%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM001-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 08:16:00 AM UTC 2026
% Result : Unsatisfiable 0.08s 0.39s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 10 unt; 0 def)
% Number of atoms : 22 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 17 ( 10 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(transitivity,axiom,
! [VAR_0,VAR_1,VAR_2] :
( equalish(VAR_0,VAR_2)
| ~ equalish(VAR_1,VAR_2)
| ~ equalish(VAR_0,VAR_1) ),
file('theBenchmark.p',transitivity) ).
cnf(c_2,plain,
( equalish(A,C)
| ~ equalish(B,C)
| ~ equalish(A,B) ),
inference(clausify,[status(thm)],[transitivity]) ).
fof(commutativity_of_addition,axiom,
! [VAR_0,VAR_1] : equalish(add(VAR_0,VAR_1),add(VAR_1,VAR_0)),
file('theBenchmark.p',commutativity_of_addition) ).
cnf(c_3,plain,
equalish(add(A,B),add(B,A)),
inference(clausify,[status(thm)],[commutativity_of_addition]) ).
fof(associativity_of_addition,axiom,
! [VAR_0,VAR_1,VAR_2] : equalish(add(VAR_0,add(VAR_1,VAR_2)),add(add(VAR_0,VAR_1),VAR_2)),
file('theBenchmark.p',associativity_of_addition) ).
cnf(c_4,plain,
equalish(add(A,add(B,C)),add(add(A,B),C)),
inference(clausify,[status(thm)],[associativity_of_addition]) ).
fof(prove_equation,axiom,
~ equalish(add(add(a,b),c),add(a,add(b,c))),
file('theBenchmark.p',prove_equation) ).
cnf(c_13,plain,
~ equalish(add(add(a,b),c),add(a,add(b,c))),
inference(clausify,[status(thm)],[prove_equation]) ).
cnf(c_212,plain,
( equalish(add(B,A),C)
| ~ equalish(add(A,B),C) ),
inference(resolve,[status(thm)],[c_2,c_3]) ).
cnf(c_15,plain,
equalish(add(add(A,B),C),add(add(C,A),B)),
inference(resolve,[status(thm)],[c_212,c_4]) ).
cnf(c_213,plain,
( equalish(A,add(C,B))
| ~ equalish(A,add(B,C)) ),
inference(resolve,[status(thm)],[c_2,c_3]) ).
cnf(c_139,plain,
~ equalish(add(add(a,b),c),add(add(b,c),a)),
inference(resolve,[status(thm)],[c_213,c_13]) ).
cnf(c_214,plain,
( equalish(add(add(B,C),A),D)
| ~ equalish(add(add(A,B),C),D) ),
inference(resolve,[status(thm)],[c_2,c_15]) ).
cnf(c_210,plain,
equalish(add(add(A,B),C),add(add(B,C),A)),
inference(resolve,[status(thm)],[c_214,c_15]) ).
cnf(c_211,plain,
$false,
inference(resolve,[status(thm)],[c_210,c_139]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM001-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.37 % Computer : n016.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Sat Sep 26 01:56:46 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.38 % Process 3937513 was started by sandbox2 on n016,
% 0.08/0.38 % Sat Sep 26 01:56:46 2026
% 0.08/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.38
% 0.08/0.38 % From the command line: assign(max_seconds, 300).
% 0.08/0.39
% 0.08/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.08/0.39
% 0.08/0.39 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.08/0.39 % Length of proof is 8.
% 0.08/0.39 % Level of proof is 3.
% 0.08/0.39 % Maximum clause weight is 26.000.
% 0.08/0.39 % Given clauses 15.
% 0.08/0.39
% 0.08/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------