TSTP Solution File: GRP536-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP536-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 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 : n023.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 01:18:49 EDT 2023
% Result : Unsatisfiable 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GRP536-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.11/0.12 % 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 : n023.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 : Mon Aug 28 21:39:40 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.12/0.37 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.12/0.37
% 0.12/0.37 % SZS status Unsatisfiable
% 0.12/0.37
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 Axiom 1 (identity): identity = divide(X, X).
% 0.12/0.37 Axiom 2 (inverse): inverse(X) = divide(divide(Y, Y), X).
% 0.12/0.37 Axiom 3 (multiply): multiply(X, Y) = divide(X, divide(divide(Z, Z), Y)).
% 0.12/0.37 Axiom 4 (single_axiom): divide(divide(X, divide(divide(X, Y), Z)), Y) = Z.
% 0.12/0.37
% 0.12/0.37 Lemma 5: divide(identity, X) = inverse(X).
% 0.12/0.37 Proof:
% 0.12/0.37 divide(identity, X)
% 0.12/0.37 = { by axiom 1 (identity) }
% 0.12/0.37 divide(divide(Y, Y), X)
% 0.12/0.37 = { by axiom 2 (inverse) R->L }
% 0.12/0.37 inverse(X)
% 0.12/0.37
% 0.12/0.37 Lemma 6: divide(X, inverse(Y)) = multiply(X, Y).
% 0.12/0.37 Proof:
% 0.12/0.37 divide(X, inverse(Y))
% 0.12/0.37 = { by lemma 5 R->L }
% 0.12/0.37 divide(X, divide(identity, Y))
% 0.12/0.37 = { by axiom 1 (identity) }
% 0.12/0.37 divide(X, divide(divide(Z, Z), Y))
% 0.12/0.37 = { by axiom 3 (multiply) R->L }
% 0.12/0.37 multiply(X, Y)
% 0.12/0.37
% 0.12/0.37 Lemma 7: divide(multiply(X, Y), X) = Y.
% 0.12/0.37 Proof:
% 0.12/0.37 divide(multiply(X, Y), X)
% 0.12/0.37 = { by lemma 6 R->L }
% 0.12/0.37 divide(divide(X, inverse(Y)), X)
% 0.12/0.37 = { by lemma 5 R->L }
% 0.12/0.37 divide(divide(X, divide(identity, Y)), X)
% 0.12/0.37 = { by axiom 1 (identity) }
% 0.12/0.37 divide(divide(X, divide(divide(X, X), Y)), X)
% 0.12/0.37 = { by axiom 4 (single_axiom) }
% 0.12/0.38 Y
% 0.12/0.38
% 0.12/0.38 Goal 1 (prove_these_axioms_4): multiply(a, b) = multiply(b, a).
% 0.12/0.38 Proof:
% 0.12/0.38 multiply(a, b)
% 0.12/0.38 = { by lemma 7 R->L }
% 0.12/0.38 multiply(divide(multiply(b, a), b), b)
% 0.12/0.38 = { by lemma 7 R->L }
% 0.12/0.38 multiply(divide(multiply(b, a), divide(multiply(multiply(b, a), b), multiply(b, a))), b)
% 0.12/0.38 = { by lemma 6 R->L }
% 0.12/0.38 multiply(divide(multiply(b, a), divide(divide(multiply(b, a), inverse(b)), multiply(b, a))), b)
% 0.12/0.38 = { by lemma 6 R->L }
% 0.12/0.38 divide(divide(multiply(b, a), divide(divide(multiply(b, a), inverse(b)), multiply(b, a))), inverse(b))
% 0.12/0.38 = { by axiom 4 (single_axiom) }
% 0.12/0.38 multiply(b, a)
% 0.12/0.38 % SZS output end Proof
% 0.12/0.38
% 0.12/0.38 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------