TSTP Solution File: ROB004-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : ROB004-1 : 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 : n006.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 0.20s 0.45s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ROB004-1 : 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 : n006.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 06:51:36 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.45 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.20/0.45
% 0.20/0.45 % SZS status Unsatisfiable
% 0.20/0.45
% 0.20/0.46 % SZS output start Proof
% 0.20/0.46 Axiom 1 (negate_d_is_c): negate(d) = c.
% 0.20/0.46 Axiom 2 (commutativity_of_add): add(X, Y) = add(Y, X).
% 0.20/0.46 Axiom 3 (c_plus_c_is_c): add(c, c) = c.
% 0.20/0.46 Axiom 4 (c_plus_d_is_d): add(c, d) = d.
% 0.20/0.46 Axiom 5 (associativity_of_add): add(add(X, Y), Z) = add(X, add(Y, Z)).
% 0.20/0.46 Axiom 6 (robbins_axiom): negate(add(negate(add(X, Y)), negate(add(X, negate(Y))))) = X.
% 0.20/0.46
% 0.20/0.46 Lemma 7: negate(add(negate(add(X, Y)), negate(add(Y, negate(X))))) = Y.
% 0.20/0.46 Proof:
% 0.20/0.46 negate(add(negate(add(X, Y)), negate(add(Y, negate(X)))))
% 0.20/0.46 = { by axiom 2 (commutativity_of_add) R->L }
% 0.20/0.46 negate(add(negate(add(Y, X)), negate(add(Y, negate(X)))))
% 0.20/0.46 = { by axiom 6 (robbins_axiom) }
% 0.20/0.46 Y
% 0.20/0.46
% 0.20/0.46 Lemma 8: add(c, add(X, c)) = add(X, c).
% 0.20/0.46 Proof:
% 0.20/0.46 add(c, add(X, c))
% 0.20/0.46 = { by axiom 2 (commutativity_of_add) R->L }
% 0.20/0.46 add(c, add(c, X))
% 0.20/0.46 = { by axiom 5 (associativity_of_add) R->L }
% 0.20/0.46 add(add(c, c), X)
% 0.20/0.46 = { by axiom 3 (c_plus_c_is_c) }
% 0.20/0.46 add(c, X)
% 0.20/0.46 = { by axiom 2 (commutativity_of_add) }
% 0.20/0.46 add(X, c)
% 0.20/0.46
% 0.20/0.46 Lemma 9: negate(add(negate(add(X, c)), negate(add(X, d)))) = X.
% 0.20/0.46 Proof:
% 0.20/0.46 negate(add(negate(add(X, c)), negate(add(X, d))))
% 0.20/0.46 = { by axiom 2 (commutativity_of_add) R->L }
% 0.20/0.46 negate(add(negate(add(X, d)), negate(add(X, c))))
% 0.20/0.46 = { by axiom 1 (negate_d_is_c) R->L }
% 0.20/0.46 negate(add(negate(add(X, d)), negate(add(X, negate(d)))))
% 0.20/0.46 = { by axiom 6 (robbins_axiom) }
% 0.20/0.46 X
% 0.20/0.46
% 0.20/0.46 Lemma 10: negate(add(negate(add(c, X)), negate(add(X, d)))) = X.
% 0.20/0.46 Proof:
% 0.20/0.46 negate(add(negate(add(c, X)), negate(add(X, d))))
% 0.20/0.46 = { by axiom 2 (commutativity_of_add) R->L }
% 0.20/0.46 negate(add(negate(add(X, c)), negate(add(X, d))))
% 0.20/0.46 = { by lemma 9 }
% 0.20/0.47 X
% 0.20/0.47
% 0.20/0.47 Lemma 11: add(X, c) = X.
% 0.20/0.47 Proof:
% 0.20/0.47 add(X, c)
% 0.20/0.47 = { by lemma 7 R->L }
% 0.20/0.47 negate(add(negate(add(c, add(X, c))), negate(add(add(X, c), negate(c)))))
% 0.20/0.47 = { by lemma 8 }
% 0.20/0.47 negate(add(negate(add(X, c)), negate(add(add(X, c), negate(c)))))
% 0.20/0.47 = { by axiom 5 (associativity_of_add) }
% 0.20/0.47 negate(add(negate(add(X, c)), negate(add(X, add(c, negate(c))))))
% 0.20/0.47 = { by lemma 10 R->L }
% 0.20/0.47 negate(add(negate(add(X, c)), negate(add(X, add(c, negate(add(negate(add(c, negate(c))), negate(add(negate(c), d)))))))))
% 0.20/0.47 = { by axiom 3 (c_plus_c_is_c) R->L }
% 0.20/0.47 negate(add(negate(add(X, c)), negate(add(X, add(c, negate(add(negate(add(c, negate(add(c, c)))), negate(add(negate(c), d)))))))))
% 0.20/0.47 = { by axiom 1 (negate_d_is_c) R->L }
% 0.20/0.47 negate(add(negate(add(X, c)), negate(add(X, add(c, negate(add(negate(add(negate(d), negate(add(c, c)))), negate(add(negate(c), d)))))))))
% 0.20/0.47 = { by axiom 1 (negate_d_is_c) R->L }
% 0.20/0.47 negate(add(negate(add(X, c)), negate(add(X, add(c, negate(add(negate(add(negate(d), negate(add(c, negate(d))))), negate(add(negate(c), d)))))))))
% 0.20/0.47 = { by axiom 4 (c_plus_d_is_d) R->L }
% 0.20/0.47 negate(add(negate(add(X, c)), negate(add(X, add(c, negate(add(negate(add(negate(add(c, d)), negate(add(c, negate(d))))), negate(add(negate(c), d)))))))))
% 0.20/0.47 = { by axiom 6 (robbins_axiom) }
% 0.20/0.47 negate(add(negate(add(X, c)), negate(add(X, add(c, negate(add(c, negate(add(negate(c), d)))))))))
% 0.20/0.47 = { by axiom 2 (commutativity_of_add) }
% 0.20/0.47 negate(add(negate(add(X, c)), negate(add(X, add(c, negate(add(c, negate(add(d, negate(c))))))))))
% 0.20/0.47 = { by axiom 1 (negate_d_is_c) R->L }
% 0.20/0.47 negate(add(negate(add(X, c)), negate(add(X, add(c, negate(add(negate(d), negate(add(d, negate(c))))))))))
% 0.20/0.47 = { by axiom 4 (c_plus_d_is_d) R->L }
% 0.20/0.47 negate(add(negate(add(X, c)), negate(add(X, add(c, negate(add(negate(add(c, d)), negate(add(d, negate(c))))))))))
% 0.20/0.47 = { by lemma 7 }
% 0.20/0.47 negate(add(negate(add(X, c)), negate(add(X, add(c, d)))))
% 0.20/0.47 = { by axiom 4 (c_plus_d_is_d) }
% 0.20/0.47 negate(add(negate(add(X, c)), negate(add(X, d))))
% 0.20/0.47 = { by lemma 9 }
% 0.20/0.47 X
% 0.20/0.47
% 0.20/0.47 Lemma 12: negate(add(negate(X), negate(negate(X)))) = c.
% 0.20/0.47 Proof:
% 0.20/0.47 negate(add(negate(X), negate(negate(X))))
% 0.20/0.47 = { by lemma 11 R->L }
% 0.20/0.47 negate(add(negate(X), negate(add(negate(X), c))))
% 0.20/0.47 = { by axiom 2 (commutativity_of_add) }
% 0.20/0.47 negate(add(negate(X), negate(add(c, negate(X)))))
% 0.20/0.47 = { by lemma 11 R->L }
% 0.20/0.47 negate(add(negate(add(X, c)), negate(add(c, negate(X)))))
% 0.20/0.47 = { by lemma 7 }
% 0.20/0.47 c
% 0.20/0.47
% 0.20/0.47 Lemma 13: negate(add(negate(X), negate(add(X, d)))) = X.
% 0.20/0.47 Proof:
% 0.20/0.47 negate(add(negate(X), negate(add(X, d))))
% 0.20/0.47 = { by lemma 11 R->L }
% 0.20/0.47 negate(add(negate(add(X, c)), negate(add(X, d))))
% 0.20/0.47 = { by lemma 11 R->L }
% 0.20/0.47 negate(add(negate(add(X, c)), negate(add(add(X, c), d))))
% 0.20/0.47 = { by lemma 8 R->L }
% 0.20/0.47 negate(add(negate(add(c, add(X, c))), negate(add(add(X, c), d))))
% 0.20/0.47 = { by lemma 10 }
% 0.20/0.47 add(X, c)
% 0.20/0.47 = { by lemma 11 }
% 0.20/0.47 X
% 0.20/0.47
% 0.20/0.47 Lemma 14: negate(add(negate(add(X, Y)), negate(add(negate(X), Y)))) = Y.
% 0.20/0.47 Proof:
% 0.20/0.47 negate(add(negate(add(X, Y)), negate(add(negate(X), Y))))
% 0.20/0.47 = { by axiom 2 (commutativity_of_add) R->L }
% 0.20/0.47 negate(add(negate(add(X, Y)), negate(add(Y, negate(X)))))
% 0.20/0.47 = { by lemma 7 }
% 0.20/0.47 Y
% 0.20/0.47
% 0.20/0.47 Lemma 15: negate(add(X, negate(add(d, add(negate(add(Y, X)), negate(add(negate(Y), X))))))) = add(negate(add(Y, X)), negate(add(negate(Y), X))).
% 0.20/0.47 Proof:
% 0.20/0.47 negate(add(X, negate(add(d, add(negate(add(Y, X)), negate(add(negate(Y), X)))))))
% 0.20/0.47 = { by axiom 2 (commutativity_of_add) R->L }
% 0.20/0.47 negate(add(X, negate(add(add(negate(add(Y, X)), negate(add(negate(Y), X))), d))))
% 0.20/0.47 = { by lemma 14 R->L }
% 0.20/0.47 negate(add(negate(add(negate(add(Y, X)), negate(add(negate(Y), X)))), negate(add(add(negate(add(Y, X)), negate(add(negate(Y), X))), d))))
% 0.20/0.47 = { by lemma 13 }
% 0.20/0.47 add(negate(add(Y, X)), negate(add(negate(Y), X)))
% 0.20/0.47
% 0.20/0.47 Goal 1 (prove_huntingtons_axiom): add(negate(add(a, negate(b))), negate(add(negate(a), negate(b)))) = b.
% 0.20/0.47 Proof:
% 0.20/0.47 add(negate(add(a, negate(b))), negate(add(negate(a), negate(b))))
% 0.20/0.47 = { by axiom 6 (robbins_axiom) R->L }
% 0.20/0.47 negate(add(negate(add(add(negate(add(a, negate(b))), negate(add(negate(a), negate(b)))), b)), negate(add(add(negate(add(a, negate(b))), negate(add(negate(a), negate(b)))), negate(b)))))
% 0.20/0.47 = { by lemma 14 R->L }
% 0.20/0.47 negate(add(negate(add(add(negate(add(a, negate(b))), negate(add(negate(a), negate(b)))), b)), negate(add(add(negate(add(a, negate(b))), negate(add(negate(a), negate(b)))), negate(add(negate(add(a, negate(b))), negate(add(negate(a), negate(b)))))))))
% 0.20/0.47 = { by lemma 15 R->L }
% 0.20/0.47 negate(add(negate(add(add(negate(add(a, negate(b))), negate(add(negate(a), negate(b)))), b)), negate(add(add(negate(add(a, negate(b))), negate(add(negate(a), negate(b)))), negate(negate(add(negate(b), negate(add(d, add(negate(add(a, negate(b))), negate(add(negate(a), negate(b)))))))))))))
% 0.20/0.47 = { by lemma 15 R->L }
% 0.20/0.47 negate(add(negate(add(add(negate(add(a, negate(b))), negate(add(negate(a), negate(b)))), b)), negate(add(negate(add(negate(b), negate(add(d, add(negate(add(a, negate(b))), negate(add(negate(a), negate(b)))))))), negate(negate(add(negate(b), negate(add(d, add(negate(add(a, negate(b))), negate(add(negate(a), negate(b)))))))))))))
% 0.20/0.47 = { by lemma 12 }
% 0.20/0.47 negate(add(negate(add(add(negate(add(a, negate(b))), negate(add(negate(a), negate(b)))), b)), c))
% 0.20/0.47 = { by lemma 11 }
% 0.20/0.47 negate(negate(add(add(negate(add(a, negate(b))), negate(add(negate(a), negate(b)))), b)))
% 0.20/0.47 = { by axiom 2 (commutativity_of_add) }
% 0.20/0.47 negate(negate(add(b, add(negate(add(a, negate(b))), negate(add(negate(a), negate(b)))))))
% 0.20/0.47 = { by lemma 11 R->L }
% 0.20/0.47 negate(add(negate(add(b, add(negate(add(a, negate(b))), negate(add(negate(a), negate(b)))))), c))
% 0.20/0.47 = { by lemma 12 R->L }
% 0.20/0.47 negate(add(negate(add(b, add(negate(add(a, negate(b))), negate(add(negate(a), negate(b)))))), negate(add(negate(add(negate(b), negate(add(b, d)))), negate(negate(add(negate(b), negate(add(b, d)))))))))
% 0.20/0.47 = { by lemma 13 }
% 0.20/0.47 negate(add(negate(add(b, add(negate(add(a, negate(b))), negate(add(negate(a), negate(b)))))), negate(add(b, negate(negate(add(negate(b), negate(add(b, d)))))))))
% 0.20/0.47 = { by lemma 13 }
% 0.20/0.47 negate(add(negate(add(b, add(negate(add(a, negate(b))), negate(add(negate(a), negate(b)))))), negate(add(b, negate(b)))))
% 0.20/0.47 = { by lemma 14 R->L }
% 0.20/0.47 negate(add(negate(add(b, add(negate(add(a, negate(b))), negate(add(negate(a), negate(b)))))), negate(add(b, negate(add(negate(add(a, negate(b))), negate(add(negate(a), negate(b)))))))))
% 0.20/0.47 = { by axiom 6 (robbins_axiom) }
% 0.20/0.47 b
% 0.20/0.47 % SZS output end Proof
% 0.20/0.47
% 0.20/0.47 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------