TSTP Solution File: ALG007-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : ALG007-1 : 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 : n015.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 0.20s 0.44s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG007-1 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 04:27:24 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.44 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.20/0.44
% 0.20/0.44 % SZS status Unsatisfiable
% 0.20/0.44
% 0.20/0.45 % SZS output start Proof
% 0.20/0.45 Axiom 1 (set_difference_2): difference(X, difference(X, Y)) = difference(Y, difference(Y, X)).
% 0.20/0.45 Axiom 2 (set_difference_1): difference(X, difference(Y, X)) = X.
% 0.20/0.45 Axiom 3 (set_difference_3_simplified): difference(difference(X, Y), Z) = difference(difference(X, Z), Y).
% 0.20/0.45
% 0.20/0.45 Lemma 4: difference(difference(X, Y), Y) = difference(X, Y).
% 0.20/0.45 Proof:
% 0.20/0.45 difference(difference(X, Y), Y)
% 0.20/0.45 = { by axiom 2 (set_difference_1) R->L }
% 0.20/0.45 difference(difference(X, Y), difference(Y, difference(X, Y)))
% 0.20/0.45 = { by axiom 2 (set_difference_1) }
% 0.20/0.45 difference(X, Y)
% 0.20/0.45
% 0.20/0.45 Lemma 5: difference(difference(X, Y), difference(X, Y)) = difference(Y, Y).
% 0.20/0.45 Proof:
% 0.20/0.45 difference(difference(X, Y), difference(X, Y))
% 0.20/0.45 = { by lemma 4 R->L }
% 0.20/0.45 difference(difference(X, Y), difference(difference(X, Y), Y))
% 0.20/0.45 = { by axiom 1 (set_difference_2) }
% 0.20/0.45 difference(Y, difference(Y, difference(X, Y)))
% 0.20/0.45 = { by axiom 2 (set_difference_1) }
% 0.20/0.45 difference(Y, Y)
% 0.20/0.45
% 0.20/0.45 Lemma 6: difference(X, X) = difference(Y, Y).
% 0.20/0.45 Proof:
% 0.20/0.45 difference(X, X)
% 0.20/0.45 = { by lemma 5 R->L }
% 0.20/0.45 difference(difference(difference(Z, Y), X), difference(difference(Z, Y), X))
% 0.20/0.45 = { by axiom 3 (set_difference_3_simplified) R->L }
% 0.20/0.45 difference(difference(difference(Z, X), Y), difference(difference(Z, Y), X))
% 0.20/0.45 = { by axiom 3 (set_difference_3_simplified) R->L }
% 0.20/0.45 difference(difference(difference(Z, X), Y), difference(difference(Z, X), Y))
% 0.20/0.45 = { by lemma 5 }
% 0.20/0.45 difference(Y, Y)
% 0.20/0.45
% 0.20/0.45 Lemma 7: difference(difference(difference(X, Y), difference(Z, W)), Z) = difference(difference(X, Z), Y).
% 0.20/0.45 Proof:
% 0.20/0.45 difference(difference(difference(X, Y), difference(Z, W)), Z)
% 0.20/0.45 = { by axiom 3 (set_difference_3_simplified) }
% 0.20/0.45 difference(difference(difference(X, Y), Z), difference(Z, W))
% 0.20/0.45 = { by axiom 3 (set_difference_3_simplified) }
% 0.20/0.45 difference(difference(difference(X, Z), Y), difference(Z, W))
% 0.20/0.45 = { by axiom 2 (set_difference_1) R->L }
% 0.20/0.45 difference(difference(difference(X, Z), Y), difference(difference(Z, difference(difference(X, Y), Z)), W))
% 0.20/0.45 = { by axiom 3 (set_difference_3_simplified) }
% 0.20/0.45 difference(difference(difference(X, Z), Y), difference(difference(Z, difference(difference(X, Z), Y)), W))
% 0.20/0.45 = { by axiom 3 (set_difference_3_simplified) R->L }
% 0.20/0.45 difference(difference(difference(X, Z), Y), difference(difference(Z, W), difference(difference(X, Z), Y)))
% 0.20/0.45 = { by axiom 2 (set_difference_1) }
% 0.20/0.45 difference(difference(X, Z), Y)
% 0.20/0.45
% 0.20/0.45 Goal 1 (prove_set_difference_3): difference(difference(a, b), c) = difference(difference(a, c), difference(b, c)).
% 0.20/0.45 Proof:
% 0.20/0.45 difference(difference(a, b), c)
% 0.20/0.45 = { by lemma 7 R->L }
% 0.20/0.45 difference(difference(difference(a, c), difference(b, c)), b)
% 0.20/0.45 = { by axiom 2 (set_difference_1) R->L }
% 0.20/0.45 difference(difference(difference(difference(a, c), difference(b, c)), difference(difference(difference(a, b), c), difference(difference(a, c), difference(b, c)))), b)
% 0.20/0.45 = { by axiom 3 (set_difference_3_simplified) R->L }
% 0.20/0.45 difference(difference(difference(difference(a, c), difference(b, c)), b), difference(difference(difference(a, b), c), difference(difference(a, c), difference(b, c))))
% 0.20/0.45 = { by lemma 7 }
% 0.20/0.45 difference(difference(difference(a, b), c), difference(difference(difference(a, b), c), difference(difference(a, c), difference(b, c))))
% 0.20/0.45 = { by axiom 1 (set_difference_2) R->L }
% 0.20/0.45 difference(difference(difference(a, c), difference(b, c)), difference(difference(difference(a, c), difference(b, c)), difference(difference(a, b), c)))
% 0.20/0.45 = { by axiom 3 (set_difference_3_simplified) }
% 0.20/0.45 difference(difference(difference(a, c), difference(b, c)), difference(difference(difference(a, c), difference(difference(a, b), c)), difference(b, c)))
% 0.20/0.45 = { by axiom 3 (set_difference_3_simplified) }
% 0.20/0.45 difference(difference(difference(a, c), difference(b, c)), difference(difference(difference(a, difference(difference(a, b), c)), c), difference(b, c)))
% 0.20/0.45 = { by lemma 4 R->L }
% 0.20/0.45 difference(difference(difference(a, c), difference(b, c)), difference(difference(difference(difference(a, difference(difference(a, b), c)), c), c), difference(b, c)))
% 0.20/0.45 = { by axiom 3 (set_difference_3_simplified) R->L }
% 0.20/0.46 difference(difference(difference(a, c), difference(b, c)), difference(difference(difference(difference(a, c), difference(difference(a, b), c)), c), difference(b, c)))
% 0.20/0.46 = { by axiom 3 (set_difference_3_simplified) R->L }
% 0.20/0.46 difference(difference(difference(a, c), difference(b, c)), difference(difference(difference(difference(a, c), difference(difference(a, c), b)), c), difference(b, c)))
% 0.20/0.46 = { by axiom 1 (set_difference_2) }
% 0.20/0.46 difference(difference(difference(a, c), difference(b, c)), difference(difference(difference(b, difference(b, difference(a, c))), c), difference(b, c)))
% 0.20/0.46 = { by axiom 3 (set_difference_3_simplified) R->L }
% 0.20/0.46 difference(difference(difference(a, c), difference(b, c)), difference(difference(difference(b, c), difference(b, difference(a, c))), difference(b, c)))
% 0.20/0.46 = { by axiom 3 (set_difference_3_simplified) R->L }
% 0.20/0.46 difference(difference(difference(a, c), difference(b, c)), difference(difference(difference(b, c), difference(b, c)), difference(b, difference(a, c))))
% 0.20/0.46 = { by lemma 6 R->L }
% 0.20/0.46 difference(difference(difference(a, c), difference(b, c)), difference(difference(difference(b, difference(a, c)), difference(b, difference(a, c))), difference(b, difference(a, c))))
% 0.20/0.46 = { by lemma 4 }
% 0.20/0.46 difference(difference(difference(a, c), difference(b, c)), difference(difference(b, difference(a, c)), difference(b, difference(a, c))))
% 0.20/0.46 = { by lemma 6 R->L }
% 0.20/0.46 difference(difference(difference(a, c), difference(b, c)), difference(difference(difference(a, c), difference(b, c)), difference(difference(a, c), difference(b, c))))
% 0.20/0.46 = { by axiom 2 (set_difference_1) }
% 0.20/0.46 difference(difference(a, c), difference(b, c))
% 0.20/0.46 % SZS output end Proof
% 0.20/0.46
% 0.20/0.46 RESULT: Unsatisfiable (the axioms are contradictory).
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