%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM847+2 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:18:12 AM UTC 2026
% Result : Theorem 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 13 unt; 0 def)
% Number of atoms : 13 ( 12 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof('ass(cond(61, 0), 0)',axiom,
! [Vd78,Vd79] : vplus(Vd79,Vd78) = vplus(Vd78,Vd79),
file('theBenchmark.p','ass(cond(61, 0), 0)') ).
fof('ass(cond(33, 0), 0)',axiom,
! [Vd46,Vd47,Vd48] : vplus(vplus(Vd46,Vd47),Vd48) = vplus(Vd46,vplus(Vd47,Vd48)),
file('theBenchmark.p','ass(cond(33, 0), 0)') ).
fof('holds(286, 441, 3)',conjecture,
vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) = vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),
file('theBenchmark.p','holds(286, 441, 3)') ).
fof('holds(286, 441, 3)_neg',negated_conjecture,
vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) != vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),
inference(assume_negation,[status(cth)],['holds(286, 441, 3)']) ).
cnf(c_28,plain,
vplus(A,B) = vplus(B,A),
inference(clausify,[status(thm)],['ass(cond(61, 0), 0)']) ).
cnf(c_31,plain,
vplus(vplus(A,B),C) = vplus(A,vplus(B,C)),
inference(clausify,[status(thm)],['ass(cond(33, 0), 0)']) ).
cnf(c_39,negated_conjecture,
vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) != vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),
inference(clausify,[status(thm)],['holds(286, 441, 3)_neg']) ).
cnf(c_47,negated_conjecture,
vplus(vd436,vplus(vmul(vd436,vd437),vmul(vd436,vd439))) != vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),
inference(paramod,[status(thm)],[c_28,c_39]) ).
cnf(c_48,negated_conjecture,
vplus(vd436,vplus(vmul(vd436,vd437),vmul(vd436,vd439))) != vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))),
inference(paramod,[status(thm)],[c_28,c_47]) ).
cnf(c_40,negated_conjecture,
vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))) != vplus(vd436,vplus(vmul(vd436,vd437),vmul(vd436,vd439))),
inference(copy,[status(thm)],[c_48]) ).
cnf(c_49,plain,
vplus(vplus(A,B),C) = vplus(B,vplus(A,C)),
inference(paramod,[status(thm)],[c_28,c_31]) ).
cnf(c_45,plain,
vplus(A,vplus(B,C)) = vplus(B,vplus(A,C)),
inference(paramod,[status(thm)],[c_31,c_49]) ).
cnf(c_46,plain,
$false,
inference(resolve,[status(thm)],[c_45,c_40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM847+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n017.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 04:08:33 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 3963657 was started by sandbox on n017,
% 0.09/0.37 % Sat Sep 26 04:08:33 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 0.14/0.39
% 0.14/0.39 % SZS status Theorem for theBenchmark
% 0.14/0.39
% 0.14/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.14/0.39 % Length of proof is 9.
% 0.14/0.39 % Level of proof is 3.
% 0.14/0.39 % Maximum clause weight is 19.000.
% 0.14/0.39 % Given clauses 6.
% 0.14/0.39
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------