TSTP Solution File: GRP670-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP670-1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 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 01:19:37 EDT 2023
% Result : Unsatisfiable 64.13s 8.84s
% Output : Proof 64.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP670-1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n024.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 28 21:59:38 EDT 2023
% 0.14/0.35 % CPUTime :
% 64.13/8.84 Command-line arguments: --no-flatten-goal
% 64.13/8.84
% 64.13/8.84 % SZS status Unsatisfiable
% 64.13/8.84
% 64.56/8.86 % SZS output start Proof
% 64.56/8.86 Axiom 1 (c05): mult(X, unit) = X.
% 64.56/8.86 Axiom 2 (c06): mult(unit, X) = X.
% 64.56/8.86 Axiom 3 (c02): ld(X, mult(X, Y)) = Y.
% 64.56/8.86 Axiom 4 (c04): rd(mult(X, Y), Y) = X.
% 64.56/8.86 Axiom 5 (c01): mult(X, ld(X, Y)) = Y.
% 64.56/8.86 Axiom 6 (c03): mult(rd(X, Y), Y) = X.
% 64.56/8.86 Axiom 7 (c07): mult(i(X), mult(X, Y)) = Y.
% 64.56/8.86 Axiom 8 (c08): mult(mult(X, Y), i(Y)) = X.
% 64.56/8.86 Axiom 9 (c09): mult(mult(X, Y), mult(Z, mult(X, Y))) = mult(mult(mult(X, mult(Y, Z)), X), Y).
% 64.56/8.86
% 64.56/8.86 Lemma 10: ld(i(X), Y) = mult(X, Y).
% 64.56/8.86 Proof:
% 64.56/8.86 ld(i(X), Y)
% 64.56/8.86 = { by axiom 7 (c07) R->L }
% 64.56/8.86 ld(i(X), mult(i(X), mult(X, Y)))
% 64.56/8.86 = { by axiom 3 (c02) }
% 64.56/8.86 mult(X, Y)
% 64.56/8.86
% 64.56/8.86 Lemma 11: mult(X, i(Y)) = rd(X, Y).
% 64.56/8.86 Proof:
% 64.56/8.86 mult(X, i(Y))
% 64.56/8.86 = { by axiom 6 (c03) R->L }
% 64.56/8.86 mult(mult(rd(X, Y), Y), i(Y))
% 64.56/8.86 = { by axiom 8 (c08) }
% 64.56/8.86 rd(X, Y)
% 64.56/8.86
% 64.56/8.86 Lemma 12: mult(i(X), Y) = ld(X, Y).
% 64.56/8.86 Proof:
% 64.56/8.86 mult(i(X), Y)
% 64.56/8.86 = { by axiom 5 (c01) R->L }
% 64.56/8.86 mult(i(X), mult(X, ld(X, Y)))
% 64.56/8.86 = { by axiom 7 (c07) }
% 64.56/8.86 ld(X, Y)
% 64.56/8.86
% 64.56/8.86 Lemma 13: rd(X, i(Y)) = mult(X, Y).
% 64.56/8.86 Proof:
% 64.56/8.86 rd(X, i(Y))
% 64.56/8.86 = { by axiom 8 (c08) R->L }
% 64.56/8.86 rd(mult(mult(X, Y), i(Y)), i(Y))
% 64.56/8.86 = { by axiom 4 (c04) }
% 64.56/8.86 mult(X, Y)
% 64.56/8.86
% 64.56/8.86 Lemma 14: rd(i(X), Y) = ld(X, i(Y)).
% 64.56/8.86 Proof:
% 64.56/8.86 rd(i(X), Y)
% 64.56/8.86 = { by lemma 11 R->L }
% 64.56/8.86 mult(i(X), i(Y))
% 64.56/8.86 = { by lemma 12 }
% 64.56/8.86 ld(X, i(Y))
% 64.56/8.86
% 64.56/8.86 Lemma 15: i(ld(X, Y)) = ld(Y, X).
% 64.56/8.86 Proof:
% 64.56/8.86 i(ld(X, Y))
% 64.56/8.86 = { by axiom 3 (c02) R->L }
% 64.56/8.86 ld(mult(X, ld(X, Y)), mult(mult(X, ld(X, Y)), i(ld(X, Y))))
% 64.56/8.86 = { by axiom 8 (c08) }
% 64.56/8.86 ld(mult(X, ld(X, Y)), X)
% 64.56/8.86 = { by axiom 5 (c01) }
% 64.56/8.86 ld(Y, X)
% 64.56/8.86
% 64.56/8.86 Lemma 16: rd(X, mult(Y, X)) = i(Y).
% 64.56/8.86 Proof:
% 64.56/8.86 rd(X, mult(Y, X))
% 64.56/8.86 = { by axiom 7 (c07) R->L }
% 64.56/8.86 rd(mult(i(Y), mult(Y, X)), mult(Y, X))
% 64.56/8.86 = { by axiom 4 (c04) }
% 64.56/8.86 i(Y)
% 64.56/8.86
% 64.56/8.86 Lemma 17: i(rd(X, Y)) = rd(Y, X).
% 64.56/8.86 Proof:
% 64.56/8.86 i(rd(X, Y))
% 64.56/8.86 = { by lemma 16 R->L }
% 64.56/8.86 rd(Y, mult(rd(X, Y), Y))
% 64.56/8.86 = { by axiom 6 (c03) }
% 64.56/8.86 rd(Y, X)
% 64.56/8.86
% 64.56/8.86 Lemma 18: mult(X, ld(Y, Z)) = rd(X, ld(Z, Y)).
% 64.56/8.86 Proof:
% 64.56/8.86 mult(X, ld(Y, Z))
% 64.56/8.86 = { by lemma 13 R->L }
% 64.56/8.86 rd(X, i(ld(Y, Z)))
% 64.56/8.86 = { by lemma 15 }
% 64.56/8.86 rd(X, ld(Z, Y))
% 64.56/8.86
% 64.56/8.86 Lemma 19: mult(ld(X, Y), Z) = ld(ld(Y, X), Z).
% 64.56/8.86 Proof:
% 64.56/8.86 mult(ld(X, Y), Z)
% 64.56/8.86 = { by lemma 10 R->L }
% 64.56/8.86 ld(i(ld(X, Y)), Z)
% 64.56/8.86 = { by lemma 15 }
% 64.56/8.86 ld(ld(Y, X), Z)
% 64.56/8.86
% 64.56/8.86 Lemma 20: mult(mult(X, Y), X) = mult(X, mult(Y, X)).
% 64.56/8.86 Proof:
% 64.56/8.86 mult(mult(X, Y), X)
% 64.56/8.86 = { by axiom 2 (c06) R->L }
% 64.56/8.86 mult(mult(X, mult(unit, Y)), X)
% 64.56/8.86 = { by axiom 1 (c05) R->L }
% 64.56/8.86 mult(mult(mult(X, mult(unit, Y)), X), unit)
% 64.56/8.86 = { by axiom 9 (c09) R->L }
% 64.56/8.86 mult(mult(X, unit), mult(Y, mult(X, unit)))
% 64.56/8.86 = { by axiom 1 (c05) }
% 64.56/8.86 mult(X, mult(Y, mult(X, unit)))
% 64.56/8.86 = { by axiom 1 (c05) }
% 64.56/8.86 mult(X, mult(Y, X))
% 64.56/8.86
% 64.56/8.86 Lemma 21: mult(rd(X, Y), Z) = ld(rd(Y, X), Z).
% 64.56/8.86 Proof:
% 64.56/8.86 mult(rd(X, Y), Z)
% 64.56/8.86 = { by lemma 10 R->L }
% 64.56/8.86 ld(i(rd(X, Y)), Z)
% 64.56/8.86 = { by lemma 17 }
% 64.56/8.87 ld(rd(Y, X), Z)
% 64.56/8.87
% 64.56/8.87 Lemma 22: rd(ld(X, Y), X) = ld(X, rd(Y, X)).
% 64.56/8.87 Proof:
% 64.56/8.87 rd(ld(X, Y), X)
% 64.56/8.87 = { by lemma 11 R->L }
% 64.56/8.87 mult(ld(X, Y), i(X))
% 64.56/8.87 = { by lemma 12 R->L }
% 64.56/8.87 mult(mult(i(X), Y), i(X))
% 64.56/8.87 = { by lemma 20 }
% 64.56/8.87 mult(i(X), mult(Y, i(X)))
% 64.56/8.87 = { by lemma 12 }
% 64.56/8.87 ld(X, mult(Y, i(X)))
% 64.56/8.87 = { by lemma 11 }
% 64.56/8.87 ld(X, rd(Y, X))
% 64.56/8.87
% 64.56/8.87 Lemma 23: rd(X, ld(X, Y)) = ld(rd(Y, X), X).
% 64.56/8.87 Proof:
% 64.56/8.87 rd(X, ld(X, Y))
% 64.56/8.87 = { by lemma 17 R->L }
% 64.56/8.87 i(rd(ld(X, Y), X))
% 64.56/8.87 = { by lemma 22 }
% 64.56/8.87 i(ld(X, rd(Y, X)))
% 64.56/8.87 = { by lemma 15 }
% 64.56/8.87 ld(rd(Y, X), X)
% 64.56/8.87
% 64.56/8.87 Lemma 24: ld(ld(X, i(Y)), Z) = mult(mult(Y, X), Z).
% 64.56/8.87 Proof:
% 64.56/8.87 ld(ld(X, i(Y)), Z)
% 64.56/8.87 = { by lemma 14 R->L }
% 64.56/8.87 ld(rd(i(X), Y), Z)
% 64.56/8.87 = { by axiom 8 (c08) R->L }
% 64.56/8.87 ld(rd(i(X), mult(mult(Y, X), i(X))), Z)
% 64.56/8.87 = { by lemma 16 }
% 64.56/8.87 ld(i(mult(Y, X)), Z)
% 64.56/8.87 = { by lemma 10 }
% 64.56/8.87 mult(mult(Y, X), Z)
% 64.56/8.87
% 64.56/8.87 Lemma 25: ld(ld(rd(mult(X, Y), Z), Z), X) = ld(ld(X, Z), rd(Y, ld(X, Z))).
% 64.56/8.87 Proof:
% 64.56/8.87 ld(ld(rd(mult(X, Y), Z), Z), X)
% 64.56/8.87 = { by lemma 23 R->L }
% 64.56/8.87 ld(rd(Z, ld(Z, mult(X, Y))), X)
% 64.56/8.87 = { by lemma 12 R->L }
% 64.56/8.87 ld(rd(Z, mult(i(Z), mult(X, Y))), X)
% 64.56/8.87 = { by lemma 21 R->L }
% 64.56/8.87 mult(rd(mult(i(Z), mult(X, Y)), Z), X)
% 64.56/8.87 = { by lemma 11 R->L }
% 64.56/8.87 mult(mult(mult(i(Z), mult(X, Y)), i(Z)), X)
% 64.56/8.87 = { by axiom 9 (c09) R->L }
% 64.56/8.87 mult(mult(i(Z), X), mult(Y, mult(i(Z), X)))
% 64.56/8.87 = { by lemma 12 }
% 64.56/8.87 mult(ld(Z, X), mult(Y, mult(i(Z), X)))
% 64.56/8.87 = { by lemma 12 }
% 64.56/8.87 mult(ld(Z, X), mult(Y, ld(Z, X)))
% 64.56/8.87 = { by lemma 19 }
% 64.56/8.87 ld(ld(X, Z), mult(Y, ld(Z, X)))
% 64.56/8.87 = { by lemma 18 }
% 64.56/8.87 ld(ld(X, Z), rd(Y, ld(X, Z)))
% 64.56/8.87
% 64.56/8.87 Goal 1 (goals): mult(mult(a, b), mult(mult(c, b), c)) = mult(mult(a, mult(mult(b, c), b)), c).
% 64.56/8.87 Proof:
% 64.56/8.87 mult(mult(a, b), mult(mult(c, b), c))
% 64.56/8.87 = { by lemma 20 }
% 64.56/8.87 mult(mult(a, b), mult(c, mult(b, c)))
% 64.56/8.87 = { by lemma 24 R->L }
% 64.56/8.87 ld(ld(b, i(a)), mult(c, mult(b, c)))
% 64.56/8.87 = { by lemma 20 R->L }
% 64.56/8.87 ld(ld(b, i(a)), mult(mult(c, b), c))
% 64.56/8.87 = { by lemma 24 R->L }
% 64.56/8.87 ld(ld(b, i(a)), ld(ld(b, i(c)), c))
% 64.56/8.87 = { by lemma 14 R->L }
% 64.56/8.87 ld(ld(b, i(a)), ld(rd(i(b), c), c))
% 64.56/8.87 = { by lemma 12 R->L }
% 64.56/8.87 ld(mult(i(b), i(a)), ld(rd(i(b), c), c))
% 64.56/8.87 = { by axiom 4 (c04) R->L }
% 64.56/8.87 ld(mult(i(b), i(a)), ld(rd(rd(mult(i(b), i(a)), i(a)), c), c))
% 64.56/8.87 = { by lemma 11 R->L }
% 64.56/8.87 ld(mult(i(b), i(a)), ld(rd(mult(mult(i(b), i(a)), i(i(a))), c), c))
% 64.56/8.87 = { by lemma 15 R->L }
% 64.56/8.87 i(ld(ld(rd(mult(mult(i(b), i(a)), i(i(a))), c), c), mult(i(b), i(a))))
% 64.56/8.87 = { by lemma 25 }
% 64.56/8.87 i(ld(ld(mult(i(b), i(a)), c), rd(i(i(a)), ld(mult(i(b), i(a)), c))))
% 64.56/8.87 = { by lemma 15 }
% 64.56/8.87 ld(rd(i(i(a)), ld(mult(i(b), i(a)), c)), ld(mult(i(b), i(a)), c))
% 64.56/8.87 = { by lemma 14 }
% 64.56/8.87 ld(ld(i(a), i(ld(mult(i(b), i(a)), c))), ld(mult(i(b), i(a)), c))
% 64.56/8.87 = { by lemma 24 }
% 64.56/8.87 mult(mult(ld(mult(i(b), i(a)), c), i(a)), ld(mult(i(b), i(a)), c))
% 64.56/8.87 = { by lemma 20 }
% 64.56/8.87 mult(ld(mult(i(b), i(a)), c), mult(i(a), ld(mult(i(b), i(a)), c)))
% 64.56/8.87 = { by lemma 19 }
% 64.56/8.87 ld(ld(c, mult(i(b), i(a))), mult(i(a), ld(mult(i(b), i(a)), c)))
% 64.56/8.87 = { by lemma 18 }
% 64.56/8.87 ld(ld(c, mult(i(b), i(a))), rd(i(a), ld(c, mult(i(b), i(a)))))
% 64.56/8.87 = { by lemma 25 R->L }
% 64.56/8.87 ld(ld(rd(mult(c, i(a)), mult(i(b), i(a))), mult(i(b), i(a))), c)
% 64.56/8.87 = { by lemma 10 R->L }
% 64.56/8.87 ld(ld(rd(ld(i(c), i(a)), mult(i(b), i(a))), mult(i(b), i(a))), c)
% 64.56/8.87 = { by lemma 23 R->L }
% 64.56/8.87 ld(rd(mult(i(b), i(a)), ld(mult(i(b), i(a)), ld(i(c), i(a)))), c)
% 64.56/8.87 = { by lemma 18 R->L }
% 64.56/8.87 ld(mult(mult(i(b), i(a)), ld(ld(i(c), i(a)), mult(i(b), i(a)))), c)
% 64.56/8.87 = { by lemma 19 R->L }
% 64.56/8.87 ld(mult(mult(i(b), i(a)), mult(ld(i(a), i(c)), mult(i(b), i(a)))), c)
% 64.56/8.87 = { by axiom 9 (c09) }
% 64.56/8.87 ld(mult(mult(mult(i(b), mult(i(a), ld(i(a), i(c)))), i(b)), i(a)), c)
% 64.56/8.87 = { by axiom 5 (c01) }
% 64.56/8.87 ld(mult(mult(mult(i(b), i(c)), i(b)), i(a)), c)
% 64.56/8.87 = { by lemma 20 }
% 64.56/8.87 ld(mult(mult(i(b), mult(i(c), i(b))), i(a)), c)
% 64.56/8.87 = { by lemma 12 }
% 64.56/8.87 ld(mult(mult(i(b), ld(c, i(b))), i(a)), c)
% 64.56/8.87 = { by lemma 18 }
% 64.56/8.87 ld(mult(rd(i(b), ld(i(b), c)), i(a)), c)
% 64.56/8.87 = { by lemma 21 }
% 64.56/8.87 ld(ld(rd(ld(i(b), c), i(b)), i(a)), c)
% 64.56/8.87 = { by lemma 22 }
% 64.56/8.87 ld(ld(ld(i(b), rd(c, i(b))), i(a)), c)
% 64.56/8.87 = { by lemma 10 }
% 64.56/8.87 ld(ld(mult(b, rd(c, i(b))), i(a)), c)
% 64.56/8.87 = { by lemma 13 R->L }
% 64.56/8.87 ld(ld(rd(b, i(rd(c, i(b)))), i(a)), c)
% 64.56/8.87 = { by lemma 17 }
% 64.56/8.87 ld(ld(rd(b, rd(i(b), c)), i(a)), c)
% 64.56/8.87 = { by lemma 14 }
% 64.56/8.87 ld(ld(rd(b, ld(b, i(c))), i(a)), c)
% 64.56/8.87 = { by lemma 23 }
% 64.56/8.87 ld(ld(ld(rd(i(c), b), b), i(a)), c)
% 64.56/8.87 = { by lemma 14 }
% 64.56/8.87 ld(ld(ld(ld(c, i(b)), b), i(a)), c)
% 64.56/8.87 = { by lemma 24 }
% 64.56/8.87 ld(ld(mult(mult(b, c), b), i(a)), c)
% 64.56/8.87 = { by lemma 20 }
% 64.56/8.87 ld(ld(mult(b, mult(c, b)), i(a)), c)
% 64.56/8.87 = { by lemma 24 }
% 64.56/8.87 mult(mult(a, mult(b, mult(c, b))), c)
% 64.56/8.87 = { by lemma 20 R->L }
% 64.56/8.87 mult(mult(a, mult(mult(b, c), b)), c)
% 64.56/8.87 % SZS output end Proof
% 64.56/8.87
% 64.56/8.87 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------