TSTP Solution File: ANA133-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : ANA133-1 : TPTP v8.1.2. Released v8.1.0.
% 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 : 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 : Wed Aug 30 17:21:25 EDT 2023
% Result : Unsatisfiable 0.21s 0.80s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ANA133-1 : TPTP v8.1.2. Released v8.1.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n004.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 18:04:37 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.80 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.21/0.80
% 0.21/0.80 % SZS status Unsatisfiable
% 0.21/0.80
% 0.21/0.81 % SZS output start Proof
% 0.21/0.81 Axiom 1 (derivative_of_x): d(x) = one.
% 0.21/0.81 Axiom 2 (commutativity_of_times): times(X, Y) = times(Y, X).
% 0.21/0.81 Axiom 3 (times_one): times(one, X) = X.
% 0.21/0.81 Axiom 4 (commutativity_of_plus): X + Y = Y + X.
% 0.21/0.81 Axiom 5 (plus_zero): zero + X = X.
% 0.21/0.81 Axiom 6 (minus): X + minus(X) = zero.
% 0.21/0.81 Axiom 7 (derivative_of_sin): d(sin(X)) = times(cos(X), d(X)).
% 0.21/0.81 Axiom 8 (derivative_of_plus): d(X + Y) = d(X) + d(Y).
% 0.21/0.81 Axiom 9 (associtivity_of_plus): X + (Y + Z) = (X + Y) + Z.
% 0.21/0.81 Axiom 10 (derivative_of_cos): d(cos(X)) = minus(times(sin(X), d(X))).
% 0.21/0.81 Axiom 11 (derivative_of_times): d(times(X, Y)) = times(X, d(Y)) + times(Y, d(X)).
% 0.21/0.81
% 0.21/0.81 Goal 1 (goal): d(X) = times(x, cos(x)).
% 0.21/0.81 The goal is true when:
% 0.21/0.81 X = cos(x) + times(x, sin(x))
% 0.21/0.81
% 0.21/0.81 Proof:
% 0.21/0.81 d(cos(x) + times(x, sin(x)))
% 0.21/0.81 = { by axiom 2 (commutativity_of_times) R->L }
% 0.21/0.81 d(cos(x) + times(sin(x), x))
% 0.21/0.81 = { by axiom 8 (derivative_of_plus) }
% 0.21/0.81 d(cos(x)) + d(times(sin(x), x))
% 0.21/0.81 = { by axiom 10 (derivative_of_cos) }
% 0.21/0.81 minus(times(sin(x), d(x))) + d(times(sin(x), x))
% 0.21/0.81 = { by axiom 2 (commutativity_of_times) }
% 0.21/0.81 minus(times(d(x), sin(x))) + d(times(sin(x), x))
% 0.21/0.81 = { by axiom 1 (derivative_of_x) }
% 0.21/0.81 minus(times(one, sin(x))) + d(times(sin(x), x))
% 0.21/0.81 = { by axiom 3 (times_one) }
% 0.21/0.81 minus(sin(x)) + d(times(sin(x), x))
% 0.21/0.81 = { by axiom 4 (commutativity_of_plus) R->L }
% 0.21/0.81 d(times(sin(x), x)) + minus(sin(x))
% 0.21/0.81 = { by axiom 11 (derivative_of_times) }
% 0.21/0.81 (times(sin(x), d(x)) + times(x, d(sin(x)))) + minus(sin(x))
% 0.21/0.81 = { by axiom 1 (derivative_of_x) }
% 0.21/0.81 (times(sin(x), one) + times(x, d(sin(x)))) + minus(sin(x))
% 0.21/0.81 = { by axiom 2 (commutativity_of_times) R->L }
% 0.21/0.81 (times(one, sin(x)) + times(x, d(sin(x)))) + minus(sin(x))
% 0.21/0.81 = { by axiom 3 (times_one) }
% 0.21/0.81 (sin(x) + times(x, d(sin(x)))) + minus(sin(x))
% 0.21/0.81 = { by axiom 9 (associtivity_of_plus) R->L }
% 0.21/0.81 sin(x) + (times(x, d(sin(x))) + minus(sin(x)))
% 0.21/0.81 = { by axiom 4 (commutativity_of_plus) }
% 0.21/0.81 sin(x) + (minus(sin(x)) + times(x, d(sin(x))))
% 0.21/0.81 = { by axiom 9 (associtivity_of_plus) }
% 0.21/0.81 (sin(x) + minus(sin(x))) + times(x, d(sin(x)))
% 0.21/0.81 = { by axiom 6 (minus) }
% 0.21/0.81 zero + times(x, d(sin(x)))
% 0.21/0.81 = { by axiom 5 (plus_zero) }
% 0.21/0.81 times(x, d(sin(x)))
% 0.21/0.81 = { by axiom 7 (derivative_of_sin) }
% 0.21/0.81 times(x, times(cos(x), d(x)))
% 0.21/0.81 = { by axiom 2 (commutativity_of_times) }
% 0.21/0.81 times(x, times(d(x), cos(x)))
% 0.21/0.81 = { by axiom 1 (derivative_of_x) }
% 0.21/0.81 times(x, times(one, cos(x)))
% 0.21/0.81 = { by axiom 3 (times_one) }
% 0.21/0.81 times(x, cos(x))
% 0.21/0.81 % SZS output end Proof
% 0.21/0.81
% 0.21/0.81 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------