TSTP Solution File: GRP704-10 by Toma---0.4
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% File : Toma---0.4
% Problem : GRP704-10 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n019.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 01:16:06 EDT 2023
% Result : Unsatisfiable 0.18s 0.55s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP704-10 : TPTP v8.1.2. Released v8.1.0.
% 0.00/0.13 % Command : toma --casc %s
% 0.13/0.33 % Computer : n019.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Aug 28 21:38:58 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.18/0.55 % SZS status Unsatisfiable
% 0.18/0.55 % SZS output start Proof
% 0.18/0.55 original problem:
% 0.18/0.55 axioms:
% 0.18/0.55 mult(A, ld(A, B)) = B
% 0.18/0.55 ld(A, mult(A, B)) = B
% 0.18/0.55 mult(rd(A, B), B) = A
% 0.18/0.55 rd(mult(A, B), B) = A
% 0.18/0.55 mult(A, unit()) = A
% 0.18/0.55 mult(unit(), A) = A
% 0.18/0.55 mult(A, mult(B, mult(B, C))) = mult(mult(mult(A, B), B), C)
% 0.18/0.55 mult(op_c(), mult(A, B)) = mult(mult(op_c(), A), B)
% 0.18/0.55 mult(A, mult(B, op_c())) = mult(mult(A, B), op_c())
% 0.18/0.55 mult(A, mult(op_c(), B)) = mult(mult(A, op_c()), B)
% 0.18/0.55 op_d() = ld(A, mult(op_c(), A))
% 0.18/0.55 op_e() = mult(mult(rd(op_c(), mult(A, B)), B), A)
% 0.18/0.55 op_f() = mult(A, mult(B, ld(mult(A, B), op_c())))
% 0.18/0.55 goal:
% 0.18/0.55 mult(op_f(), mult(x4(), x5())) != mult(mult(op_f(), x4()), x5())
% 0.18/0.55 To show the unsatisfiability of the original goal,
% 0.18/0.55 it suffices to show that mult(op_f(), mult(x4(), x5())) = mult(mult(op_f(), x4()), x5()) (skolemized goal) is valid under the axioms.
% 0.18/0.55 Here is an equational proof:
% 0.18/0.55 0: mult(X0, ld(X0, X1)) = X1.
% 0.18/0.55 Proof: Axiom.
% 0.18/0.55
% 0.18/0.55 1: ld(X0, mult(X0, X1)) = X1.
% 0.18/0.55 Proof: Axiom.
% 0.18/0.55
% 0.18/0.55 5: mult(unit(), X0) = X0.
% 0.18/0.55 Proof: Axiom.
% 0.18/0.55
% 0.18/0.55 7: mult(op_c(), mult(X0, X1)) = mult(mult(op_c(), X0), X1).
% 0.18/0.55 Proof: Axiom.
% 0.18/0.55
% 0.18/0.55 10: op_d() = ld(X0, mult(op_c(), X0)).
% 0.18/0.55 Proof: Axiom.
% 0.18/0.55
% 0.18/0.55 12: op_f() = mult(X0, mult(X1, ld(mult(X0, X1), op_c()))).
% 0.18/0.55 Proof: Axiom.
% 0.18/0.55
% 0.18/0.55 13: op_c() = op_d().
% 0.18/0.55 Proof: A critical pair between equations 1 and 10.
% 0.18/0.55
% 0.18/0.55 24: mult(X3, ld(mult(unit(), X3), op_c())) = op_f().
% 0.18/0.55 Proof: A critical pair between equations 5 and 12.
% 0.18/0.55
% 0.18/0.55 25: op_d() = op_f().
% 0.18/0.55 Proof: Rewrite equation 24,
% 0.18/0.55 lhs with equations [5,13,0]
% 0.18/0.55 rhs with equations [].
% 0.18/0.55
% 0.18/0.55 33: mult(op_d(), mult(X0, X1)) = mult(mult(op_d(), X0), X1).
% 0.18/0.55 Proof: Rewrite equation 7,
% 0.18/0.55 lhs with equations [13]
% 0.18/0.55 rhs with equations [13].
% 0.18/0.55
% 0.18/0.55 35: mult(op_f(), mult(x4(), x5())) = mult(mult(op_f(), x4()), x5()).
% 0.18/0.55 Proof: Rewrite lhs with equations [25]
% 0.18/0.55 rhs with equations [25,33].
% 0.18/0.55
% 0.18/0.55 % SZS output end Proof
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