TSTP Solution File: GRP555-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP555-1 : TPTP v8.1.2. Released v2.6.0.
% 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 : n014.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 01:18:54 EDT 2023
% Result : Unsatisfiable 0.21s 0.42s
% Output : Proof 0.21s
% 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 : GRP555-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.36 % Computer : n014.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Tue Aug 29 01:12:15 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.42 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.21/0.42
% 0.21/0.42 % SZS status Unsatisfiable
% 0.21/0.42
% 0.21/0.43 % SZS output start Proof
% 0.21/0.43 Axiom 1 (multiply): multiply(X, Y) = divide(X, inverse(Y)).
% 0.21/0.43 Axiom 2 (single_axiom): divide(divide(X, inverse(divide(Y, divide(X, Z)))), Z) = Y.
% 0.21/0.43
% 0.21/0.43 Lemma 3: divide(multiply(X, divide(Y, divide(X, Z))), Z) = Y.
% 0.21/0.43 Proof:
% 0.21/0.43 divide(multiply(X, divide(Y, divide(X, Z))), Z)
% 0.21/0.43 = { by axiom 1 (multiply) }
% 0.21/0.43 divide(divide(X, inverse(divide(Y, divide(X, Z)))), Z)
% 0.21/0.43 = { by axiom 2 (single_axiom) }
% 0.21/0.43 Y
% 0.21/0.43
% 0.21/0.43 Lemma 4: multiply(multiply(X, divide(Y, multiply(X, Z))), Z) = Y.
% 0.21/0.43 Proof:
% 0.21/0.43 multiply(multiply(X, divide(Y, multiply(X, Z))), Z)
% 0.21/0.43 = { by axiom 1 (multiply) }
% 0.21/0.43 multiply(multiply(X, divide(Y, divide(X, inverse(Z)))), Z)
% 0.21/0.43 = { by axiom 1 (multiply) }
% 0.21/0.43 divide(multiply(X, divide(Y, divide(X, inverse(Z)))), inverse(Z))
% 0.21/0.43 = { by lemma 3 }
% 0.21/0.43 Y
% 0.21/0.43
% 0.21/0.43 Lemma 5: multiply(X, divide(Y, divide(X, multiply(Z, W)))) = multiply(multiply(Z, Y), W).
% 0.21/0.43 Proof:
% 0.21/0.43 multiply(X, divide(Y, divide(X, multiply(Z, W))))
% 0.21/0.43 = { by lemma 4 R->L }
% 0.21/0.43 multiply(multiply(Z, divide(multiply(X, divide(Y, divide(X, multiply(Z, W)))), multiply(Z, W))), W)
% 0.21/0.43 = { by lemma 3 }
% 0.21/0.43 multiply(multiply(Z, Y), W)
% 0.21/0.43
% 0.21/0.43 Lemma 6: divide(multiply(X, Y), X) = Y.
% 0.21/0.43 Proof:
% 0.21/0.43 divide(multiply(X, Y), X)
% 0.21/0.43 = { by lemma 4 R->L }
% 0.21/0.43 divide(multiply(X, Y), multiply(multiply(Z, divide(X, multiply(Z, Y))), Y))
% 0.21/0.43 = { by lemma 4 R->L }
% 0.21/0.43 divide(multiply(multiply(multiply(Z, divide(X, multiply(Z, Y))), Y), Y), multiply(multiply(Z, divide(X, multiply(Z, Y))), Y))
% 0.21/0.43 = { by lemma 5 R->L }
% 0.21/0.43 divide(multiply(W, divide(Y, divide(W, multiply(multiply(Z, divide(X, multiply(Z, Y))), Y)))), multiply(multiply(Z, divide(X, multiply(Z, Y))), Y))
% 0.21/0.43 = { by lemma 3 }
% 0.21/0.43 Y
% 0.21/0.43
% 0.21/0.43 Lemma 7: multiply(multiply(X, Z), Y) = multiply(multiply(X, Y), Z).
% 0.21/0.43 Proof:
% 0.21/0.43 multiply(multiply(X, Z), Y)
% 0.21/0.43 = { by lemma 6 R->L }
% 0.21/0.43 multiply(multiply(X, divide(multiply(multiply(X, Y), Z), multiply(X, Y))), Y)
% 0.21/0.43 = { by lemma 4 }
% 0.21/0.43 multiply(multiply(X, Y), Z)
% 0.21/0.43
% 0.21/0.43 Lemma 8: multiply(multiply(inverse(X), X), Y) = Y.
% 0.21/0.43 Proof:
% 0.21/0.43 multiply(multiply(inverse(X), X), Y)
% 0.21/0.43 = { by lemma 7 }
% 0.21/0.43 multiply(multiply(inverse(X), Y), X)
% 0.21/0.43 = { by axiom 1 (multiply) }
% 0.21/0.43 divide(multiply(inverse(X), Y), inverse(X))
% 0.21/0.43 = { by lemma 6 }
% 0.21/0.44 Y
% 0.21/0.44
% 0.21/0.44 Lemma 9: multiply(Y, X) = multiply(X, Y).
% 0.21/0.44 Proof:
% 0.21/0.44 multiply(Y, X)
% 0.21/0.44 = { by lemma 8 R->L }
% 0.21/0.44 multiply(multiply(multiply(inverse(Z), Z), Y), X)
% 0.21/0.44 = { by lemma 7 R->L }
% 0.21/0.44 multiply(multiply(multiply(inverse(Z), Z), X), Y)
% 0.21/0.44 = { by lemma 8 }
% 0.21/0.44 multiply(X, Y)
% 0.21/0.44
% 0.21/0.44 Lemma 10: multiply(Z, multiply(Y, X)) = multiply(X, multiply(Y, Z)).
% 0.21/0.44 Proof:
% 0.21/0.44 multiply(Z, multiply(Y, X))
% 0.21/0.44 = { by lemma 9 }
% 0.21/0.44 multiply(multiply(Y, X), Z)
% 0.21/0.44 = { by lemma 5 R->L }
% 0.21/0.44 multiply(W, divide(X, divide(W, multiply(Y, Z))))
% 0.21/0.44 = { by lemma 9 }
% 0.21/0.44 multiply(W, divide(X, divide(W, multiply(Z, Y))))
% 0.21/0.44 = { by lemma 5 }
% 0.21/0.44 multiply(multiply(Z, X), Y)
% 0.21/0.44 = { by lemma 7 R->L }
% 0.21/0.44 multiply(multiply(Z, Y), X)
% 0.21/0.44 = { by lemma 9 R->L }
% 0.21/0.44 multiply(X, multiply(Z, Y))
% 0.21/0.44 = { by lemma 9 R->L }
% 0.21/0.44 multiply(X, multiply(Y, Z))
% 0.21/0.44
% 0.21/0.44 Goal 1 (prove_these_axioms_3): multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)).
% 0.21/0.44 Proof:
% 0.21/0.44 multiply(multiply(a3, b3), c3)
% 0.21/0.44 = { by lemma 9 R->L }
% 0.21/0.44 multiply(c3, multiply(a3, b3))
% 0.21/0.44 = { by lemma 10 R->L }
% 0.21/0.44 multiply(b3, multiply(a3, c3))
% 0.21/0.44 = { by lemma 9 }
% 0.21/0.44 multiply(b3, multiply(c3, a3))
% 0.21/0.44 = { by lemma 10 R->L }
% 0.21/0.44 multiply(a3, multiply(c3, b3))
% 0.21/0.44 = { by lemma 9 R->L }
% 0.21/0.44 multiply(a3, multiply(b3, c3))
% 0.21/0.44 % SZS output end Proof
% 0.21/0.44
% 0.21/0.44 RESULT: Unsatisfiable (the axioms are contradictory).
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