TSTP Solution File: GRP703-12 by Toma---0.4
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% File : Toma---0.4
% Problem : GRP703-12 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n012.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 0.19s 0.80s
% Output : CNFRefutation 0.19s
% 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 : GRP703-12 : TPTP v8.1.2. Released v8.1.0.
% 0.00/0.14 % Command : toma --casc %s
% 0.13/0.35 % Computer : n012.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 23:31:54 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.80 % SZS status Unsatisfiable
% 0.19/0.80 % SZS output start Proof
% 0.19/0.80 original problem:
% 0.19/0.80 axioms:
% 0.19/0.80 mult(A, ld(A, B)) = B
% 0.19/0.80 ld(A, mult(A, B)) = B
% 0.19/0.80 mult(rd(A, B), B) = A
% 0.19/0.80 rd(mult(A, B), B) = A
% 0.19/0.80 mult(A, unit()) = A
% 0.19/0.80 mult(unit(), A) = A
% 0.19/0.80 mult(A, mult(B, mult(B, C))) = mult(mult(mult(A, B), B), C)
% 0.19/0.80 mult(op_c(), mult(A, B)) = mult(mult(op_c(), A), B)
% 0.19/0.80 mult(A, mult(B, op_c())) = mult(mult(A, B), op_c())
% 0.19/0.80 mult(A, mult(op_c(), B)) = mult(mult(A, op_c()), B)
% 0.19/0.80 op_d() = ld(A, mult(op_c(), A))
% 0.19/0.80 op_e() = mult(mult(rd(op_c(), mult(A, B)), B), A)
% 0.19/0.80 op_f() = mult(A, mult(B, ld(mult(A, B), op_c())))
% 0.19/0.80 goal:
% 0.19/0.80 mult(x2(), mult(op_e(), x3())) != mult(mult(x2(), op_e()), x3())
% 0.19/0.80 To show the unsatisfiability of the original goal,
% 0.19/0.80 it suffices to show that mult(x2(), mult(op_e(), x3())) = mult(mult(x2(), op_e()), x3()) (skolemized goal) is valid under the axioms.
% 0.19/0.80 Here is an equational proof:
% 0.19/0.80 0: mult(X0, ld(X0, X1)) = X1.
% 0.19/0.80 Proof: Axiom.
% 0.19/0.80
% 0.19/0.80 1: ld(X0, mult(X0, X1)) = X1.
% 0.19/0.80 Proof: Axiom.
% 0.19/0.80
% 0.19/0.80 2: mult(rd(X0, X1), X1) = X0.
% 0.19/0.80 Proof: Axiom.
% 0.19/0.80
% 0.19/0.80 4: mult(X0, unit()) = X0.
% 0.19/0.80 Proof: Axiom.
% 0.19/0.80
% 0.19/0.80 5: mult(unit(), X0) = X0.
% 0.19/0.80 Proof: Axiom.
% 0.19/0.80
% 0.19/0.80 7: mult(op_c(), mult(X0, X1)) = mult(mult(op_c(), X0), X1).
% 0.19/0.80 Proof: Axiom.
% 0.19/0.80
% 0.19/0.80 8: mult(X0, mult(X1, op_c())) = mult(mult(X0, X1), op_c()).
% 0.19/0.80 Proof: Axiom.
% 0.19/0.80
% 0.19/0.80 10: op_d() = ld(X0, mult(op_c(), X0)).
% 0.19/0.80 Proof: Axiom.
% 0.19/0.80
% 0.19/0.80 11: op_e() = mult(mult(rd(op_c(), mult(X0, X1)), X1), X0).
% 0.19/0.80 Proof: Axiom.
% 0.19/0.80
% 0.19/0.80 12: op_f() = mult(X0, mult(X1, ld(mult(X0, X1), op_c()))).
% 0.19/0.80 Proof: Axiom.
% 0.19/0.80
% 0.19/0.80 13: op_c() = op_d().
% 0.19/0.80 Proof: A critical pair between equations 1 and 10.
% 0.19/0.80
% 0.19/0.80 19: mult(op_c(), X2) = mult(X2, op_d()).
% 0.19/0.80 Proof: A critical pair between equations 0 and 10.
% 0.19/0.80
% 0.19/0.80 23: mult(rd(op_c(), mult(unit(), X3)), X3) = op_e().
% 0.19/0.80 Proof: A critical pair between equations 4 and 11.
% 0.19/0.80
% 0.19/0.80 24: mult(X3, ld(mult(unit(), X3), op_c())) = op_f().
% 0.19/0.80 Proof: A critical pair between equations 5 and 12.
% 0.19/0.80
% 0.19/0.80 25: op_d() = op_f().
% 0.19/0.80 Proof: Rewrite equation 24,
% 0.19/0.80 lhs with equations [5,13,0]
% 0.19/0.80 rhs with equations [].
% 0.19/0.80
% 0.19/0.80 26: op_d() = op_e().
% 0.19/0.80 Proof: Rewrite equation 23,
% 0.19/0.80 lhs with equations [13,5,2]
% 0.19/0.80 rhs with equations [].
% 0.19/0.80
% 0.19/0.80 32: mult(X0, mult(X1, op_d())) = mult(op_d(), mult(X0, X1)).
% 0.19/0.80 Proof: Rewrite equation 8,
% 0.19/0.80 lhs with equations [13]
% 0.19/0.80 rhs with equations [13,19,13].
% 0.19/0.80
% 0.19/0.80 33: mult(op_d(), mult(X0, X1)) = mult(mult(op_d(), X0), X1).
% 0.19/0.80 Proof: Rewrite equation 7,
% 0.19/0.80 lhs with equations [13]
% 0.19/0.80 rhs with equations [13].
% 0.19/0.80
% 0.19/0.80 34: mult(op_d(), X2) = mult(X2, op_d()).
% 0.19/0.80 Proof: Rewrite equation 19,
% 0.19/0.80 lhs with equations [13]
% 0.19/0.80 rhs with equations [].
% 0.19/0.80
% 0.19/0.80 44: mult(op_d(), mult(X0, X3)) = mult(X0, mult(op_d(), X3)).
% 0.19/0.80 Proof: A critical pair between equations 32 and 34.
% 0.19/0.80
% 0.19/0.80 53: mult(op_f(), mult(X0, X1)) = mult(mult(op_f(), X0), X1).
% 0.19/0.80 Proof: Rewrite equation 33,
% 0.19/0.80 lhs with equations [25]
% 0.19/0.80 rhs with equations [25].
% 0.19/0.80
% 0.19/0.80 59: op_f() = op_e().
% 0.19/0.80 Proof: Rewrite equation 26,
% 0.19/0.80 lhs with equations [25]
% 0.19/0.80 rhs with equations [].
% 0.19/0.80
% 0.19/0.80 61: mult(op_f(), mult(X0, X3)) = mult(X0, mult(op_f(), X3)).
% 0.19/0.80 Proof: Rewrite equation 44,
% 0.19/0.80 lhs with equations [25]
% 0.19/0.80 rhs with equations [25].
% 0.19/0.80
% 0.19/0.80 66: mult(op_f(), X2) = mult(X2, op_f()).
% 0.19/0.80 Proof: Rewrite equation 34,
% 0.19/0.80 lhs with equations [25]
% 0.19/0.80 rhs with equations [25].
% 0.19/0.80
% 0.19/0.80 68: mult(x2(), mult(op_e(), x3())) = mult(mult(x2(), op_e()), x3()).
% 0.19/0.80 Proof: Rewrite lhs with equations [59,61]
% 0.19/0.80 rhs with equations [59,66,53].
% 0.19/0.80
% 0.19/0.80 % SZS output end Proof
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