%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ROB003-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 08:26:56 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.42s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 30 unt; 0 def)
% Number of atoms : 30 ( 29 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 7 ( 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 : 37 ( 4 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_of_add,axiom,
! [VAR_0,VAR_1] : add(VAR_0,VAR_1) = add(VAR_1,VAR_0),
file('theBenchmark.p',commutativity_of_add) ).
cnf(c_1,plain,
add(A,B) = add(B,A),
inference(clausify,[status(thm)],[commutativity_of_add]) ).
fof(associativity_of_add,axiom,
! [VAR_0,VAR_1,VAR_2] : add(add(VAR_0,VAR_1),VAR_2) = add(VAR_0,add(VAR_1,VAR_2)),
file('theBenchmark.p',associativity_of_add) ).
cnf(c_2,plain,
add(add(A,B),C) = add(A,add(B,C)),
inference(clausify,[status(thm)],[associativity_of_add]) ).
fof(robbins_axiom,axiom,
! [VAR_0,VAR_1] : negate(add(negate(add(VAR_0,VAR_1)),negate(add(VAR_0,negate(VAR_1))))) = VAR_0,
file('theBenchmark.p',robbins_axiom) ).
cnf(c_3,plain,
negate(add(negate(add(A,B)),negate(add(A,negate(B))))) = A,
inference(clausify,[status(thm)],[robbins_axiom]) ).
fof(there_exists_a_constant,axiom,
! [VAR_0] : add(VAR_0,c) = c,
file('theBenchmark.p',there_exists_a_constant) ).
cnf(c_4,plain,
add(A,c) = c,
inference(clausify,[status(thm)],[there_exists_a_constant]) ).
fof(prove_huntingtons_axiom,axiom,
add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) != b,
file('theBenchmark.p',prove_huntingtons_axiom) ).
cnf(c_5,plain,
add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) != b,
inference(clausify,[status(thm)],[prove_huntingtons_axiom]) ).
cnf(c_8,plain,
negate(add(negate(add(A,B)),negate(add(B,negate(A))))) = B,
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_9,plain,
negate(add(negate(add(A,B)),negate(add(negate(B),A)))) = A,
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_97,plain,
c = add(c,A),
inference(paramod,[status(thm)],[c_4,c_1]) ).
cnf(c_14,plain,
add(c,A) = c,
inference(copy,[status(thm)],[c_97]) ).
cnf(c_17,plain,
negate(add(negate(add(A,B)),negate(add(negate(A),B)))) = B,
inference(paramod,[status(thm)],[c_1,c_8]) ).
cnf(c_98,plain,
negate(add(negate(c),negate(add(c,negate(A))))) = c,
inference(paramod,[status(thm)],[c_4,c_8]) ).
cnf(c_26,plain,
negate(add(negate(c),negate(c))) = c,
inference(paramod,[status(thm)],[c_14,c_98]) ).
cnf(c_37,plain,
negate(add(negate(c),negate(add(negate(c),A)))) = A,
inference(paramod,[status(thm)],[c_4,c_9]) ).
cnf(c_99,plain,
negate(add(negate(add(add(negate(c),negate(c)),A)),negate(add(A,c)))) = A,
inference(paramod,[status(thm)],[c_26,c_8]) ).
cnf(c_100,plain,
negate(add(negate(add(negate(c),add(negate(c),A))),negate(add(A,c)))) = A,
inference(paramod,[status(thm)],[c_2,c_99]) ).
cnf(c_101,plain,
negate(add(negate(add(negate(c),add(negate(c),A))),negate(c))) = A,
inference(paramod,[status(thm)],[c_4,c_100]) ).
cnf(c_102,plain,
negate(add(negate(c),negate(add(negate(c),add(negate(c),A))))) = A,
inference(paramod,[status(thm)],[c_1,c_101]) ).
cnf(c_47,plain,
add(negate(c),A) = A,
inference(paramod,[status(thm)],[c_37,c_102]) ).
cnf(c_103,plain,
negate(add(negate(c),negate(A))) = A,
inference(paramod,[status(thm)],[c_47,c_37]) ).
cnf(c_49,plain,
negate(negate(A)) = A,
inference(paramod,[status(thm)],[c_47,c_103]) ).
cnf(c_104,plain,
negate(A) = add(negate(add(B,A)),negate(add(negate(B),A))),
inference(paramod,[status(thm)],[c_17,c_49]) ).
cnf(c_93,plain,
add(negate(add(A,B)),negate(add(negate(A),B))) = negate(B),
inference(copy,[status(thm)],[c_104]) ).
cnf(c_105,plain,
negate(negate(b)) != b,
inference(paramod,[status(thm)],[c_93,c_5]) ).
cnf(c_106,plain,
b != b,
inference(paramod,[status(thm)],[c_49,c_105]) ).
cnf(c_96,plain,
$false,
inference(copy,[status(thm)],[c_106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ROB003-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n003.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 06:14:38 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 2204633 was started by sandbox on n003,
% 0.09/0.37 % Sat Sep 26 06:14:38 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).
% 0.09/0.42
% 0.09/0.42 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.42
% 0.09/0.42 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.09/0.42 % Length of proof is 15.
% 0.09/0.42 % Level of proof is 6.
% 0.09/0.42 % Maximum clause weight is 43.000.
% 0.09/0.42 % Given clauses 24.
% 0.09/0.42
% 0.09/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------