%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : SET041-3 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp % Command : run_spass %d %s % Computer : n011.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 05:23:01 EDT 2022 % Result : Unsatisfiable 164.28s 164.46s % Output : Refutation 164.28s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET041-3 : TPTP v8.1.0. Released v1.0.0. % 0.03/0.13 % Command : run_spass %d %s % 0.12/0.34 % Computer : n011.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Sun Jul 10 13:01:26 EDT 2022 % 0.12/0.34 % CPUTime : % 164.28/164.46 % 164.28/164.46 SPASS V 3.9 % 164.28/164.46 SPASS beiseite: Proof found. % 164.28/164.46 % SZS status Theorem % 164.28/164.46 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p % 164.28/164.46 SPASS derived 95631 clauses, backtracked 8460 clauses, performed 34 splits and kept 45974 clauses. % 164.28/164.46 SPASS allocated 180778 KBytes. % 164.28/164.46 SPASS spent 0:2:40.21 on the problem. % 164.28/164.46 0:00:00.04 for the input. % 164.28/164.46 0:00:00.00 for the FLOTTER CNF translation. % 164.28/164.46 0:00:01.75 for inferences. % 164.28/164.46 0:0:12.46 for the backtracking. % 164.28/164.46 0:2:23.70 for the reduction. % 164.28/164.46 % 164.28/164.46 % 164.28/164.46 Here is a proof with depth 2, length 12 : % 164.28/164.46 % SZS output start Refutation % 164.28/164.46 4[0:Inp] || subset(u,v)*+ subset(v,u)* -> equal(v,u). % 164.28/164.46 24[0:Inp] function(u) || member(v,domain_of(u)) -> subset(apply(w,apply(u,v)),apply(compose(w,u),v))*r. % 164.28/164.46 25[0:Inp] function(u) || -> subset(apply(compose(v,u),w),apply(v,apply(u,w)))*l. % 164.28/164.46 26[0:Inp] || -> function(a_function)*. % 164.28/164.46 27[0:Inp] || -> member(a,domain_of(a_function))*. % 164.28/164.46 28[0:Inp] || equal(apply(compose(another_function,a_function),a),apply(another_function,apply(a_function,a)))** -> . % 164.28/164.46 10645[0:Res:24.2,4.0] function(u) || member(v,domain_of(u)) subset(apply(compose(w,u),v),apply(w,apply(u,v)))*l -> equal(apply(compose(w,u),v),apply(w,apply(u,v))). % 164.28/164.46 10657[0:MRR:10645.2,25.1] function(u) || member(v,domain_of(u)) -> equal(apply(compose(w,u),v),apply(w,apply(u,v)))**. % 164.28/164.46 116241[0:SpL:10657.2,28.0] function(a_function) || member(a,domain_of(a_function)) equal(apply(another_function,apply(a_function,a)),apply(another_function,apply(a_function,a)))* -> . % 164.28/164.46 116251[0:Obv:116241.2] function(a_function) || member(a,domain_of(a_function))* -> . % 164.28/164.46 116252[0:SSi:116251.0,26.0] || member(a,domain_of(a_function))* -> . % 164.28/164.46 116253[0:MRR:116252.0,27.0] || -> . % 164.28/164.46 % SZS output end Refutation % 164.28/164.46 Formulae used in the proof : two_sets_equal apply_for_composition1 apply_for_composition2 a_function member_of_domain prove_apply_for_composition3 % 164.28/164.46 %------------------------------------------------------------------------------