TSTP Solution File: SYO038-1.003.003 by Moca---0.1
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- Process Solution
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% File : Moca---0.1
% Problem : SYO038-1.003.003 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n024.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 : Thu Jul 21 18:42:13 EDT 2022
% Result : Unsatisfiable 1.99s 2.08s
% Output : Proof 1.99s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SYO038-1.003.003 : TPTP v8.1.0. Released v5.3.0.
% 0.06/0.12 % Command : moca.sh %s
% 0.12/0.33 % Computer : n024.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 : Sat Jul 9 14:19:43 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.99/2.08 % SZS status Unsatisfiable
% 1.99/2.08 % SZS output start Proof
% 1.99/2.08 The input problem is unsatisfiable because
% 1.99/2.08
% 1.99/2.08 [1] the following set of Horn clauses is unsatisfiable:
% 1.99/2.08
% 1.99/2.08 f(N, one) = s(one)
% 1.99/2.08 f(one, s(X)) = s(s(f(one, X)))
% 1.99/2.08 f(s(N), s(X)) = f(N, f(s(N), X))
% 1.99/2.08 d(one)
% 1.99/2.08 d(X) ==> d(s(X))
% 1.99/2.08 d(f(s(s(one)), s(s(one)))) ==> \bottom
% 1.99/2.08
% 1.99/2.08 This holds because
% 1.99/2.08
% 1.99/2.08 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 1.99/2.08
% 1.99/2.08 E:
% 1.99/2.08 d(one) = true__
% 1.99/2.08 f(N, one) = s(one)
% 1.99/2.08 f(one, s(X)) = s(s(f(one, X)))
% 1.99/2.08 f(s(N), s(X)) = f(N, f(s(N), X))
% 1.99/2.08 f1(d(X), X) = true__
% 1.99/2.08 f1(true__, X) = d(s(X))
% 1.99/2.08 f2(d(f(s(s(one)), s(s(one))))) = true__
% 1.99/2.08 f2(true__) = false__
% 1.99/2.08 G:
% 1.99/2.08 true__ = false__
% 1.99/2.08
% 1.99/2.08 This holds because
% 1.99/2.08
% 1.99/2.08 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 1.99/2.08
% 1.99/2.08
% 1.99/2.08 d(one) -> true__
% 1.99/2.08 d(s(one)) -> true__
% 1.99/2.08 d(s(s(one))) -> true__
% 1.99/2.08 d(s(s(s(one)))) -> true__
% 1.99/2.08 d(s(s(s(s(one))))) -> true__
% 1.99/2.08 d(s(s(s(s(s(one)))))) -> true__
% 1.99/2.08 d(s(s(s(s(s(s(one))))))) -> true__
% 1.99/2.08 d(s(s(s(s(s(s(s(one)))))))) -> true__
% 1.99/2.08 d(s(s(s(s(s(s(s(s(one))))))))) -> true__
% 1.99/2.08 d(s(s(s(s(s(s(s(s(s(one)))))))))) -> true__
% 1.99/2.08 d(s(s(s(s(s(s(s(s(s(s(one))))))))))) -> true__
% 1.99/2.08 d(s(s(s(s(s(s(s(s(s(s(s(one)))))))))))) -> true__
% 1.99/2.08 d(s(s(s(s(s(s(s(s(s(s(s(s(one))))))))))))) -> true__
% 1.99/2.08 d(s(s(s(s(s(s(s(s(s(s(s(s(s(one)))))))))))))) -> true__
% 1.99/2.08 d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one))))))))))))))) -> true__
% 1.99/2.08 d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one)))))))))))))))) -> true__
% 1.99/2.08 d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one))))))))))))))))) -> true__
% 1.99/2.08 f(N, one) -> s(one)
% 1.99/2.08 f(one, s(X)) -> s(s(f(one, X)))
% 1.99/2.08 f(s(N), s(X)) -> f(N, f(s(N), X))
% 1.99/2.08 f1(d(X), X) -> true__
% 1.99/2.08 f1(true__, X) -> d(s(X))
% 1.99/2.08 f2(d(f(s(s(one)), s(s(one))))) -> true__
% 1.99/2.08 f2(d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one))))))))))))))))) -> true__
% 1.99/2.08 f2(true__) -> false__
% 1.99/2.08 false__ -> true__
% 1.99/2.08 with the LPO induced by
% 1.99/2.08 f2 > f1 > d > f > s > one > false__ > true__
% 1.99/2.08
% 1.99/2.08 % SZS output end Proof
% 1.99/2.08
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