%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : MGT055-1 : TPTP v9.3.0. Released v2.4.0. % Transfm : none % Format : tptp % Command : run_spass %d %s % Computer : n003.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 : Tue Sep 8 06:19:57 AM UTC 2026 % Result : Unsatisfiable 3.55s 3.84s % Output : Refutation 3.55s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : MGT055-1 : TPTP v9.3.0. Released v2.4.0. % 0.00/0.04 % Command : run_spass %d %s % 0.09/0.36 % Computer : n003.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 : Mon Sep 7 13:28:09 UTC 2026 % 0.09/0.37 % CPUTime : % 3.55/3.84 % 3.55/3.84 SPASS V 3.9 % 3.55/3.84 SPASS beiseite: Proof found. % 3.55/3.84 % SZS status Theorem % 3.55/3.84 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p % 3.55/3.84 SPASS derived 7855 clauses, backtracked 236 clauses, performed 4 splits and kept 1806 clauses. % 3.55/3.84 SPASS allocated 81576 KBytes. % 3.55/3.84 SPASS spent 0:00:03.46 on the problem. % 3.55/3.84 0:00:00.06 for the input. % 3.55/3.84 0:00:00.00 for the FLOTTER CNF translation. % 3.55/3.84 0:00:00.20 for inferences. % 3.55/3.84 0:00:00.01 for the backtracking. % 3.55/3.84 0:00:03.12 for the reduction. % 3.55/3.84 % 3.55/3.84 % 3.55/3.84 Here is a proof with depth 5, length 86 : % 3.55/3.84 % SZS output start Refutation % 3.55/3.84 2[0:Inp] has_endowment(u) || smaller_or_equal(age(u,v),eta)* -> has_immunity(u,v). % 3.55/3.84 3[0:Inp] has_endowment(u) || has_immunity(u,v) greater(age(u,v),eta)*l -> . % 3.55/3.84 8[0:Inp] organization(u) || has_immunity(u,v) has_immunity(u,w) -> equal(hazard_of_mortality(u,w),hazard_of_mortality(u,v))*. % 3.55/3.84 9[0:Inp] organization(u) || has_immunity(u,v) -> has_immunity(u,w) greater(hazard_of_mortality(u,w),hazard_of_mortality(u,v))*. % 3.55/3.84 10[0:Inp] || dissimilar(u,v,w)* -> organization(u). % 3.55/3.84 12[0:Inp] || is_aligned(u,v) is_aligned(u,w) dissimilar(u,w,v)* -> . % 3.55/3.84 14[0:Inp] organization(u) || is_aligned(u,v) -> is_aligned(u,w) dissimilar(u,v,w)*. % 3.55/3.84 17[0:Inp] organization(u) || equal(age(u,v),zero)** -> is_aligned(u,v). % 3.55/3.84 18[0:Inp] organization(u) || is_aligned(u,v) -> is_aligned(u,w) greater(capability(u,v),capability(u,w))*. % 3.55/3.84 19[0:Inp] organization(u) || greater(age(u,v),sigma) equal(age(u,w),zero) -> dissimilar(u,w,v)*. % 3.55/3.84 20[0:Inp] organization(u) || equal(age(u,v),zero) dissimilar(u,v,w)* -> greater(age(u,w),sigma). % 3.55/3.84 21[0:Inp] organization(u) || greater(capability(u,v),capability(u,w))* -> has_immunity(u,w) has_immunity(u,v) greater(hazard_of_mortality(u,w),hazard_of_mortality(u,v)). % 3.55/3.84 22[0:Inp] || -> organization(sk2)*. % 3.55/3.84 23[0:Inp] || -> has_endowment(sk2)*. % 3.55/3.84 24[0:Inp] || -> equal(age(sk2,sk3),zero)**. % 3.55/3.84 25[0:Inp] || -> smaller_or_equal(age(sk2,sk4),eta)*. % 3.55/3.84 26[0:Inp] || -> greater(age(sk2,sk5),eta)*l. % 3.55/3.84 27[0:Inp] || -> smaller_or_equal(age(sk2,sk5),sigma)*. % 3.55/3.84 28[0:Inp] || -> greater(age(sk2,sk6),sigma)*l. % 3.55/3.84 29[0:Inp] || -> greater(sigma,eta)*l. % 3.55/3.84 30[0:Inp] || -> greater(eta,zero)*r. % 3.55/3.84 31[0:Inp] || equal(hazard_of_mortality(sk2,sk4),hazard_of_mortality(sk2,sk3)) greater(hazard_of_mortality(sk2,sk5),hazard_of_mortality(sk2,sk4)) greater(hazard_of_mortality(sk2,sk6),hazard_of_mortality(sk2,sk5))*l -> . % 3.55/3.84 32[0:Inp] || smaller_or_equal(u,v) -> equal(u,v) smaller(u,v)*. % 3.55/3.84 33[0:Inp] || smaller(u,v)* -> smaller_or_equal(u,v). % 3.55/3.84 38[0:Inp] || smaller(u,v)* -> greater(v,u). % 3.55/3.84 39[0:Inp] || greater(u,v) -> smaller(v,u)*. % 3.55/3.84 40[0:Inp] || greater(u,v)*+ greater(v,u)* -> . % 3.55/3.84 41[0:Inp] || greater(u,v)* greater(v,w)* -> greater(u,w)*. % 3.55/3.84 43[0:MRR:20.0,10.1] || equal(age(u,v),zero) dissimilar(u,v,w)* -> greater(age(u,w),sigma). % 3.55/3.84 44[0:MRR:21.3,9.1] organization(u) || greater(capability(u,v),capability(u,w))* -> has_immunity(u,w) greater(hazard_of_mortality(u,w),hazard_of_mortality(u,v)). % 3.55/3.84 46[0:Res:23.0,2.0] || smaller_or_equal(age(sk2,u),eta)* -> has_immunity(sk2,u). % 3.55/3.84 51[0:Res:22.0,9.0] || has_immunity(sk2,u) -> has_immunity(sk2,v) greater(hazard_of_mortality(sk2,v),hazard_of_mortality(sk2,u))*. % 3.55/3.84 54[0:Res:22.0,8.0] || has_immunity(sk2,u) has_immunity(sk2,v) -> equal(hazard_of_mortality(sk2,v),hazard_of_mortality(sk2,u))*. % 3.55/3.84 56[0:Res:22.0,14.0] || is_aligned(sk2,u) -> is_aligned(sk2,v) dissimilar(sk2,u,v)*. % 3.55/3.84 58[0:Res:22.0,17.0] || equal(age(sk2,u),zero)** -> is_aligned(sk2,u). % 3.55/3.84 59[0:Res:27.0,32.0] || -> equal(age(sk2,sk5),sigma) smaller(age(sk2,sk5),sigma)*. % 3.55/3.84 60[0:Res:25.0,2.1] has_endowment(sk2) || -> has_immunity(sk2,sk4)*. % 3.55/3.84 62[0:Res:24.0,43.0] || dissimilar(sk2,sk3,u)* -> greater(age(sk2,u),sigma). % 3.55/3.84 64[0:Res:24.0,17.1] organization(sk2) || -> is_aligned(sk2,sk3)*. % 3.55/3.84 71[0:Res:30.0,39.0] || -> smaller(zero,eta)*. % 3.55/3.84 77[0:Res:28.0,19.2] organization(sk2) || equal(age(sk2,u),zero) -> dissimilar(sk2,u,sk6)*. % 3.55/3.84 82[0:Res:26.0,3.1] has_endowment(sk2) || has_immunity(sk2,sk5)* -> . % 3.55/3.84 91[0:MRR:60.0,23.0] || -> has_immunity(sk2,sk4)*. % 3.55/3.84 92[0:MRR:64.0,22.0] || -> is_aligned(sk2,sk3)*. % 3.55/3.84 93[0:MRR:82.0,23.0] || has_immunity(sk2,sk5)* -> . % 3.55/3.84 94[0:MRR:77.0,22.0] || equal(age(sk2,u),zero) -> dissimilar(sk2,u,sk6)*. % 3.55/3.84 96[1:Spt:59.0] || -> equal(age(sk2,sk5),sigma)**. % 3.55/3.84 105[0:Res:71.0,33.0] || -> smaller_or_equal(zero,eta)*. % 3.55/3.84 108[0:SpL:24.0,46.0] || smaller_or_equal(zero,eta) -> has_immunity(sk2,sk3)*. % 3.55/3.84 112[0:MRR:108.0,105.0] || -> has_immunity(sk2,sk3)*. % 3.55/3.84 144[0:Res:94.1,12.2] || equal(age(sk2,u),zero)** is_aligned(sk2,sk6) is_aligned(sk2,u) -> . % 3.55/3.84 147[0:MRR:144.2,58.1] || equal(age(sk2,u),zero)** is_aligned(sk2,sk6) -> . % 3.55/3.84 149[0:SpL:24.0,147.0] || equal(zero,zero) is_aligned(sk2,sk6)* -> . % 3.55/3.84 150[0:Obv:149.0] || is_aligned(sk2,sk6)* -> . % 3.55/3.84 198[0:Res:56.2,62.0] || is_aligned(sk2,sk3) -> is_aligned(sk2,u) greater(age(sk2,u),sigma)*l. % 3.55/3.84 201[0:MRR:198.0,92.0] || -> is_aligned(sk2,u) greater(age(sk2,u),sigma)*l. % 3.55/3.84 202[1:SpR:96.0,201.1] || -> is_aligned(sk2,sk5)* greater(sigma,sigma). % 3.55/3.84 210[0:Res:201.1,40.0] || greater(sigma,age(sk2,u))*r -> is_aligned(sk2,u). % 3.55/3.84 244[0:NCh:41.2,41.0,3.2,28.0] has_endowment(sk2) || has_immunity(sk2,sk6)* greater(sigma,eta) -> . % 3.55/3.84 250[0:SSi:244.0,23.0,22.0] || has_immunity(sk2,sk6)* greater(sigma,eta) -> . % 3.55/3.84 251[0:MRR:250.1,29.0] || has_immunity(sk2,sk6)* -> . % 3.55/3.84 267[1:SpL:96.0,210.0] || greater(sigma,sigma) -> is_aligned(sk2,sk5)*. % 3.55/3.84 270[1:MRR:267.0,202.1] || -> is_aligned(sk2,sk5)*. % 3.55/3.84 567[0:Res:18.3,44.1] organization(u) organization(u) || is_aligned(u,v) -> is_aligned(u,w) has_immunity(u,w) greater(hazard_of_mortality(u,w),hazard_of_mortality(u,v))*. % 3.55/3.84 572[0:Obv:567.0] organization(u) || is_aligned(u,v) -> is_aligned(u,w) has_immunity(u,w) greater(hazard_of_mortality(u,w),hazard_of_mortality(u,v))*. % 3.55/3.84 3474[0:Res:572.4,31.2] organization(sk2) || is_aligned(sk2,sk5) equal(hazard_of_mortality(sk2,sk4),hazard_of_mortality(sk2,sk3)) greater(hazard_of_mortality(sk2,sk5),hazard_of_mortality(sk2,sk4))*l -> is_aligned(sk2,sk6) has_immunity(sk2,sk6). % 3.55/3.84 3553[0:SSi:3474.0,23.0,22.0] || is_aligned(sk2,sk5) equal(hazard_of_mortality(sk2,sk4),hazard_of_mortality(sk2,sk3)) greater(hazard_of_mortality(sk2,sk5),hazard_of_mortality(sk2,sk4))*l -> is_aligned(sk2,sk6) has_immunity(sk2,sk6). % 3.55/3.84 3554[1:MRR:3553.0,3553.3,3553.4,270.0,150.0,251.0] || equal(hazard_of_mortality(sk2,sk4),hazard_of_mortality(sk2,sk3)) greater(hazard_of_mortality(sk2,sk5),hazard_of_mortality(sk2,sk4))*l -> . % 3.55/3.84 4993[1:Res:51.2,3554.1] || has_immunity(sk2,sk4) equal(hazard_of_mortality(sk2,sk4),hazard_of_mortality(sk2,sk3))** -> has_immunity(sk2,sk5). % 3.55/3.84 5014[1:MRR:4993.0,4993.2,91.0,93.0] || equal(hazard_of_mortality(sk2,sk4),hazard_of_mortality(sk2,sk3))** -> . % 3.55/3.84 5017[1:SpL:54.2,5014.0] || has_immunity(sk2,sk4) has_immunity(sk2,u) equal(hazard_of_mortality(sk2,u),hazard_of_mortality(sk2,sk3))* -> . % 3.55/3.84 5019[1:MRR:5017.0,91.0] || has_immunity(sk2,u) equal(hazard_of_mortality(sk2,u),hazard_of_mortality(sk2,sk3))* -> . % 3.55/3.84 5020[1:EqR:5019.1] || has_immunity(sk2,sk3)* -> . % 3.55/3.84 5029[1:MRR:5020.0,112.0] || -> . % 3.55/3.84 5039[1:Spt:5029.0,59.0,96.0] || equal(age(sk2,sk5),sigma)** -> . % 3.55/3.84 5040[1:Spt:5029.0,59.1] || -> smaller(age(sk2,sk5),sigma)*. % 3.55/3.84 5043[0:MRR:3553.3,3553.4,150.0,251.0] || is_aligned(sk2,sk5) equal(hazard_of_mortality(sk2,sk4),hazard_of_mortality(sk2,sk3)) greater(hazard_of_mortality(sk2,sk5),hazard_of_mortality(sk2,sk4))*l -> . % 3.55/3.84 5048[1:Res:5040.0,38.0] || -> greater(sigma,age(sk2,sk5))*r. % 3.55/3.84 5184[1:Res:5048.0,210.0] || -> is_aligned(sk2,sk5)*. % 3.55/3.84 5252[1:MRR:5043.0,5184.0] || equal(hazard_of_mortality(sk2,sk4),hazard_of_mortality(sk2,sk3)) greater(hazard_of_mortality(sk2,sk5),hazard_of_mortality(sk2,sk4))*l -> . % 3.55/3.84 8305[1:Res:51.2,5252.1] || has_immunity(sk2,sk4) equal(hazard_of_mortality(sk2,sk4),hazard_of_mortality(sk2,sk3))** -> has_immunity(sk2,sk5). % 3.55/3.84 8330[1:MRR:8305.0,8305.2,91.0,93.0] || equal(hazard_of_mortality(sk2,sk4),hazard_of_mortality(sk2,sk3))** -> . % 3.55/3.84 8395[1:SpL:54.2,8330.0] || has_immunity(sk2,sk4) has_immunity(sk2,u) equal(hazard_of_mortality(sk2,u),hazard_of_mortality(sk2,sk3))* -> . % 3.55/3.84 8397[1:MRR:8395.0,91.0] || has_immunity(sk2,u) equal(hazard_of_mortality(sk2,u),hazard_of_mortality(sk2,sk3))* -> . % 3.55/3.84 8398[1:EqR:8397.1] || has_immunity(sk2,sk3)* -> . % 3.55/3.84 8407[1:MRR:8398.0,112.0] || -> . % 3.55/3.84 % SZS output end Refutation % 3.55/3.84 Formulae used in the proof : definition_1_39 definition_1_40 assumption_2_45 assumption_3_46 definition_2_47 definition_2_49 definition_2_51 assumption_13_54 assumption_14_55 assumption_15_56 assumption_15_57 assumption_16_58 lemma_8_59 lemma_8_60 lemma_8_61 lemma_8_62 lemma_8_63 lemma_8_64 lemma_8_65 lemma_8_66 lemma_8_67 lemma_8_68 definition_smaller_or_equal_1 definition_smaller_or_equal_2 definition_smaller_7 definition_smaller_8 meaning_postulate_greater_strict_9 meaning_postulate_greater_transitive_10 % 3.65/3.99 %------------------------------------------------------------------------------