TSTP Solution File: GRP704-12 by Toma---0.4
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% File : Toma---0.4
% Problem : GRP704-12 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %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 : 300s
% DateTime : Thu Aug 31 01:16:07 EDT 2023
% Result : Unsatisfiable 0.20s 0.76s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : GRP704-12 : TPTP v8.1.2. Released v8.1.0.
% 0.13/0.13 % Command : toma --casc %s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 00:03:38 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.76 % SZS status Unsatisfiable
% 0.20/0.76 % SZS output start Proof
% 0.20/0.76 original problem:
% 0.20/0.76 axioms:
% 0.20/0.76 mult(A, ld(A, B)) = B
% 0.20/0.76 ld(A, mult(A, B)) = B
% 0.20/0.76 mult(rd(A, B), B) = A
% 0.20/0.76 rd(mult(A, B), B) = A
% 0.20/0.76 mult(A, unit()) = A
% 0.20/0.76 mult(unit(), A) = A
% 0.20/0.76 mult(A, mult(B, mult(B, C))) = mult(mult(mult(A, B), B), C)
% 0.20/0.76 mult(op_c(), mult(A, B)) = mult(mult(op_c(), A), B)
% 0.20/0.76 mult(A, mult(B, op_c())) = mult(mult(A, B), op_c())
% 0.20/0.76 mult(A, mult(op_c(), B)) = mult(mult(A, op_c()), B)
% 0.20/0.76 op_d() = ld(A, mult(op_c(), A))
% 0.20/0.76 op_e() = mult(mult(rd(op_c(), mult(A, B)), B), A)
% 0.20/0.76 op_f() = mult(A, mult(B, ld(mult(A, B), op_c())))
% 0.20/0.76 goal:
% 0.20/0.76 mult(x4(), mult(op_f(), x5())) != mult(mult(x4(), op_f()), x5())
% 0.20/0.76 To show the unsatisfiability of the original goal,
% 0.20/0.76 it suffices to show that mult(x4(), mult(op_f(), x5())) = mult(mult(x4(), op_f()), x5()) (skolemized goal) is valid under the axioms.
% 0.20/0.76 Here is an equational proof:
% 0.20/0.76 0: mult(X0, ld(X0, X1)) = X1.
% 0.20/0.76 Proof: Axiom.
% 0.20/0.76
% 0.20/0.76 1: ld(X0, mult(X0, X1)) = X1.
% 0.20/0.76 Proof: Axiom.
% 0.20/0.76
% 0.20/0.76 2: mult(rd(X0, X1), X1) = X0.
% 0.20/0.76 Proof: Axiom.
% 0.20/0.76
% 0.20/0.76 4: mult(X0, unit()) = X0.
% 0.20/0.76 Proof: Axiom.
% 0.20/0.76
% 0.20/0.76 5: mult(unit(), X0) = X0.
% 0.20/0.76 Proof: Axiom.
% 0.20/0.76
% 0.20/0.76 7: mult(op_c(), mult(X0, X1)) = mult(mult(op_c(), X0), X1).
% 0.20/0.76 Proof: Axiom.
% 0.20/0.76
% 0.20/0.76 8: mult(X0, mult(X1, op_c())) = mult(mult(X0, X1), op_c()).
% 0.20/0.76 Proof: Axiom.
% 0.20/0.76
% 0.20/0.76 10: op_d() = ld(X0, mult(op_c(), X0)).
% 0.20/0.76 Proof: Axiom.
% 0.20/0.76
% 0.20/0.76 11: op_e() = mult(mult(rd(op_c(), mult(X0, X1)), X1), X0).
% 0.20/0.76 Proof: Axiom.
% 0.20/0.76
% 0.20/0.76 12: op_f() = mult(X0, mult(X1, ld(mult(X0, X1), op_c()))).
% 0.20/0.76 Proof: Axiom.
% 0.20/0.76
% 0.20/0.76 13: op_c() = op_d().
% 0.20/0.76 Proof: A critical pair between equations 1 and 10.
% 0.20/0.76
% 0.20/0.76 19: mult(op_c(), X2) = mult(X2, op_d()).
% 0.20/0.76 Proof: A critical pair between equations 0 and 10.
% 0.20/0.76
% 0.20/0.76 23: mult(rd(op_c(), mult(unit(), X3)), X3) = op_e().
% 0.20/0.76 Proof: A critical pair between equations 4 and 11.
% 0.20/0.76
% 0.20/0.76 24: mult(X3, ld(mult(unit(), X3), op_c())) = op_f().
% 0.20/0.76 Proof: A critical pair between equations 5 and 12.
% 0.20/0.76
% 0.20/0.76 25: op_d() = op_f().
% 0.20/0.76 Proof: Rewrite equation 24,
% 0.20/0.76 lhs with equations [5,13,0]
% 0.20/0.76 rhs with equations [].
% 0.20/0.76
% 0.20/0.76 26: op_d() = op_e().
% 0.20/0.76 Proof: Rewrite equation 23,
% 0.20/0.76 lhs with equations [13,5,2]
% 0.20/0.76 rhs with equations [].
% 0.20/0.76
% 0.20/0.76 32: mult(X0, mult(X1, op_d())) = mult(op_d(), mult(X0, X1)).
% 0.20/0.76 Proof: Rewrite equation 8,
% 0.20/0.76 lhs with equations [13]
% 0.20/0.76 rhs with equations [13,19,13].
% 0.20/0.76
% 0.20/0.76 33: mult(op_d(), mult(X0, X1)) = mult(mult(op_d(), X0), X1).
% 0.20/0.76 Proof: Rewrite equation 7,
% 0.20/0.76 lhs with equations [13]
% 0.20/0.76 rhs with equations [13].
% 0.20/0.76
% 0.20/0.76 34: mult(op_d(), X2) = mult(X2, op_d()).
% 0.20/0.76 Proof: Rewrite equation 19,
% 0.20/0.76 lhs with equations [13]
% 0.20/0.76 rhs with equations [].
% 0.20/0.76
% 0.20/0.76 44: mult(op_d(), mult(X0, X3)) = mult(X0, mult(op_d(), X3)).
% 0.20/0.76 Proof: A critical pair between equations 32 and 34.
% 0.20/0.76
% 0.20/0.76 52: mult(op_e(), mult(X0, X1)) = mult(mult(op_e(), X0), X1).
% 0.20/0.76 Proof: Rewrite equation 33,
% 0.20/0.76 lhs with equations [26]
% 0.20/0.76 rhs with equations [26].
% 0.20/0.76
% 0.20/0.76 59: op_e() = op_f().
% 0.20/0.76 Proof: Rewrite equation 25,
% 0.20/0.76 lhs with equations [26]
% 0.20/0.76 rhs with equations [].
% 0.20/0.76
% 0.20/0.76 61: mult(op_e(), mult(X0, X3)) = mult(X0, mult(op_e(), X3)).
% 0.20/0.76 Proof: Rewrite equation 44,
% 0.20/0.76 lhs with equations [26]
% 0.20/0.76 rhs with equations [26].
% 0.20/0.76
% 0.20/0.76 66: mult(op_e(), X2) = mult(X2, op_e()).
% 0.20/0.76 Proof: Rewrite equation 34,
% 0.20/0.76 lhs with equations [26]
% 0.20/0.76 rhs with equations [26].
% 0.20/0.76
% 0.20/0.76 68: mult(x4(), mult(op_f(), x5())) = mult(mult(x4(), op_f()), x5()).
% 0.20/0.76 Proof: Rewrite lhs with equations [59,61]
% 0.20/0.76 rhs with equations [59,66,52].
% 0.20/0.76
% 0.20/0.76 % SZS output end Proof
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