%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : LAT276-2 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp % Command : run_spass %d %s % Computer : n029.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 : Sun Jul 17 06:50:01 EDT 2022 % Result : Unsatisfiable 0.18s 0.40s % Output : Refutation 0.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.11 % Problem : LAT276-2 : TPTP v8.1.0. Released v3.2.0. % 0.10/0.12 % Command : run_spass %d %s % 0.12/0.33 % Computer : n029.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Wed Jun 29 15:27:22 EDT 2022 % 0.12/0.33 % CPUTime : % 0.18/0.40 % 0.18/0.40 SPASS V 3.9 % 0.18/0.40 SPASS beiseite: Proof found. % 0.18/0.40 % SZS status Theorem % 0.18/0.40 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p % 0.18/0.40 SPASS derived 20 clauses, backtracked 10 clauses, performed 3 splits and kept 37 clauses. % 0.18/0.40 SPASS allocated 63145 KBytes. % 0.18/0.40 SPASS spent 0:00:00.06 on the problem. % 0.18/0.40 0:00:00.03 for the input. % 0.18/0.40 0:00:00.00 for the FLOTTER CNF translation. % 0.18/0.40 0:00:00.00 for inferences. % 0.18/0.40 0:00:00.00 for the backtracking. % 0.18/0.40 0:00:00.00 for the reduction. % 0.18/0.40 % 0.18/0.40 % 0.18/0.40 Here is a proof with depth 4, length 47 : % 0.18/0.40 % SZS output start Refutation % 0.18/0.40 1[0:Inp] || c_in(u,v,w)* c_lessequals(v,x,tc_set(w))*+ -> c_in(u,x,w)*. % 0.18/0.40 2[0:Inp] || -> equal(c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),v_A)**. % 0.18/0.40 3[0:Inp] || c_in(u,v_A,t_a) c_lessequals(v,v_A,tc_set(t_a))+ -> c_in(v_sko__4mP(u,v,v_r),v,t_a)* c_in(c_Pair(c_Tarski_Olub(v,v_cl,t_a),u,t_a,t_a),v_r,tc_prod(t_a,t_a))*. % 0.18/0.40 4[0:Inp] || c_in(u,v_A,t_a) c_lessequals(v,v_A,tc_set(t_a)) c_in(c_Pair(v_sko__4mP(u,v,v_r),u,t_a,t_a),v_r,tc_prod(t_a,t_a))* -> c_in(c_Pair(c_Tarski_Olub(v,v_cl,t_a),u,t_a,t_a),v_r,tc_prod(t_a,t_a)). % 0.18/0.40 5[0:Inp] || c_in(u,v,t_a) c_lessequals(v,v_A,tc_set(t_a)) -> c_in(c_Pair(u,c_Tarski_Olub(v,v_cl,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))*. % 0.18/0.40 6[0:Inp] || -> equal(c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),v_r)**. % 0.18/0.40 7[0:Inp] || -> c_lessequals(v_S,v_A,tc_set(t_a))*. % 0.18/0.40 8[0:Inp] || c_in(u,v_S,t_a) c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))* -> c_in(c_Pair(u,v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))*. % 0.18/0.40 9[0:Inp] || -> c_in(v_xa,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a)* c_in(v_xa,v_S,t_a). % 0.18/0.40 10[0:Inp] || c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))* -> c_in(v_xa,v_S,t_a). % 0.18/0.40 11[0:Inp] || c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))* c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) -> . % 0.18/0.40 12[0:Inp] || c_in(u,v_S,t_a) -> c_in(c_Pair(u,v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))* c_in(v_xa,v_S,t_a). % 0.18/0.40 13[0:Rew:2.0,9.0] || -> c_in(v_xa,v_S,t_a) c_in(v_xa,v_A,t_a)*. % 0.18/0.40 14[0:Rew:6.0,10.0] || c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a))* -> c_in(v_xa,v_S,t_a). % 0.18/0.40 15[0:Rew:6.0,12.1] || c_in(u,v_S,t_a) -> c_in(v_xa,v_S,t_a) c_in(c_Pair(u,v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a))*. % 0.18/0.40 16[0:Rew:6.0,11.1,6.0,11.0] || c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a)) c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a))* -> . % 0.18/0.40 17[0:Rew:6.0,8.2,6.0,8.1] || c_in(u,v_S,t_a) c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))*+ -> c_in(c_Pair(u,v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a))*. % 0.18/0.40 18[1:Spt:15.0,15.2] || c_in(u,v_S,t_a) -> c_in(c_Pair(u,v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a))*. % 0.18/0.40 19[2:Spt:14.0] || c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a))* -> . % 0.18/0.40 23[0:Res:7.0,1.1] || c_in(u,v_S,t_a) -> c_in(u,v_A,t_a)*. % 0.18/0.40 24[0:MRR:13.0,23.0] || -> c_in(v_xa,v_A,t_a)*. % 0.18/0.40 25[0:Res:7.0,3.1] || c_in(u,v_A,t_a) -> c_in(v_sko__4mP(u,v_S,v_r),v_S,t_a) c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),u,t_a,t_a),v_r,tc_prod(t_a,t_a))*. % 0.18/0.40 26[2:Res:25.2,19.0] || c_in(v_xa,v_A,t_a) -> c_in(v_sko__4mP(v_xa,v_S,v_r),v_S,t_a)*. % 0.18/0.40 27[2:MRR:26.0,24.0] || -> c_in(v_sko__4mP(v_xa,v_S,v_r),v_S,t_a)*. % 0.18/0.40 28[1:Res:18.1,4.2] || c_in(v_sko__4mP(v_xa,u,v_r),v_S,t_a) c_in(v_xa,v_A,t_a) c_lessequals(u,v_A,tc_set(t_a)) -> c_in(c_Pair(c_Tarski_Olub(u,v_cl,t_a),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a))*. % 0.18/0.40 30[1:MRR:28.1,24.0] || c_in(v_sko__4mP(v_xa,u,v_r),v_S,t_a) c_lessequals(u,v_A,tc_set(t_a)) -> c_in(c_Pair(c_Tarski_Olub(u,v_cl,t_a),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a))*. % 0.18/0.40 31[2:Res:30.2,19.0] || c_in(v_sko__4mP(v_xa,v_S,v_r),v_S,t_a)* c_lessequals(v_S,v_A,tc_set(t_a)) -> . % 0.18/0.40 32[2:MRR:31.0,31.1,27.0,7.0] || -> . % 0.18/0.40 33[2:Spt:32.0,14.0,19.0] || -> c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a))*. % 0.18/0.40 34[2:Spt:32.0,14.1] || -> c_in(v_xa,v_S,t_a)*. % 0.18/0.40 35[2:MRR:16.1,33.0] || c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))* -> . % 0.18/0.40 36[2:Res:5.2,35.0] || c_in(v_xa,v_S,t_a) c_lessequals(v_S,v_A,tc_set(t_a))* -> . % 0.18/0.40 37[2:MRR:36.0,36.1,34.0,7.0] || -> . % 0.18/0.40 38[1:Spt:37.0,15.1] || -> c_in(v_xa,v_S,t_a)*. % 0.18/0.40 39[2:Spt:17.0,17.2] || c_in(u,v_S,t_a) -> c_in(c_Pair(u,v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a))*. % 0.18/0.40 40[2:Res:39.1,4.2] || c_in(v_sko__4mP(v_xa,u,v_r),v_S,t_a) c_in(v_xa,v_A,t_a) c_lessequals(u,v_A,tc_set(t_a)) -> c_in(c_Pair(c_Tarski_Olub(u,v_cl,t_a),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a))*. % 0.18/0.40 41[2:MRR:40.1,24.0] || c_in(v_sko__4mP(v_xa,u,v_r),v_S,t_a) c_lessequals(u,v_A,tc_set(t_a)) -> c_in(c_Pair(c_Tarski_Olub(u,v_cl,t_a),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a))*. % 0.18/0.40 43[0:Res:25.2,16.1] || c_in(v_xa,v_A,t_a) c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))* -> c_in(v_sko__4mP(v_xa,v_S,v_r),v_S,t_a). % 0.18/0.40 44[2:Res:41.2,16.1] || c_in(v_sko__4mP(v_xa,v_S,v_r),v_S,t_a) c_lessequals(v_S,v_A,tc_set(t_a)) c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))* -> . % 0.18/0.40 45[0:MRR:43.0,24.0] || c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))* -> c_in(v_sko__4mP(v_xa,v_S,v_r),v_S,t_a). % 0.18/0.40 46[2:MRR:44.1,7.0] || c_in(v_sko__4mP(v_xa,v_S,v_r),v_S,t_a) c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))* -> . % 0.18/0.40 47[2:MRR:46.0,45.1] || c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))* -> . % 0.18/0.40 48[2:Res:5.2,47.0] || c_in(v_xa,v_S,t_a) c_lessequals(v_S,v_A,tc_set(t_a))* -> . % 0.18/0.40 49[2:MRR:48.0,48.1,38.0,7.0] || -> . % 0.18/0.40 50[2:Spt:49.0,17.1] || c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))* -> . % 0.18/0.40 51[2:Res:5.2,50.0] || c_in(v_xa,v_S,t_a) c_lessequals(v_S,v_A,tc_set(t_a))* -> . % 0.18/0.40 52[2:MRR:51.0,51.1,38.0,7.0] || -> . % 0.18/0.40 % SZS output end Refutation % 0.18/0.40 Formulae used in the proof : cls_Set_OsubsetD_0 cls_Tarski_OA_A_61_61_Apset_Acl_0 cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AL1_A_58_AA_59_AALL_Ax_58S1_O_A_Ix_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ilub_AS1_Acl_M_AL1_J_A_58_Ar_A_61_61_ATrue_0 cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AL1_A_58_AA_59_AALL_Ax_58S1_O_A_Ix_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ilub_AS1_Acl_M_AL1_J_A_58_Ar_A_61_61_ATrue_1 cls_Tarski_O_91_124_AS1_A_60_61_AA_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ix1_M_Alub_AS1_Acl_J_A_58_Ar_A_61_61_ATrue_0 cls_Tarski_Or_A_61_61_Aorder_Acl_0 cls_conjecture_0 cls_conjecture_10 cls_conjecture_3 cls_conjecture_4 cls_conjecture_6 cls_conjecture_9 % 0.18/0.40 %------------------------------------------------------------------------------