
% Output   : Refutation 0.23s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem  : SET831-2 : TPTP v8.1.0. Released v3.2.0.
% 0.08/0.14  % Command  : run_spass %d %s
% 0.15/0.36  % Computer : n010.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 600
% 0.15/0.36  % DateTime : Mon Jul 11 02:37:30 EDT 2022
% 0.15/0.36  % CPUTime  : 
% 0.23/0.55  
% 0.23/0.55  SPASS V 3.9 
% 0.23/0.55  SPASS beiseite: Proof found.
% 0.23/0.55  % SZS status Theorem
% 0.23/0.55  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.23/0.55  SPASS derived 992 clauses, backtracked 13 clauses, performed 2 splits and kept 331 clauses.
% 0.23/0.55  SPASS allocated 64178 KBytes.
% 0.23/0.55  SPASS spent	0:00:00.18 on the problem.
% 0.23/0.55  		0:00:00.04 for the input.
% 0.23/0.55  		0:00:00.00 for the FLOTTER CNF translation.
% 0.23/0.55  		0:00:00.02 for inferences.
% 0.23/0.55  		0:00:00.00 for the backtracking.
% 0.23/0.55  		0:00:00.09 for the reduction.
% 0.23/0.55  
% 0.23/0.55  
% 0.23/0.55  Here is a proof with depth 5, length 76 :
% 0.23/0.55  % SZS output start Refutation
% 0.23/0.55  1[0:Inp] || c_in(u,c_inter(v,w,x),x)* -> c_in(u,w,x).
% 0.23/0.55  2[0:Inp] || c_in(u,c_inter(v,w,x),x)* -> c_in(u,v,x).
% 0.23/0.55  3[0:Inp] || c_in(u,v,w) c_in(u,x,w) -> c_in(u,c_inter(v,x,w),w)*.
% 0.23/0.55  4[0:Inp] || c_in(u,v,w)* c_lessequals(v,x,tc_set(w))*+ -> c_in(u,x,w)*.
% 0.23/0.55  5[0:Inp] ||  -> c_lessequals(u,v,tc_set(w)) c_in(c_Main_OsubsetI__1(u,v,w),u,w)*.
% 0.23/0.55  6[0:Inp] || c_in(c_Main_OsubsetI__1(u,v,w),v,w)* -> c_lessequals(u,v,tc_set(w)).
% 0.23/0.55  7[0:Inp] || c_lessequals(u,v,tc_set(w))*+ c_lessequals(v,u,tc_set(w))* -> equal(u,v).
% 0.23/0.55  8[0:Inp] ||  -> equal(c_inter(v_Y,v_Z,t_a),v_X) c_lessequals(v_X,v_Y,tc_set(t_a))*.
% 0.23/0.55  9[0:Inp] ||  -> equal(c_inter(v_Y,v_Z,t_a),v_X) c_lessequals(v_X,v_Z,tc_set(t_a))*.
% 0.23/0.55  10[0:Inp] || equal(c_inter(v_Y,v_Z,t_a),v_X) c_lessequals(v_X,v_Y,tc_set(t_a)) c_lessequals(v_X,v_Z,tc_set(t_a)) -> c_lessequals(v_x,v_Y,tc_set(t_a))*.
% 0.23/0.55  11[0:Inp] || equal(c_inter(v_Y,v_Z,t_a),v_X) c_lessequals(v_X,v_Y,tc_set(t_a)) c_lessequals(v_X,v_Z,tc_set(t_a)) -> c_lessequals(v_x,v_Z,tc_set(t_a))*.
% 0.23/0.55  12[0:Inp] || equal(c_inter(v_Y,v_Z,t_a),v_X) c_lessequals(v_X,v_Y,tc_set(t_a)) c_lessequals(v_X,v_Z,tc_set(t_a)) c_lessequals(v_x,v_X,tc_set(t_a))* -> .
% 0.23/0.55  13[0:Inp] || c_lessequals(u,v_Y,tc_set(t_a)) c_lessequals(u,v_Z,tc_set(t_a))* -> equal(c_inter(v_Y,v_Z,t_a),v_X) c_lessequals(u,v_X,tc_set(t_a)).
% 0.23/0.55  14[1:Spt:9.0] ||  -> equal(c_inter(v_Y,v_Z,t_a),v_X)**.
% 0.23/0.55  15[1:Rew:14.0,12.0] || equal(v_X,v_X) c_lessequals(v_X,v_Y,tc_set(t_a)) c_lessequals(v_X,v_Z,tc_set(t_a)) c_lessequals(v_x,v_X,tc_set(t_a))* -> .
% 0.23/0.55  16[1:Rew:14.0,10.0] || equal(v_X,v_X) c_lessequals(v_X,v_Y,tc_set(t_a)) c_lessequals(v_X,v_Z,tc_set(t_a)) -> c_lessequals(v_x,v_Y,tc_set(t_a))*.
% 0.23/0.55  17[1:Rew:14.0,11.0] || equal(v_X,v_X) c_lessequals(v_X,v_Y,tc_set(t_a)) c_lessequals(v_X,v_Z,tc_set(t_a)) -> c_lessequals(v_x,v_Z,tc_set(t_a))*.
% 0.23/0.55  18[1:Obv:16.0] || c_lessequals(v_X,v_Y,tc_set(t_a)) c_lessequals(v_X,v_Z,tc_set(t_a)) -> c_lessequals(v_x,v_Y,tc_set(t_a))*.
% 0.23/0.55  19[1:Obv:17.0] || c_lessequals(v_X,v_Y,tc_set(t_a)) c_lessequals(v_X,v_Z,tc_set(t_a)) -> c_lessequals(v_x,v_Z,tc_set(t_a))*.
% 0.23/0.55  20[1:Obv:15.0] || c_lessequals(v_X,v_Y,tc_set(t_a)) c_lessequals(v_X,v_Z,tc_set(t_a)) c_lessequals(v_x,v_X,tc_set(t_a))* -> .
% 0.23/0.55  22[1:SpL:14.0,2.0] || c_in(u,v_X,t_a) -> c_in(u,v_Y,t_a)*.
% 0.23/0.55  23[0:Res:5.1,2.0] ||  -> c_lessequals(c_inter(u,v,w),x,tc_set(w)) c_in(c_Main_OsubsetI__1(c_inter(u,v,w),x,w),u,w)*.
% 0.23/0.55  24[1:SpL:14.0,1.0] || c_in(u,v_X,t_a) -> c_in(u,v_Z,t_a)*.
% 0.23/0.55  25[0:Res:5.1,1.0] ||  -> c_lessequals(c_inter(u,v,w),x,tc_set(w)) c_in(c_Main_OsubsetI__1(c_inter(u,v,w),x,w),v,w)*.
% 0.23/0.55  27[1:Res:22.1,6.0] || c_in(c_Main_OsubsetI__1(u,v_Y,t_a),v_X,t_a)* -> c_lessequals(u,v_Y,tc_set(t_a)).
% 0.23/0.55  29[1:Res:24.1,6.0] || c_in(c_Main_OsubsetI__1(u,v_Z,t_a),v_X,t_a)* -> c_lessequals(u,v_Z,tc_set(t_a)).
% 0.23/0.55  30[1:Res:5.1,27.0] ||  -> c_lessequals(v_X,v_Y,tc_set(t_a))* c_lessequals(v_X,v_Y,tc_set(t_a))*.
% 0.23/0.55  31[1:Obv:30.0] ||  -> c_lessequals(v_X,v_Y,tc_set(t_a))*.
% 0.23/0.55  32[1:MRR:18.0,31.0] || c_lessequals(v_X,v_Z,tc_set(t_a)) -> c_lessequals(v_x,v_Y,tc_set(t_a))*.
% 0.23/0.55  33[1:MRR:19.0,31.0] || c_lessequals(v_X,v_Z,tc_set(t_a)) -> c_lessequals(v_x,v_Z,tc_set(t_a))*.
% 0.23/0.55  34[1:MRR:20.0,31.0] || c_lessequals(v_X,v_Z,tc_set(t_a)) c_lessequals(v_x,v_X,tc_set(t_a))* -> .
% 0.23/0.55  35[2:Spt:32.0] || c_lessequals(v_X,v_Z,tc_set(t_a))* -> .
% 0.23/0.55  36[1:Res:5.1,29.0] ||  -> c_lessequals(v_X,v_Z,tc_set(t_a))* c_lessequals(v_X,v_Z,tc_set(t_a))*.
% 0.23/0.55  37[1:Obv:36.0] ||  -> c_lessequals(v_X,v_Z,tc_set(t_a))*.
% 0.23/0.55  38[2:MRR:37.0,35.0] ||  -> .
% 0.23/0.55  39[2:Spt:38.0,32.0,35.0] ||  -> c_lessequals(v_X,v_Z,tc_set(t_a))*.
% 0.23/0.55  40[2:Spt:38.0,32.1] ||  -> c_lessequals(v_x,v_Y,tc_set(t_a))*.
% 0.23/0.55  42[1:MRR:33.0,37.0] ||  -> c_lessequals(v_x,v_Z,tc_set(t_a))*.
% 0.23/0.55  43[1:MRR:34.0,37.0] || c_lessequals(v_x,v_X,tc_set(t_a))* -> .
% 0.23/0.55  51[2:Res:40.0,4.1] || c_in(u,v_x,t_a)* -> c_in(u,v_Y,t_a).
% 0.23/0.55  53[1:Res:42.0,4.1] || c_in(u,v_x,t_a)* -> c_in(u,v_Z,t_a).
% 0.23/0.55  54[2:Res:5.1,51.0] ||  -> c_lessequals(v_x,u,tc_set(t_a)) c_in(c_Main_OsubsetI__1(v_x,u,t_a),v_Y,t_a)*.
% 0.23/0.55  55[1:Res:5.1,53.0] ||  -> c_lessequals(v_x,u,tc_set(t_a)) c_in(c_Main_OsubsetI__1(v_x,u,t_a),v_Z,t_a)*.
% 0.23/0.55  60[1:SpR:14.0,3.2] || c_in(u,v_Y,t_a) c_in(u,v_Z,t_a)* -> c_in(u,v_X,t_a).
% 0.23/0.55  61[0:Res:3.2,6.0] || c_in(c_Main_OsubsetI__1(u,c_inter(v,w,x),x),v,x)*+ c_in(c_Main_OsubsetI__1(u,c_inter(v,w,x),x),w,x)* -> c_lessequals(u,c_inter(v,w,x),tc_set(x)).
% 0.23/0.55  65[1:Res:55.1,60.1] || c_in(c_Main_OsubsetI__1(v_x,u,t_a),v_Y,t_a)* -> c_lessequals(v_x,u,tc_set(t_a)) c_in(c_Main_OsubsetI__1(v_x,u,t_a),v_X,t_a).
% 0.23/0.55  67[2:MRR:65.0,54.1] ||  -> c_lessequals(v_x,u,tc_set(t_a)) c_in(c_Main_OsubsetI__1(v_x,u,t_a),v_X,t_a)*.
% 0.23/0.55  68[2:Res:67.1,6.0] ||  -> c_lessequals(v_x,v_X,tc_set(t_a))* c_lessequals(v_x,v_X,tc_set(t_a))*.
% 0.23/0.55  71[2:Obv:68.0] ||  -> c_lessequals(v_x,v_X,tc_set(t_a))*.
% 0.23/0.55  72[2:MRR:71.0,43.0] ||  -> .
% 0.23/0.55  75[1:Spt:72.0,9.0,14.0] || equal(c_inter(v_Y,v_Z,t_a),v_X)** -> .
% 0.23/0.55  76[1:Spt:72.0,9.1] ||  -> c_lessequals(v_X,v_Z,tc_set(t_a))*.
% 0.23/0.55  77[1:MRR:8.0,75.0] ||  -> c_lessequals(v_X,v_Y,tc_set(t_a))*.
% 0.23/0.55  78[1:MRR:13.2,75.0] || c_lessequals(u,v_Y,tc_set(t_a)) c_lessequals(u,v_Z,tc_set(t_a))* -> c_lessequals(u,v_X,tc_set(t_a)).
% 0.23/0.55  80[1:Res:76.0,4.1] || c_in(u,v_X,t_a) -> c_in(u,v_Z,t_a)*.
% 0.23/0.55  82[1:Res:77.0,4.1] || c_in(u,v_X,t_a) -> c_in(u,v_Y,t_a)*.
% 0.23/0.55  87[0:Res:23.1,6.0] ||  -> c_lessequals(c_inter(u,v,w),u,tc_set(w))* c_lessequals(c_inter(u,v,w),u,tc_set(w))*.
% 0.23/0.55  90[0:Obv:87.0] ||  -> c_lessequals(c_inter(u,v,w),u,tc_set(w))*.
% 0.23/0.55  92[1:Res:90.0,78.1] || c_lessequals(c_inter(v_Z,u,t_a),v_Y,tc_set(t_a))* -> c_lessequals(c_inter(v_Z,u,t_a),v_X,tc_set(t_a)).
% 0.23/0.55  101[0:Res:25.1,6.0] ||  -> c_lessequals(c_inter(u,v,w),v,tc_set(w))* c_lessequals(c_inter(u,v,w),v,tc_set(w))*.
% 0.23/0.55  105[0:Obv:101.0] ||  -> c_lessequals(c_inter(u,v,w),v,tc_set(w))*.
% 0.23/0.55  125[0:Res:25.1,61.0] || c_in(c_Main_OsubsetI__1(c_inter(u,v,w),c_inter(v,x,w),w),x,w)* -> c_lessequals(c_inter(u,v,w),c_inter(v,x,w),tc_set(w)) c_lessequals(c_inter(u,v,w),c_inter(v,x,w),tc_set(w)).
% 0.23/0.55  128[1:Res:82.1,61.0] || c_in(c_Main_OsubsetI__1(u,c_inter(v_Y,v,t_a),t_a),v_X,t_a)*+ c_in(c_Main_OsubsetI__1(u,c_inter(v_Y,v,t_a),t_a),v,t_a)* -> c_lessequals(u,c_inter(v_Y,v,t_a),tc_set(t_a)).
% 0.23/0.55  130[0:Obv:125.1] || c_in(c_Main_OsubsetI__1(c_inter(u,v,w),c_inter(v,x,w),w),x,w)* -> c_lessequals(c_inter(u,v,w),c_inter(v,x,w),tc_set(w)).
% 0.23/0.55  472[0:Res:23.1,130.0] ||  -> c_lessequals(c_inter(u,v,w),c_inter(v,u,w),tc_set(w))* c_lessequals(c_inter(u,v,w),c_inter(v,u,w),tc_set(w))*.
% 0.23/0.55  483[0:Obv:472.0] ||  -> c_lessequals(c_inter(u,v,w),c_inter(v,u,w),tc_set(w))*.
% 0.23/0.55  503[0:Res:483.0,7.0] || c_lessequals(c_inter(u,v,w),c_inter(v,u,w),tc_set(w))* -> equal(c_inter(v,u,w),c_inter(u,v,w)).
% 0.23/0.55  506[0:MRR:503.0,483.0] ||  -> equal(c_inter(u,v,w),c_inter(v,u,w))*.
% 0.23/0.55  886[1:Res:5.1,128.0] || c_in(c_Main_OsubsetI__1(v_X,c_inter(v_Y,u,t_a),t_a),u,t_a)* -> c_lessequals(v_X,c_inter(v_Y,u,t_a),tc_set(t_a)) c_lessequals(v_X,c_inter(v_Y,u,t_a),tc_set(t_a)).
% 0.23/0.55  893[1:Obv:886.1] || c_in(c_Main_OsubsetI__1(v_X,c_inter(v_Y,u,t_a),t_a),u,t_a)* -> c_lessequals(v_X,c_inter(v_Y,u,t_a),tc_set(t_a)).
% 0.23/0.55  1159[1:Res:105.0,92.0] ||  -> c_lessequals(c_inter(v_Z,v_Y,t_a),v_X,tc_set(t_a))*.
% 0.23/0.55  1165[1:Rew:506.0,1159.0] ||  -> c_lessequals(c_inter(v_Y,v_Z,t_a),v_X,tc_set(t_a))*.
% 0.23/0.55  1169[1:Res:1165.0,7.0] || c_lessequals(v_X,c_inter(v_Y,v_Z,t_a),tc_set(t_a))* -> equal(c_inter(v_Y,v_Z,t_a),v_X).
% 0.23/0.55  1171[1:MRR:1169.1,75.0] || c_lessequals(v_X,c_inter(v_Y,v_Z,t_a),tc_set(t_a))* -> .
% 0.23/0.55  1253[1:Res:80.1,893.0] || c_in(c_Main_OsubsetI__1(v_X,c_inter(v_Y,v_Z,t_a),t_a),v_X,t_a)* -> c_lessequals(v_X,c_inter(v_Y,v_Z,t_a),tc_set(t_a)).
% 0.23/0.55  1258[1:MRR:1253.0,1253.1,5.1,1171.0] ||  -> .
% 0.23/0.55  % SZS output end Refutation
% 0.23/0.55  Formulae used in the proof : cls_Set_OIntE_0 cls_Set_OIntE_1 cls_Set_OIntI_0 cls_Set_OsubsetD_0 cls_Set_OsubsetI_0 cls_Set_OsubsetI_1 cls_Set_Osubset__antisym_0 cls_conjecture_0 cls_conjecture_1 cls_conjecture_2 cls_conjecture_3 cls_conjecture_4 cls_conjecture_5
% 0.23/0.56  
%------------------------------------------------------------------------------