TSTP Solution File: ALG006-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : ALG006-1 : TPTP v8.1.2. Released v2.2.0.
% 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 : n028.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 : Wed Aug 30 16:41:58 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 : ALG006-1 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.16/0.35 % Computer : n028.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Mon Aug 28 06:17:24 EDT 2023
% 0.16/0.35 % 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
% 0.21/0.44 % SZS output start Proof
% 0.21/0.44 Axiom 1 (set_difference_2): difference(X, difference(X, Y)) = difference(Y, difference(Y, X)).
% 0.21/0.44 Axiom 2 (set_difference_1): difference(X, difference(Y, X)) = X.
% 0.21/0.44 Axiom 3 (set_difference_3): difference(difference(X, Y), Z) = difference(difference(X, Z), difference(Y, Z)).
% 0.21/0.44
% 0.21/0.44 Lemma 4: difference(difference(X, Y), Y) = difference(X, Y).
% 0.21/0.44 Proof:
% 0.21/0.44 difference(difference(X, Y), Y)
% 0.21/0.44 = { by axiom 2 (set_difference_1) R->L }
% 0.21/0.44 difference(difference(X, Y), difference(Y, difference(X, Y)))
% 0.21/0.44 = { by axiom 2 (set_difference_1) }
% 0.21/0.44 difference(X, Y)
% 0.21/0.44
% 0.21/0.44 Lemma 5: difference(difference(Y, Y), X) = difference(X, X).
% 0.21/0.44 Proof:
% 0.21/0.44 difference(difference(Y, Y), X)
% 0.21/0.44 = { by axiom 3 (set_difference_3) }
% 0.21/0.44 difference(difference(Y, X), difference(Y, X))
% 0.21/0.44 = { by lemma 4 R->L }
% 0.21/0.44 difference(difference(Y, X), difference(difference(Y, X), X))
% 0.21/0.44 = { by axiom 1 (set_difference_2) }
% 0.21/0.44 difference(X, difference(X, difference(Y, X)))
% 0.21/0.44 = { by axiom 2 (set_difference_1) }
% 0.21/0.44 difference(X, X)
% 0.21/0.44
% 0.21/0.44 Lemma 6: difference(difference(W, W), difference(V, Z)) = difference(difference(X, X), difference(Y, Z)).
% 0.21/0.44 Proof:
% 0.21/0.44 difference(difference(W, W), difference(V, Z))
% 0.21/0.44 = { by lemma 5 }
% 0.21/0.44 difference(difference(V, Z), difference(V, Z))
% 0.21/0.44 = { by lemma 4 R->L }
% 0.21/0.44 difference(difference(V, Z), difference(difference(V, Z), Z))
% 0.21/0.44 = { by axiom 1 (set_difference_2) }
% 0.21/0.44 difference(Z, difference(Z, difference(V, Z)))
% 0.21/0.44 = { by axiom 2 (set_difference_1) }
% 0.21/0.44 difference(Z, Z)
% 0.21/0.44 = { by axiom 2 (set_difference_1) R->L }
% 0.21/0.44 difference(Z, difference(Z, difference(Y, Z)))
% 0.21/0.44 = { by axiom 1 (set_difference_2) R->L }
% 0.21/0.44 difference(difference(Y, Z), difference(difference(Y, Z), Z))
% 0.21/0.44 = { by lemma 4 }
% 0.21/0.44 difference(difference(Y, Z), difference(Y, Z))
% 0.21/0.44 = { by lemma 5 R->L }
% 0.21/0.44 difference(difference(X, X), difference(Y, Z))
% 0.21/0.44
% 0.21/0.44 Lemma 7: difference(difference(X, X), difference(Y, Z)) = difference(W, W).
% 0.21/0.44 Proof:
% 0.21/0.44 difference(difference(X, X), difference(Y, Z))
% 0.21/0.44 = { by lemma 6 }
% 0.21/0.44 difference(difference(W, W), difference(difference(W, W), Z))
% 0.21/0.44 = { by axiom 1 (set_difference_2) R->L }
% 0.21/0.44 difference(Z, difference(Z, difference(W, W)))
% 0.21/0.44 = { by lemma 4 R->L }
% 0.21/0.44 difference(difference(Z, difference(Z, difference(W, W))), difference(Z, difference(W, W)))
% 0.21/0.44 = { by axiom 3 (set_difference_3) }
% 0.21/0.44 difference(difference(Z, difference(Z, difference(W, W))), difference(difference(Z, difference(W, W)), difference(Z, difference(W, W))))
% 0.21/0.44 = { by lemma 5 R->L }
% 0.21/0.44 difference(difference(Z, difference(Z, difference(W, W))), difference(difference(W, W), difference(Z, difference(W, W))))
% 0.21/0.44 = { by axiom 3 (set_difference_3) R->L }
% 0.21/0.44 difference(difference(Z, difference(W, W)), difference(Z, difference(W, W)))
% 0.21/0.44 = { by lemma 5 R->L }
% 0.21/0.44 difference(difference(V, V), difference(Z, difference(W, W)))
% 0.21/0.44 = { by lemma 6 R->L }
% 0.21/0.44 difference(difference(W, W), difference(U, difference(W, W)))
% 0.21/0.44 = { by axiom 2 (set_difference_1) }
% 0.21/0.44 difference(W, W)
% 0.21/0.44
% 0.21/0.44 Lemma 8: difference(Y, Y) = difference(X, X).
% 0.21/0.44 Proof:
% 0.21/0.44 difference(Y, Y)
% 0.21/0.44 = { by lemma 7 R->L }
% 0.21/0.44 difference(difference(Z, Z), difference(W, V))
% 0.21/0.44 = { by lemma 7 }
% 0.21/0.44 difference(X, X)
% 0.21/0.44
% 0.21/0.44 Lemma 9: difference(X, difference(Y, Y)) = X.
% 0.21/0.44 Proof:
% 0.21/0.44 difference(X, difference(Y, Y))
% 0.21/0.44 = { by lemma 7 R->L }
% 0.21/0.44 difference(X, difference(difference(Z, Z), difference(W, V)))
% 0.21/0.44 = { by lemma 7 }
% 0.21/0.44 difference(X, difference(X, X))
% 0.21/0.44 = { by axiom 2 (set_difference_1) }
% 0.21/0.44 X
% 0.21/0.44
% 0.21/0.44 Lemma 10: difference(difference(difference(X, Y), Z), difference(difference(X, Z), Y)) = difference(W, W).
% 0.21/0.44 Proof:
% 0.21/0.44 difference(difference(difference(X, Y), Z), difference(difference(X, Z), Y))
% 0.21/0.44 = { by axiom 3 (set_difference_3) }
% 0.21/0.44 difference(difference(difference(X, Z), difference(Y, Z)), difference(difference(X, Z), Y))
% 0.21/0.44 = { by lemma 4 R->L }
% 0.21/0.44 difference(difference(difference(difference(X, Z), Z), difference(Y, Z)), difference(difference(X, Z), Y))
% 0.21/0.44 = { by axiom 3 (set_difference_3) R->L }
% 0.21/0.44 difference(difference(difference(difference(X, Z), Y), Z), difference(difference(X, Z), Y))
% 0.21/0.44 = { by axiom 3 (set_difference_3) }
% 0.21/0.44 difference(difference(difference(difference(X, Z), Y), difference(difference(X, Z), Y)), difference(Z, difference(difference(X, Z), Y)))
% 0.21/0.44 = { by lemma 8 }
% 0.21/0.44 difference(difference(difference(Z, difference(difference(X, Z), Y)), difference(Z, difference(difference(X, Z), Y))), difference(Z, difference(difference(X, Z), Y)))
% 0.21/0.44 = { by lemma 4 }
% 0.21/0.44 difference(difference(Z, difference(difference(X, Z), Y)), difference(Z, difference(difference(X, Z), Y)))
% 0.21/0.44 = { by lemma 8 R->L }
% 0.21/0.44 difference(W, W)
% 0.21/0.44
% 0.21/0.44 Goal 1 (prove_set_difference_3_simplified): difference(difference(a, c), b) = difference(difference(a, b), c).
% 0.21/0.44 Proof:
% 0.21/0.44 difference(difference(a, c), b)
% 0.21/0.44 = { by lemma 9 R->L }
% 0.21/0.44 difference(difference(difference(a, c), b), difference(X, X))
% 0.21/0.44 = { by lemma 10 R->L }
% 0.21/0.44 difference(difference(difference(a, c), b), difference(difference(difference(a, c), b), difference(difference(a, b), c)))
% 0.21/0.44 = { by axiom 1 (set_difference_2) }
% 0.21/0.45 difference(difference(difference(a, b), c), difference(difference(difference(a, b), c), difference(difference(a, c), b)))
% 0.21/0.45 = { by lemma 10 }
% 0.21/0.45 difference(difference(difference(a, b), c), difference(Y, Y))
% 0.21/0.45 = { by lemma 9 }
% 0.21/0.45 difference(difference(a, b), c)
% 0.21/0.45 % SZS output end Proof
% 0.21/0.45
% 0.21/0.45 RESULT: Unsatisfiable (the axioms are contradictory).
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