TSTP Solution File: LAT144-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT144-1 : TPTP v8.1.2. Released v3.1.0.
% 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 : n031.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 06:27:33 EDT 2023
% Result : Unsatisfiable 93.75s 12.30s
% Output : Proof 93.75s
% 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 : LAT144-1 : TPTP v8.1.2. Released v3.1.0.
% 0.12/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n031.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Aug 24 08:36:05 EDT 2023
% 0.12/0.34 % CPUTime :
% 93.75/12.30 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 93.75/12.30
% 93.75/12.30 % SZS status Unsatisfiable
% 93.75/12.30
% 93.75/12.31 % SZS output start Proof
% 93.75/12.31 Axiom 1 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 93.75/12.31 Axiom 2 (commutativity_of_join): join(X, Y) = join(Y, X).
% 93.75/12.31 Axiom 3 (absorption1): meet(X, join(X, Y)) = X.
% 93.75/12.31 Axiom 4 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 93.75/12.31 Axiom 5 (absorption2): join(X, meet(X, Y)) = X.
% 93.75/12.31 Axiom 6 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 93.75/12.31 Axiom 7 (equation_H32): meet(X, join(Y, meet(X, meet(Z, W)))) = meet(X, join(Y, meet(Z, join(meet(X, W), meet(Y, W))))).
% 93.75/12.31
% 93.75/12.31 Lemma 8: meet(Y, meet(X, Z)) = meet(X, meet(Y, Z)).
% 93.75/12.31 Proof:
% 93.75/12.31 meet(Y, meet(X, Z))
% 93.75/12.31 = { by axiom 1 (commutativity_of_meet) R->L }
% 93.75/12.31 meet(meet(X, Z), Y)
% 93.75/12.31 = { by axiom 4 (associativity_of_meet) }
% 93.75/12.31 meet(X, meet(Z, Y))
% 93.75/12.31 = { by axiom 1 (commutativity_of_meet) }
% 93.75/12.31 meet(X, meet(Y, Z))
% 93.75/12.31
% 93.75/12.31 Goal 1 (prove_H2): meet(a, join(b, meet(a, c))) = meet(a, join(b, meet(c, join(meet(a, join(b, c)), meet(b, c))))).
% 93.75/12.31 Proof:
% 93.75/12.31 meet(a, join(b, meet(a, c)))
% 93.75/12.31 = { by axiom 3 (absorption1) R->L }
% 93.75/12.31 meet(a, join(b, meet(a, meet(c, join(c, b)))))
% 93.75/12.31 = { by axiom 2 (commutativity_of_join) R->L }
% 93.75/12.31 meet(a, join(b, meet(a, meet(c, join(b, c)))))
% 93.75/12.31 = { by lemma 8 R->L }
% 93.75/12.31 meet(a, join(b, meet(c, meet(a, join(b, c)))))
% 93.75/12.31 = { by axiom 3 (absorption1) R->L }
% 93.75/12.31 meet(a, join(b, meet(c, meet(meet(a, join(b, c)), join(meet(a, join(b, c)), meet(b, c))))))
% 93.75/12.31 = { by lemma 8 R->L }
% 93.75/12.31 meet(a, join(b, meet(meet(a, join(b, c)), meet(c, join(meet(a, join(b, c)), meet(b, c))))))
% 93.75/12.31 = { by axiom 1 (commutativity_of_meet) R->L }
% 93.75/12.31 meet(a, join(b, meet(meet(c, join(meet(a, join(b, c)), meet(b, c))), meet(a, join(b, c)))))
% 93.75/12.31 = { by lemma 8 }
% 93.75/12.31 meet(a, join(b, meet(a, meet(meet(c, join(meet(a, join(b, c)), meet(b, c))), join(b, c)))))
% 93.75/12.31 = { by axiom 7 (equation_H32) }
% 93.75/12.31 meet(a, join(b, meet(meet(c, join(meet(a, join(b, c)), meet(b, c))), join(meet(a, join(b, c)), meet(b, join(b, c))))))
% 93.75/12.31 = { by axiom 3 (absorption1) }
% 93.75/12.31 meet(a, join(b, meet(meet(c, join(meet(a, join(b, c)), meet(b, c))), join(meet(a, join(b, c)), b))))
% 93.75/12.31 = { by axiom 5 (absorption2) R->L }
% 93.75/12.31 meet(a, join(b, meet(meet(c, join(meet(a, join(b, c)), meet(b, c))), join(meet(a, join(b, c)), join(b, meet(b, c))))))
% 93.75/12.31 = { by axiom 2 (commutativity_of_join) R->L }
% 93.75/12.31 meet(a, join(b, meet(meet(c, join(meet(a, join(b, c)), meet(b, c))), join(meet(a, join(b, c)), join(meet(b, c), b)))))
% 93.75/12.31 = { by axiom 6 (associativity_of_join) R->L }
% 93.75/12.31 meet(a, join(b, meet(meet(c, join(meet(a, join(b, c)), meet(b, c))), join(join(meet(a, join(b, c)), meet(b, c)), b))))
% 93.75/12.31 = { by axiom 1 (commutativity_of_meet) R->L }
% 93.75/12.31 meet(a, join(b, meet(join(join(meet(a, join(b, c)), meet(b, c)), b), meet(c, join(meet(a, join(b, c)), meet(b, c))))))
% 93.75/12.31 = { by lemma 8 }
% 93.75/12.31 meet(a, join(b, meet(c, meet(join(join(meet(a, join(b, c)), meet(b, c)), b), join(meet(a, join(b, c)), meet(b, c))))))
% 93.75/12.31 = { by axiom 1 (commutativity_of_meet) }
% 93.75/12.31 meet(a, join(b, meet(c, meet(join(meet(a, join(b, c)), meet(b, c)), join(join(meet(a, join(b, c)), meet(b, c)), b)))))
% 93.75/12.31 = { by axiom 3 (absorption1) }
% 93.75/12.31 meet(a, join(b, meet(c, join(meet(a, join(b, c)), meet(b, c)))))
% 93.75/12.31 % SZS output end Proof
% 93.75/12.31
% 93.75/12.31 RESULT: Unsatisfiable (the axioms are contradictory).
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