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