TSTP Solution File: LAT241-10 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : LAT241-10 : TPTP v8.1.2. Released v7.5.0.
% 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 : n019.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 06:27:54 EDT 2023
% Result : Unsatisfiable 0.19s 0.73s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT241-10 : TPTP v8.1.2. Released v7.5.0.
% 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 : n019.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 : Thu Aug 24 05:08:59 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.73 Command-line arguments: --no-flatten-goal
% 0.19/0.73
% 0.19/0.73 % SZS status Unsatisfiable
% 0.19/0.73
% 0.19/0.74 % SZS output start Proof
% 0.19/0.74 Axiom 1 (commutativity_of_join): join(X, Y) = join(Y, X).
% 0.19/0.74 Axiom 2 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 0.19/0.74 Axiom 3 (prove_distributivity_hypothesis): meet(b, a) = a.
% 0.19/0.74 Axiom 4 (complement_join): join(X, complement(X)) = one.
% 0.19/0.74 Axiom 5 (complement_meet): meet(X, complement(X)) = zero.
% 0.19/0.74 Axiom 6 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.19/0.74 Axiom 7 (absorption2): join(X, meet(X, Y)) = X.
% 0.19/0.74 Axiom 8 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 0.19/0.74 Axiom 9 (absorption1): meet(X, join(X, Y)) = X.
% 0.19/0.74 Axiom 10 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 0.19/0.74 Axiom 11 (equation_H51): meet(X, join(Y, meet(Z, join(X, W)))) = meet(X, join(Y, join(meet(X, Z), meet(Z, W)))).
% 0.19/0.74 Axiom 12 (meet_join_complement): ifeq(join(X, Y), one, ifeq(meet(X, Y), zero, complement(X), Y), Y) = Y.
% 0.19/0.74
% 0.19/0.74 Lemma 13: meet(X, one) = X.
% 0.19/0.74 Proof:
% 0.19/0.74 meet(X, one)
% 0.19/0.74 = { by axiom 4 (complement_join) R->L }
% 0.19/0.74 meet(X, join(X, complement(X)))
% 0.19/0.74 = { by axiom 9 (absorption1) }
% 0.19/0.74 X
% 0.19/0.74
% 0.19/0.74 Lemma 14: join(X, zero) = X.
% 0.19/0.74 Proof:
% 0.19/0.74 join(X, zero)
% 0.19/0.74 = { by axiom 5 (complement_meet) R->L }
% 0.19/0.74 join(X, meet(X, complement(X)))
% 0.19/0.74 = { by axiom 7 (absorption2) }
% 0.19/0.74 X
% 0.19/0.74
% 0.19/0.74 Goal 1 (prove_distributivity): join(complement(b), complement(a)) = complement(a).
% 0.19/0.74 Proof:
% 0.19/0.74 join(complement(b), complement(a))
% 0.19/0.74 = { by axiom 12 (meet_join_complement) R->L }
% 0.19/0.74 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(a, join(complement(b), complement(a))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 0.19/0.74 = { by axiom 1 (commutativity_of_join) R->L }
% 0.19/0.74 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(a, join(complement(a), complement(b))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 0.19/0.74 = { by lemma 13 R->L }
% 0.19/0.74 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(a, join(complement(a), meet(complement(b), one))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 0.19/0.74 = { by axiom 4 (complement_join) R->L }
% 0.19/0.74 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(a, join(complement(a), meet(complement(b), join(a, complement(a))))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 0.19/0.74 = { by axiom 7 (absorption2) R->L }
% 0.19/0.74 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(a, join(complement(a), meet(complement(b), join(join(a, meet(a, complement(b))), complement(a))))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 0.19/0.74 = { by axiom 8 (associativity_of_join) }
% 0.19/0.74 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(a, join(complement(a), meet(complement(b), join(a, join(meet(a, complement(b)), complement(a)))))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 0.19/0.74 = { by axiom 1 (commutativity_of_join) }
% 0.19/0.74 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(a, join(complement(a), meet(complement(b), join(a, join(complement(a), meet(a, complement(b))))))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 0.19/0.74 = { by axiom 11 (equation_H51) }
% 0.19/0.74 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(a, join(complement(a), join(meet(a, complement(b)), meet(complement(b), join(complement(a), meet(a, complement(b))))))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 0.19/0.74 = { by axiom 2 (commutativity_of_meet) R->L }
% 0.19/0.74 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(a, join(complement(a), join(meet(a, complement(b)), meet(join(complement(a), meet(a, complement(b))), complement(b))))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 0.19/0.74 = { by axiom 8 (associativity_of_join) R->L }
% 0.19/0.74 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(a, join(join(complement(a), meet(a, complement(b))), meet(join(complement(a), meet(a, complement(b))), complement(b)))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 0.19/0.74 = { by axiom 7 (absorption2) }
% 0.19/0.74 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(a, join(complement(a), meet(a, complement(b)))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 0.19/0.74 = { by axiom 3 (prove_distributivity_hypothesis) R->L }
% 0.19/0.74 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(a, join(complement(a), meet(meet(b, a), complement(b)))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 0.19/0.74 = { by axiom 10 (associativity_of_meet) }
% 0.19/0.74 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(a, join(complement(a), meet(b, meet(a, complement(b))))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 0.19/0.74 = { by axiom 2 (commutativity_of_meet) R->L }
% 0.19/0.74 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(a, join(complement(a), meet(b, meet(complement(b), a)))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 0.19/0.74 = { by axiom 10 (associativity_of_meet) R->L }
% 0.19/0.74 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(a, join(complement(a), meet(meet(b, complement(b)), a))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 0.19/0.74 = { by axiom 5 (complement_meet) }
% 0.19/0.74 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(a, join(complement(a), meet(zero, a))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 0.19/0.74 = { by lemma 14 R->L }
% 0.19/0.74 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(a, join(complement(a), join(meet(zero, a), zero))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 0.19/0.74 = { by axiom 1 (commutativity_of_join) }
% 0.19/0.74 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(a, join(complement(a), join(zero, meet(zero, a)))), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 0.19/0.74 = { by axiom 7 (absorption2) }
% 0.19/0.74 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(a, join(complement(a), zero)), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 0.19/0.74 = { by lemma 14 }
% 0.19/0.74 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(meet(a, complement(a)), zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 0.19/0.74 = { by axiom 5 (complement_meet) }
% 0.19/0.74 ifeq(join(a, join(complement(b), complement(a))), one, ifeq(zero, zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 0.19/0.74 = { by axiom 1 (commutativity_of_join) R->L }
% 0.19/0.74 ifeq(join(a, join(complement(a), complement(b))), one, ifeq(zero, zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 0.19/0.74 = { by axiom 8 (associativity_of_join) R->L }
% 0.19/0.74 ifeq(join(join(a, complement(a)), complement(b)), one, ifeq(zero, zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 0.19/0.74 = { by axiom 4 (complement_join) }
% 0.19/0.74 ifeq(join(one, complement(b)), one, ifeq(zero, zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 0.19/0.74 = { by lemma 13 R->L }
% 0.19/0.74 ifeq(join(one, meet(complement(b), one)), one, ifeq(zero, zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 0.19/0.74 = { by axiom 2 (commutativity_of_meet) }
% 0.19/0.74 ifeq(join(one, meet(one, complement(b))), one, ifeq(zero, zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 0.19/0.74 = { by axiom 7 (absorption2) }
% 0.19/0.74 ifeq(one, one, ifeq(zero, zero, complement(a), join(complement(b), complement(a))), join(complement(b), complement(a)))
% 0.19/0.74 = { by axiom 6 (ifeq_axiom) }
% 0.19/0.74 ifeq(zero, zero, complement(a), join(complement(b), complement(a)))
% 0.19/0.74 = { by axiom 6 (ifeq_axiom) }
% 0.19/0.74 complement(a)
% 0.19/0.74 % SZS output end Proof
% 0.19/0.74
% 0.19/0.74 RESULT: Unsatisfiable (the axioms are contradictory).
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