TSTP Solution File: GRP409-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP409-1 : TPTP v8.1.2. Released v2.6.0.
% 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 01:18:18 EDT 2023
% Result : Unsatisfiable 0.19s 0.40s
% 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 : GRP409-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.16/0.34 % Computer : n019.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Mon Aug 28 21:33:43 EDT 2023
% 0.16/0.34 % CPUTime :
% 0.19/0.40 Command-line arguments: --no-flatten-goal
% 0.19/0.40
% 0.19/0.40 % SZS status Unsatisfiable
% 0.19/0.40
% 0.19/0.42 % SZS output start Proof
% 0.19/0.42 Axiom 1 (single_axiom): multiply(multiply(inverse(multiply(X, inverse(multiply(Y, Z)))), multiply(X, inverse(Z))), inverse(multiply(inverse(Z), Z))) = Y.
% 0.19/0.42
% 0.19/0.42 Lemma 2: multiply(inverse(multiply(X, inverse(multiply(multiply(Y, inverse(multiply(inverse(Z), Z))), Z)))), multiply(X, inverse(Z))) = Y.
% 0.19/0.42 Proof:
% 0.19/0.42 multiply(inverse(multiply(X, inverse(multiply(multiply(Y, inverse(multiply(inverse(Z), Z))), Z)))), multiply(X, inverse(Z)))
% 0.19/0.42 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.42 multiply(multiply(inverse(multiply(W, inverse(multiply(multiply(inverse(multiply(X, inverse(multiply(multiply(Y, inverse(multiply(inverse(Z), Z))), Z)))), multiply(X, inverse(Z))), inverse(multiply(inverse(Z), Z)))))), multiply(W, inverse(inverse(multiply(inverse(Z), Z))))), inverse(multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(Z), Z)))))
% 0.19/0.42 = { by axiom 1 (single_axiom) }
% 0.19/0.42 multiply(multiply(inverse(multiply(W, inverse(multiply(Y, inverse(multiply(inverse(Z), Z)))))), multiply(W, inverse(inverse(multiply(inverse(Z), Z))))), inverse(multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(Z), Z)))))
% 0.19/0.42 = { by axiom 1 (single_axiom) }
% 0.19/0.42 Y
% 0.19/0.42
% 0.19/0.42 Lemma 3: inverse(multiply(X, inverse(multiply(multiply(multiply(Y, multiply(X, inverse(Z))), inverse(multiply(inverse(Z), Z))), Z)))) = Y.
% 0.19/0.42 Proof:
% 0.19/0.42 inverse(multiply(X, inverse(multiply(multiply(multiply(Y, multiply(X, inverse(Z))), inverse(multiply(inverse(Z), Z))), Z))))
% 0.19/0.42 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.42 multiply(multiply(inverse(multiply(W, inverse(multiply(inverse(multiply(X, inverse(multiply(multiply(multiply(Y, multiply(X, inverse(Z))), inverse(multiply(inverse(Z), Z))), Z)))), multiply(X, inverse(Z)))))), multiply(W, inverse(multiply(X, inverse(Z))))), inverse(multiply(inverse(multiply(X, inverse(Z))), multiply(X, inverse(Z)))))
% 0.19/0.42 = { by lemma 2 }
% 0.19/0.42 multiply(multiply(inverse(multiply(W, inverse(multiply(Y, multiply(X, inverse(Z)))))), multiply(W, inverse(multiply(X, inverse(Z))))), inverse(multiply(inverse(multiply(X, inverse(Z))), multiply(X, inverse(Z)))))
% 0.19/0.42 = { by axiom 1 (single_axiom) }
% 0.19/0.42 Y
% 0.19/0.43
% 0.19/0.43 Lemma 4: multiply(inverse(X), multiply(multiply(inverse(multiply(Y, inverse(multiply(X, Z)))), multiply(Y, inverse(Z))), W)) = multiply(inverse(multiply(V, inverse(multiply(inverse(Z), Z)))), multiply(V, W)).
% 0.19/0.43 Proof:
% 0.19/0.43 multiply(inverse(X), multiply(multiply(inverse(multiply(Y, inverse(multiply(X, Z)))), multiply(Y, inverse(Z))), W))
% 0.19/0.43 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.43 multiply(inverse(multiply(multiply(inverse(multiply(Y, inverse(multiply(X, Z)))), multiply(Y, inverse(Z))), inverse(multiply(inverse(Z), Z)))), multiply(multiply(inverse(multiply(Y, inverse(multiply(X, Z)))), multiply(Y, inverse(Z))), W))
% 0.19/0.43 = { by lemma 3 R->L }
% 0.19/0.43 multiply(inverse(multiply(multiply(inverse(multiply(Y, inverse(multiply(X, Z)))), multiply(Y, inverse(Z))), inverse(multiply(inverse(Z), Z)))), multiply(multiply(inverse(multiply(Y, inverse(multiply(X, Z)))), multiply(Y, inverse(Z))), inverse(multiply(U, inverse(multiply(multiply(multiply(W, multiply(U, inverse(T))), inverse(multiply(inverse(T), T))), T))))))
% 0.19/0.43 = { by lemma 2 R->L }
% 0.19/0.43 multiply(inverse(multiply(multiply(inverse(multiply(Y, inverse(multiply(X, Z)))), multiply(Y, inverse(Z))), inverse(multiply(inverse(multiply(U, inverse(multiply(multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(multiply(multiply(multiply(W, multiply(U, inverse(T))), inverse(multiply(inverse(T), T))), T)), multiply(multiply(multiply(W, multiply(U, inverse(T))), inverse(multiply(inverse(T), T))), T)))), multiply(multiply(multiply(W, multiply(U, inverse(T))), inverse(multiply(inverse(T), T))), T))))), multiply(U, inverse(multiply(multiply(multiply(W, multiply(U, inverse(T))), inverse(multiply(inverse(T), T))), T))))))), multiply(multiply(inverse(multiply(Y, inverse(multiply(X, Z)))), multiply(Y, inverse(Z))), inverse(multiply(U, inverse(multiply(multiply(multiply(W, multiply(U, inverse(T))), inverse(multiply(inverse(T), T))), T))))))
% 0.19/0.43 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.43 multiply(multiply(inverse(multiply(S, inverse(multiply(multiply(inverse(multiply(multiply(inverse(multiply(Y, inverse(multiply(X, Z)))), multiply(Y, inverse(Z))), inverse(multiply(inverse(multiply(U, inverse(multiply(multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(multiply(multiply(multiply(W, multiply(U, inverse(T))), inverse(multiply(inverse(T), T))), T)), multiply(multiply(multiply(W, multiply(U, inverse(T))), inverse(multiply(inverse(T), T))), T)))), multiply(multiply(multiply(W, multiply(U, inverse(T))), inverse(multiply(inverse(T), T))), T))))), multiply(U, inverse(multiply(multiply(multiply(W, multiply(U, inverse(T))), inverse(multiply(inverse(T), T))), T))))))), multiply(multiply(inverse(multiply(Y, inverse(multiply(X, Z)))), multiply(Y, inverse(Z))), inverse(multiply(U, inverse(multiply(multiply(multiply(W, multiply(U, inverse(T))), inverse(multiply(inverse(T), T))), T)))))), inverse(multiply(inverse(multiply(U, inverse(multiply(multiply(multiply(W, multiply(U, inverse(T))), inverse(multiply(inverse(T), T))), T)))), multiply(U, inverse(multiply(multiply(multiply(W, multiply(U, inverse(T))), inverse(multiply(inverse(T), T))), T))))))))), multiply(S, inverse(inverse(multiply(inverse(multiply(U, inverse(multiply(multiply(multiply(W, multiply(U, inverse(T))), inverse(multiply(inverse(T), T))), T)))), multiply(U, inverse(multiply(multiply(multiply(W, multiply(U, inverse(T))), inverse(multiply(inverse(T), T))), T)))))))), inverse(multiply(inverse(inverse(multiply(inverse(multiply(U, inverse(multiply(multiply(multiply(W, multiply(U, inverse(T))), inverse(multiply(inverse(T), T))), T)))), multiply(U, inverse(multiply(multiply(multiply(W, multiply(U, inverse(T))), inverse(multiply(inverse(T), T))), T)))))), inverse(multiply(inverse(multiply(U, inverse(multiply(multiply(multiply(W, multiply(U, inverse(T))), inverse(multiply(inverse(T), T))), T)))), multiply(U, inverse(multiply(multiply(multiply(W, multiply(U, inverse(T))), inverse(multiply(inverse(T), T))), T))))))))
% 0.19/0.43 = { by axiom 1 (single_axiom) }
% 0.19/0.43 multiply(multiply(inverse(multiply(S, inverse(inverse(multiply(U, inverse(multiply(multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(multiply(multiply(multiply(W, multiply(U, inverse(T))), inverse(multiply(inverse(T), T))), T)), multiply(multiply(multiply(W, multiply(U, inverse(T))), inverse(multiply(inverse(T), T))), T)))), multiply(multiply(multiply(W, multiply(U, inverse(T))), inverse(multiply(inverse(T), T))), T)))))))), multiply(S, inverse(inverse(multiply(inverse(multiply(U, inverse(multiply(multiply(multiply(W, multiply(U, inverse(T))), inverse(multiply(inverse(T), T))), T)))), multiply(U, inverse(multiply(multiply(multiply(W, multiply(U, inverse(T))), inverse(multiply(inverse(T), T))), T)))))))), inverse(multiply(inverse(inverse(multiply(inverse(multiply(U, inverse(multiply(multiply(multiply(W, multiply(U, inverse(T))), inverse(multiply(inverse(T), T))), T)))), multiply(U, inverse(multiply(multiply(multiply(W, multiply(U, inverse(T))), inverse(multiply(inverse(T), T))), T)))))), inverse(multiply(inverse(multiply(U, inverse(multiply(multiply(multiply(W, multiply(U, inverse(T))), inverse(multiply(inverse(T), T))), T)))), multiply(U, inverse(multiply(multiply(multiply(W, multiply(U, inverse(T))), inverse(multiply(inverse(T), T))), T))))))))
% 0.19/0.43 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.43 multiply(multiply(inverse(multiply(S, inverse(multiply(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(U, inverse(multiply(multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(multiply(multiply(multiply(W, multiply(U, inverse(T))), inverse(multiply(inverse(T), T))), T)), multiply(multiply(multiply(W, multiply(U, inverse(T))), inverse(multiply(inverse(T), T))), T)))), multiply(multiply(multiply(W, multiply(U, inverse(T))), inverse(multiply(inverse(T), T))), T))))), multiply(U, inverse(multiply(multiply(multiply(W, multiply(U, inverse(T))), inverse(multiply(inverse(T), T))), T))))))), multiply(V, inverse(multiply(U, inverse(multiply(multiply(multiply(W, multiply(U, inverse(T))), inverse(multiply(inverse(T), T))), T)))))), inverse(multiply(inverse(multiply(U, inverse(multiply(multiply(multiply(W, multiply(U, inverse(T))), inverse(multiply(inverse(T), T))), T)))), multiply(U, inverse(multiply(multiply(multiply(W, multiply(U, inverse(T))), inverse(multiply(inverse(T), T))), T))))))))), multiply(S, inverse(inverse(multiply(inverse(multiply(U, inverse(multiply(multiply(multiply(W, multiply(U, inverse(T))), inverse(multiply(inverse(T), T))), T)))), multiply(U, inverse(multiply(multiply(multiply(W, multiply(U, inverse(T))), inverse(multiply(inverse(T), T))), T)))))))), inverse(multiply(inverse(inverse(multiply(inverse(multiply(U, inverse(multiply(multiply(multiply(W, multiply(U, inverse(T))), inverse(multiply(inverse(T), T))), T)))), multiply(U, inverse(multiply(multiply(multiply(W, multiply(U, inverse(T))), inverse(multiply(inverse(T), T))), T)))))), inverse(multiply(inverse(multiply(U, inverse(multiply(multiply(multiply(W, multiply(U, inverse(T))), inverse(multiply(inverse(T), T))), T)))), multiply(U, inverse(multiply(multiply(multiply(W, multiply(U, inverse(T))), inverse(multiply(inverse(T), T))), T))))))))
% 0.19/0.43 = { by axiom 1 (single_axiom) }
% 0.19/0.44 multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(U, inverse(multiply(multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(multiply(multiply(multiply(W, multiply(U, inverse(T))), inverse(multiply(inverse(T), T))), T)), multiply(multiply(multiply(W, multiply(U, inverse(T))), inverse(multiply(inverse(T), T))), T)))), multiply(multiply(multiply(W, multiply(U, inverse(T))), inverse(multiply(inverse(T), T))), T))))), multiply(U, inverse(multiply(multiply(multiply(W, multiply(U, inverse(T))), inverse(multiply(inverse(T), T))), T))))))), multiply(V, inverse(multiply(U, inverse(multiply(multiply(multiply(W, multiply(U, inverse(T))), inverse(multiply(inverse(T), T))), T))))))
% 0.19/0.44 = { by lemma 2 }
% 0.19/0.44 multiply(inverse(multiply(V, inverse(multiply(inverse(Z), Z)))), multiply(V, inverse(multiply(U, inverse(multiply(multiply(multiply(W, multiply(U, inverse(T))), inverse(multiply(inverse(T), T))), T))))))
% 0.19/0.44 = { by lemma 3 }
% 0.19/0.44 multiply(inverse(multiply(V, inverse(multiply(inverse(Z), Z)))), multiply(V, W))
% 0.19/0.44
% 0.19/0.44 Goal 1 (prove_these_axioms_1): multiply(inverse(a1), a1) = multiply(inverse(b1), b1).
% 0.19/0.44 Proof:
% 0.19/0.44 multiply(inverse(a1), a1)
% 0.19/0.44 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.44 multiply(inverse(a1), multiply(multiply(inverse(multiply(X, inverse(multiply(a1, Y)))), multiply(X, inverse(Y))), inverse(multiply(inverse(Y), Y))))
% 0.19/0.44 = { by lemma 4 }
% 0.19/0.44 multiply(inverse(multiply(Z, inverse(multiply(inverse(Y), Y)))), multiply(Z, inverse(multiply(inverse(Y), Y))))
% 0.19/0.44 = { by lemma 4 R->L }
% 0.19/0.44 multiply(inverse(b1), multiply(multiply(inverse(multiply(W, inverse(multiply(b1, Y)))), multiply(W, inverse(Y))), inverse(multiply(inverse(Y), Y))))
% 0.19/0.44 = { by axiom 1 (single_axiom) }
% 0.19/0.44 multiply(inverse(b1), b1)
% 0.19/0.44 % SZS output end Proof
% 0.19/0.44
% 0.19/0.44 RESULT: Unsatisfiable (the axioms are contradictory).
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