%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : LCL442-2 : TPTP v9.3.1. Released v3.2.0. % Transfm : none % Format : tptp % Command : run_spass %d %s % Computer : n016.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 01:07:32 PM UTC 2026 % Result : Unsatisfiable 0.09s 0.44s % Output : Refutation 0.09s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL442-2 : TPTP v9.3.1. Released v3.2.0. % 0.00/0.04 % Command : run_spass %d %s % 0.09/0.36 % Computer : n016.cluster.edu % 0.09/0.36 % Model : x86_64 x86_64 % 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.36 % Memory : 8046.5625MB % 0.09/0.36 % OS : Linux 6.8.0-71-generic % 0.09/0.36 % CPULimit : 300 % 0.09/0.36 % WCLimit : 300 % 0.09/0.36 % DateTime : Sat Sep 5 20:38:16 UTC 2026 % 0.09/0.37 % CPUTime : % 0.09/0.44 % 0.09/0.44 SPASS V 3.9 % 0.09/0.44 SPASS beiseite: Proof found. % 0.09/0.44 % SZS status Theorem % 0.09/0.44 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p % 0.09/0.44 SPASS derived 56 clauses, backtracked 13 clauses, performed 2 splits and kept 55 clauses. % 0.09/0.44 SPASS allocated 63176 KBytes. % 0.09/0.44 SPASS spent 0:00:00.06 on the problem. % 0.09/0.44 0:00:00.03 for the input. % 0.09/0.44 0:00:00.00 for the FLOTTER CNF translation. % 0.09/0.44 0:00:00.00 for inferences. % 0.09/0.44 0:00:00.00 for the backtracking. % 0.09/0.44 0:00:00.00 for the reduction. % 0.09/0.44 % 0.09/0.44 % 0.09/0.44 Here is a proof with depth 3, length 37 : % 0.09/0.44 % SZS output start Refutation % 0.09/0.44 1[0:Inp] || c_in(c_PropLog_Opl_Oop_A_N_62(u,c_PropLog_Opl_Ofalse,v),c_PropLog_Othms(w,v),tc_PropLog_Opl(v))*+ -> c_in(c_PropLog_Opl_Oop_A_N_62(u,x,v),c_PropLog_Othms(w,v),tc_PropLog_Opl(v))*. % 0.09/0.44 2[0:Inp] || c_in(u,c_PropLog_Othms(v,w),tc_PropLog_Opl(w)) c_in(c_PropLog_Opl_Oop_A_N_62(x,c_PropLog_Opl_Ofalse,w),c_PropLog_Othms(v,w),tc_PropLog_Opl(w)) -> c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(u,x,w),c_PropLog_Opl_Ofalse,w),c_PropLog_Othms(v,w),tc_PropLog_Opl(w))*. % 0.09/0.44 3[0:Inp] || c_in(u,c_PropLog_Othms(v,w),tc_PropLog_Opl(w)) -> c_in(u,c_PropLog_Othms(c_union(v,x,tc_PropLog_Opl(w)),w),tc_PropLog_Opl(w))*. % 0.09/0.44 4[0:Inp] || c_in(u,c_PropLog_Othms(v,w),tc_PropLog_Opl(w)) -> c_in(u,c_PropLog_Othms(c_union(x,v,tc_PropLog_Opl(w)),w),tc_PropLog_Opl(w))*. % 0.09/0.44 5[0:Inp] || c_in(u,c_PropLog_Othms(v,w),tc_PropLog_Opl(w)) -> c_in(c_PropLog_Opl_Oop_A_N_62(x,u,w),c_PropLog_Othms(v,w),tc_PropLog_Opl(w))*. % 0.09/0.44 6[0:Inp] || c_PropLog_Oeval(v_tt,v_pl1,t_a) -> c_in(v_pl1,c_PropLog_Othms(c_PropLog_Ohyps(v_pl1,v_tt,t_a),t_a),tc_PropLog_Opl(t_a))*. % 0.09/0.44 7[0:Inp] || -> c_PropLog_Oeval(v_tt,v_pl1,t_a) c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_PropLog_Ohyps(v_pl1,v_tt,t_a),t_a),tc_PropLog_Opl(t_a))*. % 0.09/0.44 8[0:Inp] || c_PropLog_Oeval(v_tt,v_pl2,t_a) -> c_in(v_pl2,c_PropLog_Othms(c_PropLog_Ohyps(v_pl2,v_tt,t_a),t_a),tc_PropLog_Opl(t_a))*. % 0.09/0.44 9[0:Inp] || -> c_PropLog_Oeval(v_tt,v_pl2,t_a) c_in(c_PropLog_Opl_Oop_A_N_62(v_pl2,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_PropLog_Ohyps(v_pl2,v_tt,t_a),t_a),tc_PropLog_Opl(t_a))*. % 0.09/0.44 10[0:Inp] || c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1,v_pl2,t_a),c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1,v_tt,t_a),c_PropLog_Ohyps(v_pl2,v_tt,t_a),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))* -> c_PropLog_Oeval(v_tt,v_pl1,t_a). % 0.09/0.44 11[0:Inp] || c_PropLog_Oeval(v_tt,v_pl2,t_a) c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1,v_pl2,t_a),c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1,v_tt,t_a),c_PropLog_Ohyps(v_pl2,v_tt,t_a),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))* -> . % 0.09/0.44 12[0:Inp] || c_PropLog_Oeval(v_tt,v_pl1,t_a) c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pl1,v_pl2,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1,v_tt,t_a),c_PropLog_Ohyps(v_pl2,v_tt,t_a),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))* -> c_PropLog_Oeval(v_tt,v_pl2,t_a). % 0.09/0.44 13[1:Spt:10.1] || -> c_PropLog_Oeval(v_tt,v_pl1,t_a)*. % 0.09/0.44 14[1:MRR:6.0,13.0] || -> c_in(v_pl1,c_PropLog_Othms(c_PropLog_Ohyps(v_pl1,v_tt,t_a),t_a),tc_PropLog_Opl(t_a))*. % 0.09/0.44 15[1:MRR:12.0,13.0] || c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pl1,v_pl2,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1,v_tt,t_a),c_PropLog_Ohyps(v_pl2,v_tt,t_a),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))* -> c_PropLog_Oeval(v_tt,v_pl2,t_a). % 0.09/0.44 16[2:Spt:11.0] || c_PropLog_Oeval(v_tt,v_pl2,t_a)* -> . % 0.09/0.44 17[2:MRR:9.0,16.0] || -> c_in(c_PropLog_Opl_Oop_A_N_62(v_pl2,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_PropLog_Ohyps(v_pl2,v_tt,t_a),t_a),tc_PropLog_Opl(t_a))*. % 0.09/0.44 18[2:MRR:15.1,16.0] || c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pl1,v_pl2,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1,v_tt,t_a),c_PropLog_Ohyps(v_pl2,v_tt,t_a),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))* -> . % 0.09/0.44 19[2:Res:17.0,1.0] || -> c_in(c_PropLog_Opl_Oop_A_N_62(v_pl2,u,t_a),c_PropLog_Othms(c_PropLog_Ohyps(v_pl2,v_tt,t_a),t_a),tc_PropLog_Opl(t_a))*. % 0.09/0.44 21[0:Res:4.1,1.0] || c_in(c_PropLog_Opl_Oop_A_N_62(u,c_PropLog_Opl_Ofalse,v),c_PropLog_Othms(w,v),tc_PropLog_Opl(v)) -> c_in(c_PropLog_Opl_Oop_A_N_62(u,x,v),c_PropLog_Othms(c_union(y,w,tc_PropLog_Opl(v)),v),tc_PropLog_Opl(v))*. % 0.09/0.44 22[0:Res:3.1,1.0] || c_in(c_PropLog_Opl_Oop_A_N_62(u,c_PropLog_Opl_Ofalse,v),c_PropLog_Othms(w,v),tc_PropLog_Opl(v)) -> c_in(c_PropLog_Opl_Oop_A_N_62(u,x,v),c_PropLog_Othms(c_union(w,y,tc_PropLog_Opl(v)),v),tc_PropLog_Opl(v))*. % 0.09/0.44 30[2:Res:2.2,18.0] || c_in(v_pl1,c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1,v_tt,t_a),c_PropLog_Ohyps(v_pl2,v_tt,t_a),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) c_in(c_PropLog_Opl_Oop_A_N_62(v_pl2,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1,v_tt,t_a),c_PropLog_Ohyps(v_pl2,v_tt,t_a),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))* -> . % 0.09/0.44 52[2:Res:21.1,30.1] || c_in(c_PropLog_Opl_Oop_A_N_62(v_pl2,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_PropLog_Ohyps(v_pl2,v_tt,t_a),t_a),tc_PropLog_Opl(t_a)) c_in(v_pl1,c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1,v_tt,t_a),c_PropLog_Ohyps(v_pl2,v_tt,t_a),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))* -> . % 0.09/0.44 53[2:MRR:52.0,19.0] || c_in(v_pl1,c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1,v_tt,t_a),c_PropLog_Ohyps(v_pl2,v_tt,t_a),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))* -> . % 0.09/0.44 57[2:Res:3.1,53.0] || c_in(v_pl1,c_PropLog_Othms(c_PropLog_Ohyps(v_pl1,v_tt,t_a),t_a),tc_PropLog_Opl(t_a))* -> . % 0.09/0.44 58[2:MRR:57.0,14.0] || -> . % 0.09/0.44 59[2:Spt:58.0,11.0,16.0] || -> c_PropLog_Oeval(v_tt,v_pl2,t_a)*. % 0.09/0.44 60[2:Spt:58.0,11.1] || c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1,v_pl2,t_a),c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1,v_tt,t_a),c_PropLog_Ohyps(v_pl2,v_tt,t_a),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))* -> . % 0.09/0.44 61[2:MRR:8.0,59.0] || -> c_in(v_pl2,c_PropLog_Othms(c_PropLog_Ohyps(v_pl2,v_tt,t_a),t_a),tc_PropLog_Opl(t_a))*. % 0.09/0.44 63[2:Res:4.1,60.0] || c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1,v_pl2,t_a),c_PropLog_Othms(c_PropLog_Ohyps(v_pl2,v_tt,t_a),t_a),tc_PropLog_Opl(t_a))* -> . % 0.09/0.44 68[2:Res:5.1,63.0] || c_in(v_pl2,c_PropLog_Othms(c_PropLog_Ohyps(v_pl2,v_tt,t_a),t_a),tc_PropLog_Opl(t_a))* -> . % 0.09/0.44 70[2:MRR:68.0,61.0] || -> . % 0.09/0.44 71[1:Spt:70.0,10.1,13.0] || c_PropLog_Oeval(v_tt,v_pl1,t_a)* -> . % 0.09/0.44 72[1:Spt:70.0,10.0] || c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1,v_pl2,t_a),c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1,v_tt,t_a),c_PropLog_Ohyps(v_pl2,v_tt,t_a),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))* -> . % 0.09/0.44 73[1:MRR:7.0,71.0] || -> c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_PropLog_Ohyps(v_pl1,v_tt,t_a),t_a),tc_PropLog_Opl(t_a))*. % 0.09/0.44 78[1:Res:22.1,72.0] || c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_PropLog_Ohyps(v_pl1,v_tt,t_a),t_a),tc_PropLog_Opl(t_a))* -> . % 0.09/0.44 80[1:MRR:78.0,73.0] || -> . % 0.09/0.44 % SZS output end Refutation % 0.09/0.44 Formulae used in the proof : cls_PropLog_Ofalse__imp_0 cls_PropLog_Oimp__false_0 cls_PropLog_Oweaken__left__Un1_0 cls_PropLog_Oweaken__left__Un2_0 cls_PropLog_Oweaken__right_0 cls_conjecture_0 cls_conjecture_1 cls_conjecture_2 cls_conjecture_3 cls_conjecture_4 cls_conjecture_5 cls_conjecture_9 % 0.09/0.44 %------------------------------------------------------------------------------