TSTP Solution File: ROB005-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : ROB005-1 : TPTP v8.1.2. Released v1.0.0.
% 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 : n004.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 14:09:06 EDT 2023
% Result : Unsatisfiable 5.90s 1.16s
% Output : Proof 6.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ROB005-1 : TPTP v8.1.2. Released v1.0.0.
% 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 : n004.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 06:44:52 EDT 2023
% 0.13/0.34 % CPUTime :
% 5.90/1.16 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 5.90/1.16
% 5.90/1.16 % SZS status Unsatisfiable
% 5.90/1.16
% 6.25/1.21 % SZS output start Proof
% 6.25/1.21 Axiom 1 (commutativity_of_add): add(X, Y) = add(Y, X).
% 6.25/1.21 Axiom 2 (idempotence): add(c, c) = c.
% 6.25/1.21 Axiom 3 (associativity_of_add): add(add(X, Y), Z) = add(X, add(Y, Z)).
% 6.25/1.21 Axiom 4 (robbins_axiom): negate(add(negate(add(X, Y)), negate(add(X, negate(Y))))) = X.
% 6.25/1.21
% 6.25/1.21 Lemma 5: negate(add(negate(add(X, Y)), negate(add(Y, negate(X))))) = Y.
% 6.25/1.21 Proof:
% 6.25/1.21 negate(add(negate(add(X, Y)), negate(add(Y, negate(X)))))
% 6.25/1.21 = { by axiom 1 (commutativity_of_add) R->L }
% 6.25/1.21 negate(add(negate(add(Y, X)), negate(add(Y, negate(X)))))
% 6.25/1.21 = { by axiom 4 (robbins_axiom) }
% 6.25/1.21 Y
% 6.25/1.21
% 6.25/1.21 Lemma 6: negate(add(negate(add(X, Y)), negate(add(negate(X), Y)))) = Y.
% 6.25/1.21 Proof:
% 6.25/1.21 negate(add(negate(add(X, Y)), negate(add(negate(X), Y))))
% 6.25/1.21 = { by axiom 1 (commutativity_of_add) R->L }
% 6.25/1.21 negate(add(negate(add(X, Y)), negate(add(Y, negate(X)))))
% 6.25/1.21 = { by lemma 5 }
% 6.25/1.21 Y
% 6.25/1.21
% 6.25/1.21 Lemma 7: add(Y, add(X, Z)) = add(X, add(Y, Z)).
% 6.25/1.21 Proof:
% 6.25/1.21 add(Y, add(X, Z))
% 6.25/1.21 = { by axiom 1 (commutativity_of_add) R->L }
% 6.25/1.21 add(add(X, Z), Y)
% 6.25/1.21 = { by axiom 3 (associativity_of_add) }
% 6.25/1.21 add(X, add(Z, Y))
% 6.25/1.21 = { by axiom 1 (commutativity_of_add) }
% 6.25/1.21 add(X, add(Y, Z))
% 6.25/1.21
% 6.25/1.21 Lemma 8: add(c, add(X, c)) = add(X, c).
% 6.25/1.21 Proof:
% 6.25/1.21 add(c, add(X, c))
% 6.25/1.21 = { by axiom 1 (commutativity_of_add) R->L }
% 6.25/1.21 add(c, add(c, X))
% 6.25/1.21 = { by axiom 3 (associativity_of_add) R->L }
% 6.25/1.21 add(add(c, c), X)
% 6.25/1.21 = { by axiom 2 (idempotence) }
% 6.25/1.21 add(c, X)
% 6.25/1.21 = { by axiom 1 (commutativity_of_add) }
% 6.25/1.21 add(X, c)
% 6.25/1.21
% 6.25/1.21 Lemma 9: negate(add(negate(c), negate(add(c, negate(c))))) = c.
% 6.25/1.21 Proof:
% 6.25/1.21 negate(add(negate(c), negate(add(c, negate(c)))))
% 6.25/1.21 = { by axiom 2 (idempotence) R->L }
% 6.25/1.21 negate(add(negate(add(c, c)), negate(add(c, negate(c)))))
% 6.25/1.21 = { by axiom 4 (robbins_axiom) }
% 6.25/1.21 c
% 6.25/1.21
% 6.25/1.21 Lemma 10: negate(add(negate(c), negate(add(negate(c), add(c, negate(c)))))) = c.
% 6.25/1.21 Proof:
% 6.25/1.21 negate(add(negate(c), negate(add(negate(c), add(c, negate(c))))))
% 6.25/1.21 = { by axiom 1 (commutativity_of_add) R->L }
% 6.25/1.21 negate(add(negate(c), negate(add(negate(c), add(negate(c), c)))))
% 6.25/1.21 = { by axiom 1 (commutativity_of_add) R->L }
% 6.25/1.21 negate(add(negate(add(negate(c), add(negate(c), c))), negate(c)))
% 6.25/1.21 = { by lemma 8 R->L }
% 6.25/1.21 negate(add(negate(add(negate(c), add(c, add(negate(c), c)))), negate(c)))
% 6.25/1.21 = { by axiom 3 (associativity_of_add) R->L }
% 6.25/1.21 negate(add(negate(add(negate(c), add(add(c, negate(c)), c))), negate(c)))
% 6.25/1.21 = { by axiom 3 (associativity_of_add) R->L }
% 6.25/1.21 negate(add(negate(add(add(negate(c), add(c, negate(c))), c)), negate(c)))
% 6.25/1.21 = { by axiom 4 (robbins_axiom) R->L }
% 6.25/1.21 negate(add(negate(add(add(negate(c), add(c, negate(c))), c)), negate(add(negate(add(negate(c), add(c, negate(c)))), negate(add(negate(c), negate(add(c, negate(c)))))))))
% 6.25/1.21 = { by lemma 9 }
% 6.25/1.21 negate(add(negate(add(add(negate(c), add(c, negate(c))), c)), negate(add(negate(add(negate(c), add(c, negate(c)))), c))))
% 6.25/1.21 = { by axiom 1 (commutativity_of_add) }
% 6.25/1.21 negate(add(negate(add(add(negate(c), add(c, negate(c))), c)), negate(add(c, negate(add(negate(c), add(c, negate(c))))))))
% 6.25/1.21 = { by lemma 5 }
% 6.25/1.21 c
% 6.25/1.21
% 6.25/1.21 Lemma 11: negate(add(negate(add(X, Y)), negate(add(negate(Y), X)))) = X.
% 6.25/1.21 Proof:
% 6.25/1.21 negate(add(negate(add(X, Y)), negate(add(negate(Y), X))))
% 6.25/1.21 = { by axiom 1 (commutativity_of_add) R->L }
% 6.25/1.21 negate(add(negate(add(X, Y)), negate(add(X, negate(Y)))))
% 6.25/1.21 = { by axiom 4 (robbins_axiom) }
% 6.25/1.22 X
% 6.25/1.22
% 6.25/1.22 Lemma 12: negate(add(negate(add(X, c)), negate(add(X, add(negate(c), negate(add(c, negate(c)))))))) = X.
% 6.25/1.22 Proof:
% 6.25/1.22 negate(add(negate(add(X, c)), negate(add(X, add(negate(c), negate(add(c, negate(c))))))))
% 6.25/1.22 = { by axiom 1 (commutativity_of_add) R->L }
% 6.25/1.22 negate(add(negate(add(X, add(negate(c), negate(add(c, negate(c)))))), negate(add(X, c))))
% 6.25/1.22 = { by lemma 9 R->L }
% 6.25/1.22 negate(add(negate(add(X, add(negate(c), negate(add(c, negate(c)))))), negate(add(X, negate(add(negate(c), negate(add(c, negate(c)))))))))
% 6.25/1.22 = { by axiom 4 (robbins_axiom) }
% 6.25/1.22 X
% 6.25/1.22
% 6.25/1.22 Lemma 13: add(negate(c), add(negate(c), X)) = add(X, negate(c)).
% 6.25/1.22 Proof:
% 6.25/1.22 add(negate(c), add(negate(c), X))
% 6.25/1.22 = { by axiom 3 (associativity_of_add) R->L }
% 6.25/1.22 add(add(negate(c), negate(c)), X)
% 6.25/1.22 = { by lemma 5 R->L }
% 6.25/1.22 add(negate(add(negate(add(add(c, negate(c)), add(negate(c), negate(c)))), negate(add(add(negate(c), negate(c)), negate(add(c, negate(c))))))), X)
% 6.25/1.22 = { by axiom 3 (associativity_of_add) }
% 6.25/1.22 add(negate(add(negate(add(c, add(negate(c), add(negate(c), negate(c))))), negate(add(add(negate(c), negate(c)), negate(add(c, negate(c))))))), X)
% 6.25/1.22 = { by lemma 6 R->L }
% 6.25/1.22 add(negate(add(negate(add(negate(add(c, negate(add(c, add(negate(c), add(negate(c), negate(c))))))), negate(add(negate(c), negate(add(c, add(negate(c), add(negate(c), negate(c))))))))), negate(add(add(negate(c), negate(c)), negate(add(c, negate(c))))))), X)
% 6.25/1.22 = { by lemma 7 }
% 6.25/1.22 add(negate(add(negate(add(negate(add(c, negate(add(negate(c), add(c, add(negate(c), negate(c))))))), negate(add(negate(c), negate(add(c, add(negate(c), add(negate(c), negate(c))))))))), negate(add(add(negate(c), negate(c)), negate(add(c, negate(c))))))), X)
% 6.25/1.22 = { by lemma 7 }
% 6.25/1.22 add(negate(add(negate(add(negate(add(c, negate(add(negate(c), add(negate(c), add(c, negate(c))))))), negate(add(negate(c), negate(add(c, add(negate(c), add(negate(c), negate(c))))))))), negate(add(add(negate(c), negate(c)), negate(add(c, negate(c))))))), X)
% 6.25/1.22 = { by axiom 1 (commutativity_of_add) R->L }
% 6.25/1.22 add(negate(add(negate(add(negate(add(negate(add(negate(c), add(negate(c), add(c, negate(c))))), c)), negate(add(negate(c), negate(add(c, add(negate(c), add(negate(c), negate(c))))))))), negate(add(add(negate(c), negate(c)), negate(add(c, negate(c))))))), X)
% 6.25/1.22 = { by lemma 10 R->L }
% 6.25/1.22 add(negate(add(negate(add(negate(add(negate(add(negate(c), add(negate(c), add(c, negate(c))))), negate(add(negate(c), negate(add(negate(c), add(c, negate(c)))))))), negate(add(negate(c), negate(add(c, add(negate(c), add(negate(c), negate(c))))))))), negate(add(add(negate(c), negate(c)), negate(add(c, negate(c))))))), X)
% 6.25/1.22 = { by axiom 4 (robbins_axiom) }
% 6.25/1.22 add(negate(add(negate(add(negate(c), negate(add(negate(c), negate(add(c, add(negate(c), add(negate(c), negate(c))))))))), negate(add(add(negate(c), negate(c)), negate(add(c, negate(c))))))), X)
% 6.25/1.22 = { by lemma 7 }
% 6.25/1.22 add(negate(add(negate(add(negate(c), negate(add(negate(c), negate(add(negate(c), add(c, add(negate(c), negate(c))))))))), negate(add(add(negate(c), negate(c)), negate(add(c, negate(c))))))), X)
% 6.25/1.22 = { by lemma 7 }
% 6.25/1.22 add(negate(add(negate(add(negate(c), negate(add(negate(c), negate(add(negate(c), add(negate(c), add(c, negate(c))))))))), negate(add(add(negate(c), negate(c)), negate(add(c, negate(c))))))), X)
% 6.25/1.22 = { by axiom 1 (commutativity_of_add) R->L }
% 6.25/1.22 add(negate(add(negate(add(negate(c), negate(add(negate(c), negate(add(negate(c), add(negate(c), add(negate(c), c)))))))), negate(add(add(negate(c), negate(c)), negate(add(c, negate(c))))))), X)
% 6.25/1.22 = { by lemma 8 R->L }
% 6.25/1.22 add(negate(add(negate(add(negate(c), negate(add(negate(c), negate(add(negate(c), add(negate(c), add(c, add(negate(c), c))))))))), negate(add(add(negate(c), negate(c)), negate(add(c, negate(c))))))), X)
% 6.25/1.22 = { by axiom 3 (associativity_of_add) R->L }
% 6.25/1.22 add(negate(add(negate(add(negate(c), negate(add(negate(c), negate(add(negate(c), add(negate(c), add(add(c, negate(c)), c)))))))), negate(add(add(negate(c), negate(c)), negate(add(c, negate(c))))))), X)
% 6.25/1.22 = { by axiom 3 (associativity_of_add) R->L }
% 6.25/1.22 add(negate(add(negate(add(negate(c), negate(add(negate(c), negate(add(negate(c), add(add(negate(c), add(c, negate(c))), c))))))), negate(add(add(negate(c), negate(c)), negate(add(c, negate(c))))))), X)
% 6.25/1.22 = { by lemma 10 R->L }
% 6.25/1.22 add(negate(add(negate(add(negate(c), negate(add(negate(c), negate(add(negate(c), add(add(negate(c), add(c, negate(c))), negate(add(negate(c), negate(add(negate(c), add(c, negate(c))))))))))))), negate(add(add(negate(c), negate(c)), negate(add(c, negate(c))))))), X)
% 6.25/1.22 = { by axiom 1 (commutativity_of_add) R->L }
% 6.25/1.22 add(negate(add(negate(add(negate(c), negate(add(negate(c), negate(add(negate(c), add(negate(add(negate(c), negate(add(negate(c), add(c, negate(c)))))), add(negate(c), add(c, negate(c)))))))))), negate(add(add(negate(c), negate(c)), negate(add(c, negate(c))))))), X)
% 6.25/1.22 = { by lemma 7 }
% 6.25/1.22 add(negate(add(negate(add(negate(c), negate(add(negate(c), negate(add(negate(add(negate(c), negate(add(negate(c), add(c, negate(c)))))), add(negate(c), add(negate(c), add(c, negate(c)))))))))), negate(add(add(negate(c), negate(c)), negate(add(c, negate(c))))))), X)
% 6.25/1.22 = { by axiom 1 (commutativity_of_add) R->L }
% 6.25/1.22 add(negate(add(negate(add(negate(c), negate(add(negate(add(negate(add(negate(c), negate(add(negate(c), add(c, negate(c)))))), add(negate(c), add(negate(c), add(c, negate(c)))))), negate(c))))), negate(add(add(negate(c), negate(c)), negate(add(c, negate(c))))))), X)
% 6.25/1.22 = { by axiom 4 (robbins_axiom) R->L }
% 6.25/1.22 add(negate(add(negate(add(negate(c), negate(add(negate(add(negate(add(negate(c), negate(add(negate(c), add(c, negate(c)))))), add(negate(c), add(negate(c), add(c, negate(c)))))), negate(add(negate(add(negate(c), add(negate(c), add(c, negate(c))))), negate(add(negate(c), negate(add(negate(c), add(c, negate(c)))))))))))), negate(add(add(negate(c), negate(c)), negate(add(c, negate(c))))))), X)
% 6.25/1.22 = { by lemma 11 }
% 6.25/1.22 add(negate(add(negate(add(negate(c), negate(add(negate(c), negate(add(negate(c), add(c, negate(c)))))))), negate(add(add(negate(c), negate(c)), negate(add(c, negate(c))))))), X)
% 6.25/1.22 = { by lemma 10 }
% 6.25/1.22 add(negate(add(negate(add(negate(c), c)), negate(add(add(negate(c), negate(c)), negate(add(c, negate(c))))))), X)
% 6.25/1.22 = { by axiom 1 (commutativity_of_add) }
% 6.25/1.22 add(negate(add(negate(add(c, negate(c))), negate(add(add(negate(c), negate(c)), negate(add(c, negate(c))))))), X)
% 6.25/1.22 = { by axiom 3 (associativity_of_add) }
% 6.25/1.22 add(negate(add(negate(add(c, negate(c))), negate(add(negate(c), add(negate(c), negate(add(c, negate(c)))))))), X)
% 6.25/1.22 = { by axiom 1 (commutativity_of_add) R->L }
% 6.25/1.22 add(negate(add(negate(add(negate(c), c)), negate(add(negate(c), add(negate(c), negate(add(c, negate(c)))))))), X)
% 6.25/1.22 = { by lemma 12 }
% 6.25/1.22 add(negate(c), X)
% 6.25/1.22 = { by axiom 1 (commutativity_of_add) }
% 6.25/1.22 add(X, negate(c))
% 6.25/1.22
% 6.25/1.22 Lemma 14: add(c, add(c, X)) = add(X, c).
% 6.25/1.22 Proof:
% 6.25/1.22 add(c, add(c, X))
% 6.25/1.22 = { by axiom 1 (commutativity_of_add) R->L }
% 6.25/1.22 add(c, add(X, c))
% 6.25/1.22 = { by lemma 8 }
% 6.25/1.22 add(X, c)
% 6.25/1.22
% 6.25/1.22 Lemma 15: add(X, negate(add(c, negate(c)))) = X.
% 6.25/1.22 Proof:
% 6.25/1.22 add(X, negate(add(c, negate(c))))
% 6.25/1.22 = { by lemma 6 R->L }
% 6.25/1.22 negate(add(negate(add(c, add(X, negate(add(c, negate(c)))))), negate(add(negate(c), add(X, negate(add(c, negate(c))))))))
% 6.25/1.22 = { by lemma 7 R->L }
% 6.25/1.22 negate(add(negate(add(X, add(c, negate(add(c, negate(c)))))), negate(add(negate(c), add(X, negate(add(c, negate(c))))))))
% 6.25/1.22 = { by axiom 1 (commutativity_of_add) R->L }
% 6.25/1.22 negate(add(negate(add(X, add(negate(add(c, negate(c))), c))), negate(add(negate(c), add(X, negate(add(c, negate(c))))))))
% 6.25/1.22 = { by lemma 13 R->L }
% 6.25/1.22 negate(add(negate(add(X, add(negate(add(negate(c), add(negate(c), c))), c))), negate(add(negate(c), add(X, negate(add(c, negate(c))))))))
% 6.25/1.22 = { by axiom 2 (idempotence) R->L }
% 6.25/1.22 negate(add(negate(add(X, add(negate(add(negate(c), add(negate(add(c, c)), c))), c))), negate(add(negate(c), add(X, negate(add(c, negate(c))))))))
% 6.25/1.22 = { by axiom 3 (associativity_of_add) R->L }
% 6.25/1.22 negate(add(negate(add(X, add(negate(add(add(negate(c), negate(add(c, c))), c)), c))), negate(add(negate(c), add(X, negate(add(c, negate(c))))))))
% 6.25/1.23 = { by lemma 14 R->L }
% 6.25/1.23 negate(add(negate(add(X, add(negate(add(c, add(c, add(negate(c), negate(add(c, c)))))), c))), negate(add(negate(c), add(X, negate(add(c, negate(c))))))))
% 6.25/1.23 = { by axiom 4 (robbins_axiom) R->L }
% 6.25/1.23 negate(add(negate(add(X, negate(add(negate(add(add(negate(add(c, add(c, add(negate(c), negate(add(c, c)))))), c), add(c, c))), negate(add(add(negate(add(c, add(c, add(negate(c), negate(add(c, c)))))), c), negate(add(c, c)))))))), negate(add(negate(c), add(X, negate(add(c, negate(c))))))))
% 6.25/1.23 = { by axiom 3 (associativity_of_add) }
% 6.25/1.23 negate(add(negate(add(X, negate(add(negate(add(negate(add(c, add(c, add(negate(c), negate(add(c, c)))))), add(c, add(c, c)))), negate(add(add(negate(add(c, add(c, add(negate(c), negate(add(c, c)))))), c), negate(add(c, c)))))))), negate(add(negate(c), add(X, negate(add(c, negate(c))))))))
% 6.25/1.23 = { by axiom 3 (associativity_of_add) }
% 6.25/1.23 negate(add(negate(add(X, negate(add(negate(add(negate(add(c, add(c, add(negate(c), negate(add(c, c)))))), add(c, add(c, c)))), negate(add(negate(add(c, add(c, add(negate(c), negate(add(c, c)))))), add(c, negate(add(c, c))))))))), negate(add(negate(c), add(X, negate(add(c, negate(c))))))))
% 6.25/1.23 = { by lemma 8 }
% 6.25/1.23 negate(add(negate(add(X, negate(add(negate(add(negate(add(c, add(c, add(negate(c), negate(add(c, c)))))), add(c, c))), negate(add(negate(add(c, add(c, add(negate(c), negate(add(c, c)))))), add(c, negate(add(c, c))))))))), negate(add(negate(c), add(X, negate(add(c, negate(c))))))))
% 6.25/1.23 = { by axiom 1 (commutativity_of_add) }
% 6.25/1.23 negate(add(negate(add(X, negate(add(negate(add(negate(add(c, add(c, add(negate(c), negate(add(c, c)))))), add(c, c))), negate(add(add(c, negate(add(c, c))), negate(add(c, add(c, add(negate(c), negate(add(c, c)))))))))))), negate(add(negate(c), add(X, negate(add(c, negate(c))))))))
% 6.25/1.23 = { by axiom 3 (associativity_of_add) }
% 6.25/1.23 negate(add(negate(add(X, negate(add(negate(add(negate(add(c, add(c, add(negate(c), negate(add(c, c)))))), add(c, c))), negate(add(c, add(negate(add(c, c)), negate(add(c, add(c, add(negate(c), negate(add(c, c))))))))))))), negate(add(negate(c), add(X, negate(add(c, negate(c))))))))
% 6.25/1.23 = { by axiom 1 (commutativity_of_add) }
% 6.25/1.23 negate(add(negate(add(X, negate(add(negate(add(add(c, c), negate(add(c, add(c, add(negate(c), negate(add(c, c)))))))), negate(add(c, add(negate(add(c, c)), negate(add(c, add(c, add(negate(c), negate(add(c, c))))))))))))), negate(add(negate(c), add(X, negate(add(c, negate(c))))))))
% 6.25/1.23 = { by axiom 3 (associativity_of_add) }
% 6.25/1.23 negate(add(negate(add(X, negate(add(negate(add(c, add(c, negate(add(c, add(c, add(negate(c), negate(add(c, c))))))))), negate(add(c, add(negate(add(c, c)), negate(add(c, add(c, add(negate(c), negate(add(c, c))))))))))))), negate(add(negate(c), add(X, negate(add(c, negate(c))))))))
% 6.25/1.23 = { by axiom 1 (commutativity_of_add) R->L }
% 6.25/1.23 negate(add(negate(add(X, negate(add(negate(add(c, add(c, negate(add(c, add(c, add(negate(add(c, c)), negate(c)))))))), negate(add(c, add(negate(add(c, c)), negate(add(c, add(c, add(negate(c), negate(add(c, c))))))))))))), negate(add(negate(c), add(X, negate(add(c, negate(c))))))))
% 6.25/1.23 = { by lemma 7 }
% 6.25/1.23 negate(add(negate(add(X, negate(add(negate(add(c, add(c, negate(add(c, add(negate(add(c, c)), add(c, negate(c)))))))), negate(add(c, add(negate(add(c, c)), negate(add(c, add(c, add(negate(c), negate(add(c, c))))))))))))), negate(add(negate(c), add(X, negate(add(c, negate(c))))))))
% 6.25/1.23 = { by lemma 7 }
% 6.25/1.23 negate(add(negate(add(X, negate(add(negate(add(c, add(c, negate(add(negate(add(c, c)), add(c, add(c, negate(c)))))))), negate(add(c, add(negate(add(c, c)), negate(add(c, add(c, add(negate(c), negate(add(c, c))))))))))))), negate(add(negate(c), add(X, negate(add(c, negate(c))))))))
% 6.25/1.23 = { by axiom 1 (commutativity_of_add) R->L }
% 6.25/1.23 negate(add(negate(add(X, negate(add(negate(add(c, add(negate(add(negate(add(c, c)), add(c, add(c, negate(c))))), c))), negate(add(c, add(negate(add(c, c)), negate(add(c, add(c, add(negate(c), negate(add(c, c))))))))))))), negate(add(negate(c), add(X, negate(add(c, negate(c))))))))
% 6.25/1.23 = { by lemma 7 }
% 6.25/1.23 negate(add(negate(add(X, negate(add(negate(add(negate(add(negate(add(c, c)), add(c, add(c, negate(c))))), add(c, c))), negate(add(c, add(negate(add(c, c)), negate(add(c, add(c, add(negate(c), negate(add(c, c))))))))))))), negate(add(negate(c), add(X, negate(add(c, negate(c))))))))
% 6.25/1.23 = { by lemma 5 R->L }
% 6.25/1.23 negate(add(negate(add(X, negate(add(negate(add(negate(add(negate(add(c, c)), add(c, add(c, negate(c))))), negate(add(negate(add(c, add(c, c))), negate(add(add(c, c), negate(c))))))), negate(add(c, add(negate(add(c, c)), negate(add(c, add(c, add(negate(c), negate(add(c, c))))))))))))), negate(add(negate(c), add(X, negate(add(c, negate(c))))))))
% 6.25/1.23 = { by lemma 8 }
% 6.25/1.23 negate(add(negate(add(X, negate(add(negate(add(negate(add(negate(add(c, c)), add(c, add(c, negate(c))))), negate(add(negate(add(c, c)), negate(add(add(c, c), negate(c))))))), negate(add(c, add(negate(add(c, c)), negate(add(c, add(c, add(negate(c), negate(add(c, c))))))))))))), negate(add(negate(c), add(X, negate(add(c, negate(c))))))))
% 6.25/1.23 = { by axiom 3 (associativity_of_add) }
% 6.25/1.23 negate(add(negate(add(X, negate(add(negate(add(negate(add(negate(add(c, c)), add(c, add(c, negate(c))))), negate(add(negate(add(c, c)), negate(add(c, add(c, negate(c)))))))), negate(add(c, add(negate(add(c, c)), negate(add(c, add(c, add(negate(c), negate(add(c, c))))))))))))), negate(add(negate(c), add(X, negate(add(c, negate(c))))))))
% 6.25/1.23 = { by axiom 4 (robbins_axiom) }
% 6.25/1.23 negate(add(negate(add(X, negate(add(negate(add(c, c)), negate(add(c, add(negate(add(c, c)), negate(add(c, add(c, add(negate(c), negate(add(c, c))))))))))))), negate(add(negate(c), add(X, negate(add(c, negate(c))))))))
% 6.25/1.23 = { by axiom 2 (idempotence) }
% 6.25/1.23 negate(add(negate(add(X, negate(add(negate(c), negate(add(c, add(negate(add(c, c)), negate(add(c, add(c, add(negate(c), negate(add(c, c))))))))))))), negate(add(negate(c), add(X, negate(add(c, negate(c))))))))
% 6.25/1.23 = { by axiom 2 (idempotence) }
% 6.25/1.23 negate(add(negate(add(X, negate(add(negate(c), negate(add(c, add(negate(c), negate(add(c, add(c, add(negate(c), negate(add(c, c))))))))))))), negate(add(negate(c), add(X, negate(add(c, negate(c))))))))
% 6.25/1.23 = { by axiom 2 (idempotence) }
% 6.25/1.23 negate(add(negate(add(X, negate(add(negate(c), negate(add(c, add(negate(c), negate(add(c, add(c, add(negate(c), negate(c)))))))))))), negate(add(negate(c), add(X, negate(add(c, negate(c))))))))
% 6.25/1.23 = { by lemma 14 }
% 6.25/1.23 negate(add(negate(add(X, negate(add(negate(c), negate(add(c, add(negate(c), negate(add(add(negate(c), negate(c)), c))))))))), negate(add(negate(c), add(X, negate(add(c, negate(c))))))))
% 6.25/1.23 = { by axiom 3 (associativity_of_add) }
% 6.25/1.23 negate(add(negate(add(X, negate(add(negate(c), negate(add(c, add(negate(c), negate(add(negate(c), add(negate(c), c)))))))))), negate(add(negate(c), add(X, negate(add(c, negate(c))))))))
% 6.25/1.23 = { by lemma 13 }
% 6.25/1.23 negate(add(negate(add(X, negate(add(negate(c), negate(add(c, add(negate(c), negate(add(c, negate(c)))))))))), negate(add(negate(c), add(X, negate(add(c, negate(c))))))))
% 6.25/1.23 = { by axiom 2 (idempotence) R->L }
% 6.25/1.23 negate(add(negate(add(X, negate(add(negate(add(c, c)), negate(add(c, add(negate(c), negate(add(c, negate(c)))))))))), negate(add(negate(c), add(X, negate(add(c, negate(c))))))))
% 6.25/1.23 = { by lemma 12 }
% 6.25/1.23 negate(add(negate(add(X, c)), negate(add(negate(c), add(X, negate(add(c, negate(c))))))))
% 6.25/1.23 = { by lemma 7 }
% 6.25/1.23 negate(add(negate(add(X, c)), negate(add(X, add(negate(c), negate(add(c, negate(c))))))))
% 6.25/1.23 = { by lemma 12 }
% 6.25/1.23 X
% 6.25/1.23
% 6.25/1.23 Lemma 16: add(negate(add(c, negate(c))), X) = X.
% 6.25/1.23 Proof:
% 6.25/1.23 add(negate(add(c, negate(c))), X)
% 6.25/1.23 = { by axiom 1 (commutativity_of_add) R->L }
% 6.25/1.23 add(X, negate(add(c, negate(c))))
% 6.25/1.23 = { by lemma 15 }
% 6.25/1.23 X
% 6.25/1.23
% 6.25/1.23 Lemma 17: negate(add(c, negate(c))) = negate(add(X, negate(X))).
% 6.25/1.23 Proof:
% 6.25/1.23 negate(add(c, negate(c)))
% 6.25/1.23 = { by axiom 4 (robbins_axiom) R->L }
% 6.25/1.23 negate(add(negate(add(negate(add(c, negate(c))), add(negate(add(X, Y)), negate(add(X, negate(Y)))))), negate(add(negate(add(c, negate(c))), negate(add(negate(add(X, Y)), negate(add(X, negate(Y)))))))))
% 6.25/1.23 = { by axiom 4 (robbins_axiom) }
% 6.25/1.23 negate(add(negate(add(negate(add(c, negate(c))), add(negate(add(X, Y)), negate(add(X, negate(Y)))))), negate(add(negate(add(c, negate(c))), X))))
% 6.25/1.23 = { by axiom 1 (commutativity_of_add) }
% 6.25/1.23 negate(add(negate(add(negate(add(c, negate(c))), X)), negate(add(negate(add(c, negate(c))), add(negate(add(X, Y)), negate(add(X, negate(Y))))))))
% 6.25/1.23 = { by lemma 16 }
% 6.25/1.23 negate(add(negate(X), negate(add(negate(add(c, negate(c))), add(negate(add(X, Y)), negate(add(X, negate(Y))))))))
% 6.25/1.23 = { by lemma 16 }
% 6.25/1.23 negate(add(negate(X), negate(add(negate(add(X, Y)), negate(add(X, negate(Y)))))))
% 6.25/1.23 = { by axiom 4 (robbins_axiom) }
% 6.25/1.23 negate(add(negate(X), X))
% 6.25/1.23 = { by axiom 1 (commutativity_of_add) }
% 6.25/1.23 negate(add(X, negate(X)))
% 6.25/1.23
% 6.25/1.23 Lemma 18: add(X, negate(add(Y, negate(Y)))) = X.
% 6.25/1.23 Proof:
% 6.25/1.23 add(X, negate(add(Y, negate(Y))))
% 6.25/1.23 = { by lemma 17 R->L }
% 6.25/1.24 add(X, negate(add(c, negate(c))))
% 6.25/1.24 = { by lemma 15 }
% 6.25/1.24 X
% 6.25/1.24
% 6.25/1.24 Lemma 19: negate(negate(add(X, X))) = X.
% 6.25/1.24 Proof:
% 6.25/1.24 negate(negate(add(X, X)))
% 6.25/1.24 = { by lemma 18 R->L }
% 6.25/1.24 negate(add(negate(add(X, X)), negate(add(X, negate(X)))))
% 6.25/1.24 = { by axiom 4 (robbins_axiom) }
% 6.25/1.24 X
% 6.25/1.24
% 6.25/1.24 Lemma 20: add(negate(add(X, negate(X))), Y) = Y.
% 6.25/1.24 Proof:
% 6.25/1.24 add(negate(add(X, negate(X))), Y)
% 6.25/1.24 = { by lemma 17 R->L }
% 6.25/1.24 add(negate(add(c, negate(c))), Y)
% 6.25/1.24 = { by lemma 16 }
% 6.25/1.24 Y
% 6.25/1.24
% 6.25/1.24 Lemma 21: negate(negate(X)) = X.
% 6.25/1.24 Proof:
% 6.25/1.24 negate(negate(X))
% 6.25/1.24 = { by lemma 18 R->L }
% 6.25/1.24 negate(add(negate(X), negate(add(X, negate(X)))))
% 6.25/1.24 = { by axiom 1 (commutativity_of_add) R->L }
% 6.25/1.24 negate(add(negate(X), negate(add(negate(X), X))))
% 6.25/1.24 = { by axiom 4 (robbins_axiom) R->L }
% 6.25/1.24 negate(add(negate(add(negate(add(negate(X), negate(add(X, X)))), negate(add(negate(X), negate(negate(add(X, X))))))), negate(add(negate(X), X))))
% 6.25/1.24 = { by lemma 19 }
% 6.25/1.24 negate(add(negate(add(negate(add(negate(X), negate(add(X, X)))), negate(add(negate(X), X)))), negate(add(negate(X), X))))
% 6.25/1.24 = { by axiom 1 (commutativity_of_add) }
% 6.25/1.24 negate(add(negate(add(negate(add(negate(X), X)), negate(add(negate(X), negate(add(X, X)))))), negate(add(negate(X), X))))
% 6.25/1.24 = { by axiom 1 (commutativity_of_add) }
% 6.25/1.24 negate(add(negate(add(negate(add(X, negate(X))), negate(add(negate(X), negate(add(X, X)))))), negate(add(negate(X), X))))
% 6.25/1.24 = { by lemma 20 }
% 6.25/1.24 negate(add(negate(negate(add(negate(X), negate(add(X, X))))), negate(add(negate(X), X))))
% 6.25/1.24 = { by axiom 1 (commutativity_of_add) R->L }
% 6.25/1.24 negate(add(negate(negate(add(negate(add(X, X)), negate(X)))), negate(add(negate(X), X))))
% 6.25/1.24 = { by lemma 20 R->L }
% 6.25/1.24 negate(add(negate(add(negate(add(negate(add(X, X)), negate(negate(add(X, X))))), negate(add(negate(add(X, X)), negate(X))))), negate(add(negate(X), X))))
% 6.25/1.24 = { by lemma 19 }
% 6.25/1.24 negate(add(negate(add(negate(add(negate(add(X, X)), X)), negate(add(negate(add(X, X)), negate(X))))), negate(add(negate(X), X))))
% 6.25/1.24 = { by axiom 1 (commutativity_of_add) }
% 6.25/1.24 negate(add(negate(add(negate(add(X, negate(add(X, X)))), negate(add(negate(add(X, X)), negate(X))))), negate(add(negate(X), X))))
% 6.25/1.24 = { by lemma 5 }
% 6.25/1.24 negate(add(negate(add(X, X)), negate(add(negate(X), X))))
% 6.25/1.24 = { by lemma 11 }
% 6.25/1.24 X
% 6.25/1.24
% 6.25/1.24 Goal 1 (prove_huntingtons_axiom): add(negate(add(a, negate(b))), negate(add(negate(a), negate(b)))) = b.
% 6.25/1.24 Proof:
% 6.25/1.24 add(negate(add(a, negate(b))), negate(add(negate(a), negate(b))))
% 6.25/1.24 = { by axiom 1 (commutativity_of_add) R->L }
% 6.25/1.24 add(negate(add(a, negate(b))), negate(add(negate(b), negate(a))))
% 6.25/1.24 = { by axiom 1 (commutativity_of_add) R->L }
% 6.25/1.24 add(negate(add(negate(b), a)), negate(add(negate(b), negate(a))))
% 6.25/1.24 = { by lemma 21 R->L }
% 6.25/1.24 negate(negate(add(negate(add(negate(b), a)), negate(add(negate(b), negate(a))))))
% 6.25/1.24 = { by axiom 4 (robbins_axiom) }
% 6.25/1.24 negate(negate(b))
% 6.25/1.24 = { by lemma 21 }
% 6.25/1.24 b
% 6.25/1.24 % SZS output end Proof
% 6.25/1.24
% 6.25/1.24 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------