0.12/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.12/0.13 % Command : nanocop_casc.sh %s %d 0.14/0.34 % Computer : n019.cluster.edu 0.14/0.34 % Model : x86_64 x86_64 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.34 % Memory : 8042.1875MB 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.34 % CPULimit : 180 0.14/0.34 % DateTime : Thu Aug 29 12:33:22 EDT 2019 0.21/0.34 % CPUTime : 101.13/97.85 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p 101.13/97.85 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p 101.13/97.85 101.13/97.85 - the following list represents a non-clausal connection proof 101.13/97.85 (a tree in which each node is labelled with a nested clause) 101.13/97.85 - I^V is a skolem term f_I(V) for variable list V 101.13/97.85 - (I^K)^V:C is the (nested) clause C with index (I^K)^V, in which 101.13/97.85 I is the unique index of C, K distinguishes different copies 101.13/97.85 of C, and V is the list of (instantiated) variables in C 101.13/97.86 101.13/97.86 [(221 ^ 0) ^ [] : [-(int_leq(219 ^ [], n))], [(118 ^ 1) ^ [219 ^ [], 218 ^ []] : [int_leq(219 ^ [], n), int_leq(int_one, 218 ^ []), int_leq(218 ^ [], n), int_leq(int_one, 219 ^ []), 133 ^ 1 : [(134 ^ 1) ^ [197 ^ [219 ^ [], 218 ^ []]] : [219 ^ [] = plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]), int_less(int_zero, 197 ^ [219 ^ [], 218 ^ []]), 141 ^ 1 : [(142 ^ 1) ^ [218 ^ []] : [-(real_zero = a(218 ^ [], plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]))), int_leq(218 ^ [], 218 ^ []), int_leq(int_one, 218 ^ [])]]], (152 ^ 1) ^ [_26752] : [218 ^ [] = plus(219 ^ [], _26752), int_less(int_zero, _26752), 159 ^ 1 : [(160 ^ 1) ^ [_26786] : [-(a(plus(_26786, _26752), _26786) = qr(plus(_26786, _26752), _26786)), int_leq(int_one, _26786), int_leq(_26786, 219 ^ [])]]]]], [(225 ^ 2) ^ [] : [-(int_leq(int_one, 218 ^ []))]], [(180 ^ 2) ^ [n, 218 ^ []] : [-(int_leq(218 ^ [], n)), 181 ^ 2 : [(182 ^ 2) ^ [] : [int_less(218 ^ [], n)], (184 ^ 2) ^ [] : [n = 218 ^ []]]], [(20 ^ 5) ^ [n, 219 ^ [], 218 ^ [], 218 ^ []] : [-(int_less(218 ^ [], n)), int_less(218 ^ [], 219 ^ []), 218 ^ [] = 218 ^ [], 219 ^ [] = n], [(223 ^ 6) ^ [] : [-(int_less(218 ^ [], 219 ^ []))]], [(10 ^ 6) ^ [218 ^ [], plus(n, 197 ^ [218 ^ [], n]), 218 ^ []] : [-(218 ^ [] = 218 ^ []), 218 ^ [] = plus(n, 197 ^ [218 ^ [], n]), plus(n, 197 ^ [218 ^ [], n]) = 218 ^ []], [(194 ^ 7) ^ [218 ^ [], n] : [-(218 ^ [] = plus(n, 197 ^ [218 ^ [], n])), 198 ^ 7 : [(199 ^ 7) ^ [] : []], int_less(n, 218 ^ [])], [(188 ^ 8) ^ [218 ^ [], n] : [-(int_less(n, 218 ^ [])), -(int_leq(218 ^ [], n))], [_28186 ^ _28187 : [int_leq(218 ^ [], n)]]]], [(4 ^ 7) ^ [plus(n, 197 ^ [218 ^ [], n]), 218 ^ []] : [-(plus(n, 197 ^ [218 ^ [], n]) = 218 ^ []), 218 ^ [] = plus(n, 197 ^ [218 ^ [], n])], [_28348 ^ _28349 : [-(218 ^ [] = plus(n, 197 ^ [218 ^ [], n]))]]]], [(4 ^ 6) ^ [219 ^ [], n] : [-(219 ^ [] = n), n = 219 ^ []], [(170 ^ 7) ^ [n, 219 ^ []] : [-(n = 219 ^ []), int_leq(219 ^ [], n), -(int_less(219 ^ [], n))], [_28635 ^ _28636 : [-(int_leq(219 ^ [], n))]], [(80 ^ 8) ^ [n, 219 ^ [], 218 ^ []] : [int_less(219 ^ [], n), -(int_less(218 ^ [], n)), int_less(218 ^ [], 219 ^ [])], [_28818 ^ _28819 : [int_less(218 ^ [], n)]], [_28836 ^ _28837 : [-(int_less(218 ^ [], 219 ^ []))]]]]]]], [(108 ^ 2) ^ [219 ^ []] : [-(int_leq(int_one, 219 ^ [])), int_less(int_zero, 219 ^ [])], [(20 ^ 3) ^ [219 ^ [], 219 ^ [], int_zero, 218 ^ []] : [-(int_less(int_zero, 219 ^ [])), int_less(218 ^ [], 219 ^ []), 218 ^ [] = int_zero, 219 ^ [] = 219 ^ []], [(223 ^ 4) ^ [] : [-(int_less(218 ^ [], 219 ^ []))]], [(170 ^ 4) ^ [218 ^ [], int_zero] : [-(218 ^ [] = int_zero), int_leq(int_zero, 218 ^ []), -(int_less(int_zero, 218 ^ []))], [(180 ^ 5) ^ [218 ^ [], int_zero] : [-(int_leq(int_zero, 218 ^ [])), 181 ^ 5 : [(182 ^ 5) ^ [] : [int_less(int_zero, 218 ^ [])], (184 ^ 5) ^ [] : [218 ^ [] = int_zero]]], [(102 ^ 8) ^ [218 ^ []] : [-(int_less(int_zero, 218 ^ [])), int_leq(int_one, 218 ^ [])], [_29740 ^ _29741 : [-(int_leq(int_one, 218 ^ []))]]]], [(80 ^ 5) ^ [219 ^ [], 218 ^ [], int_zero] : [int_less(int_zero, 218 ^ []), -(int_less(int_zero, 219 ^ [])), int_less(218 ^ [], 219 ^ [])], [_29931 ^ _29932 : [int_less(int_zero, 219 ^ [])]], [_29949 ^ _29950 : [-(int_less(218 ^ [], 219 ^ []))]]]], [(10 ^ 4) ^ [219 ^ [], plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]), 219 ^ []] : [-(219 ^ [] = 219 ^ []), 219 ^ [] = plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]), plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]) = 219 ^ []], [(10 ^ 5) ^ [plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]), plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]), 219 ^ []] : [-(219 ^ [] = plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []])), 219 ^ [] = plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]), plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]) = plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []])], [(194 ^ 6) ^ [219 ^ [], 218 ^ []] : [-(219 ^ [] = plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []])), 198 ^ 6 : [(199 ^ 6) ^ [] : []], int_less(218 ^ [], 219 ^ [])], [(223 ^ 7) ^ [] : [-(int_less(218 ^ [], 219 ^ []))]]], [(2 ^ 6) ^ [plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []])] : [-(plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]) = plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]))]]], [(4 ^ 5) ^ [plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]), 219 ^ []] : [-(plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]) = 219 ^ []), 219 ^ [] = plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []])], [_30895 ^ _30896 : [-(219 ^ [] = plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]))]]]]]], [(10 ^ 4) ^ [plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]), plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]), 219 ^ []] : [-(219 ^ [] = plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []])), 219 ^ [] = plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]), plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]) = plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []])], [(194 ^ 5) ^ [219 ^ [], 218 ^ []] : [-(219 ^ [] = plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []])), 198 ^ 5 : [(199 ^ 5) ^ [] : []], int_less(218 ^ [], 219 ^ [])], [(223 ^ 6) ^ [] : [-(int_less(218 ^ [], 219 ^ []))]]], [(170 ^ 5) ^ [plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]), plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []])] : [-(plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]) = plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []])), int_leq(plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]), plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []])), -(int_less(plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]), plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []])))], [(180 ^ 6) ^ [plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]), plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []])] : [-(int_leq(plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]), plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]))), 181 ^ 6 : [(182 ^ 6) ^ [] : [int_less(plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]), plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]))], (184 ^ 6) ^ [] : [plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]) = plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []])]]], [(188 ^ 9) ^ [plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]), plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []])] : [-(int_less(plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]), plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]))), -(int_leq(plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]), plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []])))], [_31890 ^ _31891 : [int_leq(plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]), plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]))]]]], [(194 ^ 6) ^ [plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]), plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []])] : [int_less(plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]), plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []])), 198 ^ 6 : [(199 ^ 6) ^ [] : [-(plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]) = plus(plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]), 197 ^ [plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]), plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []])]))], (201 ^ 6) ^ [] : [-(int_less(int_zero, 197 ^ [plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]), plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []])]))]]], [(10 ^ 9) ^ [plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]), plus(plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]), 197 ^ [plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]), plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []])]), plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []])] : [plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]) = plus(plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]), 197 ^ [plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]), plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []])]), -(plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]) = plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []])), plus(plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]), 197 ^ [plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]), plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []])]) = plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []])], [_32307 ^ _32308 : [plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]) = plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []])]], [(4 ^ 10) ^ [plus(plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]), 197 ^ [plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]), plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []])]), plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []])] : [-(plus(plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]), 197 ^ [plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]), plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []])]) = plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []])), plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]) = plus(plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]), 197 ^ [plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]), plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []])])], [_32463 ^ _32464 : [-(plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]) = plus(plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]), 197 ^ [plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]), plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []])]))]]]]]]], [(194 ^ 4) ^ [219 ^ [], 218 ^ []] : [-(int_less(int_zero, 197 ^ [219 ^ [], 218 ^ []])), 198 ^ 4 : [(201 ^ 4) ^ [] : []], int_less(218 ^ [], 219 ^ [])], [(223 ^ 5) ^ [] : [-(int_less(218 ^ [], 219 ^ []))]]], [(10 ^ 6) ^ [a(218 ^ [], plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []])), real_zero, real_zero] : [real_zero = a(218 ^ [], plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []])), -(real_zero = a(218 ^ [], plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]))), real_zero = real_zero], [(10 ^ 7) ^ [a(218 ^ [], 219 ^ []), a(218 ^ [], plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []])), real_zero] : [real_zero = a(218 ^ [], plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []])), -(real_zero = a(218 ^ [], 219 ^ [])), a(218 ^ [], plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []])) = a(218 ^ [], 219 ^ [])], [(227 ^ 8) ^ [] : [real_zero = a(218 ^ [], 219 ^ [])]], [(4 ^ 8) ^ [a(218 ^ [], plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []])), a(218 ^ [], 219 ^ [])] : [-(a(218 ^ [], plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []])) = a(218 ^ [], 219 ^ [])), a(218 ^ [], 219 ^ []) = a(218 ^ [], plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]))], [(68 ^ 9) ^ [plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]), 219 ^ [], 218 ^ [], 218 ^ []] : [-(a(218 ^ [], 219 ^ []) = a(218 ^ [], plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]))), 218 ^ [] = 218 ^ [], 219 ^ [] = plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []])], [(2 ^ 10) ^ [218 ^ []] : [-(218 ^ [] = 218 ^ [])]], [_33680 ^ _33681 : [-(219 ^ [] = plus(218 ^ [], 197 ^ [219 ^ [], 218 ^ []]))]]]]], [(170 ^ 7) ^ [real_zero, real_zero] : [-(real_zero = real_zero), int_leq(real_zero, real_zero), -(int_less(real_zero, real_zero))], [(180 ^ 8) ^ [real_zero, real_zero] : [-(int_leq(real_zero, real_zero)), 181 ^ 8 : [(182 ^ 8) ^ [] : [int_less(real_zero, real_zero)], (184 ^ 8) ^ [] : [real_zero = real_zero]]], [(188 ^ 11) ^ [real_zero, real_zero] : [-(int_less(real_zero, real_zero)), -(int_leq(real_zero, real_zero))], [_34198 ^ _34199 : [int_leq(real_zero, real_zero)]]]], [(194 ^ 8) ^ [real_zero, real_zero] : [int_less(real_zero, real_zero), 198 ^ 8 : [(199 ^ 8) ^ [] : [-(real_zero = plus(real_zero, 197 ^ [real_zero, real_zero]))], (201 ^ 8) ^ [] : [-(int_less(int_zero, 197 ^ [real_zero, real_zero]))]]], [(10 ^ 11) ^ [real_zero, plus(real_zero, 197 ^ [real_zero, real_zero]), real_zero] : [real_zero = plus(real_zero, 197 ^ [real_zero, real_zero]), -(real_zero = real_zero), plus(real_zero, 197 ^ [real_zero, real_zero]) = real_zero], [_34615 ^ _34616 : [real_zero = real_zero]], [(4 ^ 12) ^ [plus(real_zero, 197 ^ [real_zero, real_zero]), real_zero] : [-(plus(real_zero, 197 ^ [real_zero, real_zero]) = real_zero), real_zero = plus(real_zero, 197 ^ [real_zero, real_zero])], [_34771 ^ _34772 : [-(real_zero = plus(real_zero, 197 ^ [real_zero, real_zero]))]]]]]]], [(180 ^ 6) ^ [218 ^ [], 218 ^ []] : [-(int_leq(218 ^ [], 218 ^ [])), 181 ^ 6 : [(182 ^ 6) ^ [] : [int_less(218 ^ [], 218 ^ [])], (184 ^ 6) ^ [] : [218 ^ [] = 218 ^ []]]], [(188 ^ 9) ^ [218 ^ [], 218 ^ []] : [-(int_less(218 ^ [], 218 ^ [])), -(int_leq(218 ^ [], 218 ^ []))], [_35173 ^ _35174 : [int_leq(218 ^ [], 218 ^ [])]]]], [_35199 ^ _35200 : [-(int_leq(int_one, 218 ^ []))]]]] 101.13/97.86 101.13/97.87 % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p 101.13/97.87 EOF