TSTP Solution File: NUN133-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : NUN133-1 : 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 : n005.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 12:52:03 EDT 2023
% Result : Unsatisfiable 7.01s 1.32s
% Output : Proof 7.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUN133-1 : TPTP v8.1.2. Released v8.1.0.
% 0.12/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n005.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Aug 27 09:55:38 EDT 2023
% 0.14/0.35 % CPUTime :
% 7.01/1.32 Command-line arguments: --flatten
% 7.01/1.32
% 7.01/1.32 % SZS status Unsatisfiable
% 7.01/1.32
% 7.01/1.33 % SZS output start Proof
% 7.01/1.33 Axiom 1 (plus_comm): X + Y = Y + X.
% 7.01/1.33 Axiom 2 (times_comm): times(X, Y) = times(Y, X).
% 7.01/1.33 Axiom 3 (times_s): times(s(X), Y) = Y + times(X, Y).
% 7.01/1.33 Axiom 4 (plus_sum): sum(X) + sum(X) = times(X, s(X)).
% 7.01/1.33 Axiom 5 (sum_s): sum(s(X)) = s(X) + sum(X).
% 7.01/1.33 Axiom 6 (plus_assoc): X + (Y + Z) = (X + Y) + Z.
% 7.01/1.33 Axiom 7 (induction_hypothesis): times(sum(a), sum(a)) = cubes(a).
% 7.01/1.33 Axiom 8 (distr): times(X, Y + Z) = times(X, Y) + times(X, Z).
% 7.01/1.33 Axiom 9 (cubes_s): cubes(s(X)) = times(s(X), times(s(X), s(X))) + cubes(X).
% 7.01/1.33
% 7.01/1.33 Goal 1 (goal): times(sum(s(a)), sum(s(a))) = cubes(s(a)).
% 7.01/1.33 Proof:
% 7.01/1.33 times(sum(s(a)), sum(s(a)))
% 7.01/1.33 = { by axiom 5 (sum_s) }
% 7.01/1.33 times(sum(s(a)), s(a) + sum(a))
% 7.01/1.33 = { by axiom 8 (distr) }
% 7.01/1.33 times(sum(s(a)), s(a)) + times(sum(s(a)), sum(a))
% 7.01/1.33 = { by axiom 2 (times_comm) R->L }
% 7.01/1.33 times(s(a), sum(s(a))) + times(sum(s(a)), sum(a))
% 7.01/1.33 = { by axiom 2 (times_comm) R->L }
% 7.01/1.33 times(s(a), sum(s(a))) + times(sum(a), sum(s(a)))
% 7.01/1.33 = { by axiom 5 (sum_s) }
% 7.01/1.33 times(s(a), sum(s(a))) + times(sum(a), s(a) + sum(a))
% 7.01/1.33 = { by axiom 1 (plus_comm) R->L }
% 7.01/1.33 times(s(a), sum(s(a))) + times(sum(a), sum(a) + s(a))
% 7.01/1.33 = { by axiom 8 (distr) }
% 7.01/1.33 times(s(a), sum(s(a))) + (times(sum(a), sum(a)) + times(sum(a), s(a)))
% 7.01/1.33 = { by axiom 2 (times_comm) }
% 7.01/1.33 times(s(a), sum(s(a))) + (times(sum(a), sum(a)) + times(s(a), sum(a)))
% 7.01/1.33 = { by axiom 1 (plus_comm) R->L }
% 7.01/1.33 times(s(a), sum(s(a))) + (times(s(a), sum(a)) + times(sum(a), sum(a)))
% 7.01/1.33 = { by axiom 6 (plus_assoc) }
% 7.01/1.33 (times(s(a), sum(s(a))) + times(s(a), sum(a))) + times(sum(a), sum(a))
% 7.01/1.33 = { by axiom 8 (distr) R->L }
% 7.01/1.33 times(s(a), sum(s(a)) + sum(a)) + times(sum(a), sum(a))
% 7.01/1.33 = { by axiom 1 (plus_comm) }
% 7.01/1.33 times(sum(a), sum(a)) + times(s(a), sum(s(a)) + sum(a))
% 7.01/1.33 = { by axiom 5 (sum_s) }
% 7.01/1.33 times(sum(a), sum(a)) + times(s(a), (s(a) + sum(a)) + sum(a))
% 7.01/1.33 = { by axiom 6 (plus_assoc) R->L }
% 7.01/1.33 times(sum(a), sum(a)) + times(s(a), s(a) + (sum(a) + sum(a)))
% 7.01/1.33 = { by axiom 4 (plus_sum) }
% 7.01/1.33 times(sum(a), sum(a)) + times(s(a), s(a) + times(a, s(a)))
% 7.01/1.33 = { by axiom 3 (times_s) R->L }
% 7.01/1.33 times(sum(a), sum(a)) + times(s(a), times(s(a), s(a)))
% 7.01/1.33 = { by axiom 7 (induction_hypothesis) }
% 7.01/1.33 cubes(a) + times(s(a), times(s(a), s(a)))
% 7.01/1.33 = { by axiom 1 (plus_comm) R->L }
% 7.01/1.33 times(s(a), times(s(a), s(a))) + cubes(a)
% 7.01/1.33 = { by axiom 9 (cubes_s) R->L }
% 7.01/1.33 cubes(s(a))
% 7.01/1.33 % SZS output end Proof
% 7.01/1.33
% 7.01/1.33 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------