%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ROB004-1 : 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 : n014.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 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 7
% Syntax : Number of formulae : 49 ( 49 unt; 0 def)
% Number of atoms : 49 ( 48 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 : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn 7 !; 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(negate_d_is_c,axiom,
negate(d) = c,
file('theBenchmark.p',negate_d_is_c) ).
cnf(c_4,plain,
negate(d) = c,
inference(clausify,[status(thm)],[negate_d_is_c]) ).
fof(c_plus_d_is_d,axiom,
add(c,d) = d,
file('theBenchmark.p',c_plus_d_is_d) ).
cnf(c_5,plain,
add(c,d) = d,
inference(clausify,[status(thm)],[c_plus_d_is_d]) ).
fof(c_plus_c_is_c,axiom,
add(c,c) = c,
file('theBenchmark.p',c_plus_c_is_c) ).
cnf(c_6,plain,
add(c,c) = c,
inference(clausify,[status(thm)],[c_plus_c_is_c]) ).
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_7,plain,
add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) != b,
inference(clausify,[status(thm)],[prove_huntingtons_axiom]) ).
cnf(c_10,plain,
negate(add(negate(add(A,B)),negate(add(B,negate(A))))) = B,
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_11,plain,
negate(add(negate(add(A,B)),negate(add(negate(B),A)))) = A,
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_174,plain,
negate(add(negate(d),negate(add(c,negate(d))))) = c,
inference(paramod,[status(thm)],[c_5,c_3]) ).
cnf(c_175,plain,
negate(add(c,negate(add(c,negate(d))))) = c,
inference(paramod,[status(thm)],[c_4,c_174]) ).
cnf(c_176,plain,
negate(add(c,negate(add(c,c)))) = c,
inference(paramod,[status(thm)],[c_4,c_175]) ).
cnf(c_19,plain,
negate(add(c,negate(c))) = c,
inference(paramod,[status(thm)],[c_6,c_176]) ).
cnf(c_177,plain,
add(add(A,c),c) = add(A,c),
inference(paramod,[status(thm)],[c_6,c_2]) ).
cnf(c_21,plain,
add(c,add(A,c)) = add(A,c),
inference(paramod,[status(thm)],[c_1,c_177]) ).
cnf(c_178,plain,
negate(add(negate(add(A,add(c,negate(c)))),negate(add(A,c)))) = A,
inference(paramod,[status(thm)],[c_19,c_3]) ).
cnf(c_25,plain,
negate(add(negate(add(A,c)),negate(add(A,add(c,negate(c)))))) = A,
inference(paramod,[status(thm)],[c_1,c_178]) ).
cnf(c_35,plain,
negate(add(negate(add(A,B)),negate(add(negate(A),B)))) = B,
inference(paramod,[status(thm)],[c_1,c_10]) ).
cnf(c_53,plain,
negate(add(negate(add(A,c)),negate(add(c,negate(add(A,c)))))) = c,
inference(paramod,[status(thm)],[c_21,c_3]) ).
cnf(c_179,plain,
negate(add(negate(add(A,c)),negate(add(add(A,c),negate(c))))) = add(A,c),
inference(paramod,[status(thm)],[c_21,c_10]) ).
cnf(c_180,plain,
negate(add(negate(add(A,c)),negate(add(A,add(c,negate(c)))))) = add(A,c),
inference(paramod,[status(thm)],[c_2,c_179]) ).
cnf(c_181,plain,
A = add(A,c),
inference(paramod,[status(thm)],[c_25,c_180]) ).
cnf(c_54,plain,
add(A,c) = A,
inference(copy,[status(thm)],[c_181]) ).
cnf(c_182,plain,
negate(add(negate(A),negate(add(c,negate(add(A,c)))))) = c,
inference(paramod,[status(thm)],[c_54,c_53]) ).
cnf(c_55,plain,
negate(add(negate(A),negate(add(c,negate(A))))) = c,
inference(paramod,[status(thm)],[c_54,c_182]) ).
cnf(c_183,plain,
add(c,A) = add(A,c),
inference(paramod,[status(thm)],[c_54,c_21]) ).
cnf(c_59,plain,
add(c,A) = A,
inference(paramod,[status(thm)],[c_54,c_183]) ).
cnf(c_63,plain,
negate(add(negate(A),negate(negate(A)))) = c,
inference(paramod,[status(thm)],[c_59,c_55]) ).
cnf(c_184,plain,
negate(add(A,negate(negate(add(negate(add(A,B)),negate(add(A,negate(B)))))))) = c,
inference(paramod,[status(thm)],[c_3,c_63]) ).
cnf(c_89,plain,
negate(add(A,negate(A))) = c,
inference(paramod,[status(thm)],[c_3,c_184]) ).
cnf(c_185,plain,
negate(add(negate(add(negate(negate(A)),A)),c)) = negate(negate(A)),
inference(paramod,[status(thm)],[c_63,c_11]) ).
cnf(c_186,plain,
negate(add(negate(add(A,negate(negate(A)))),c)) = negate(negate(A)),
inference(paramod,[status(thm)],[c_1,c_185]) ).
cnf(c_187,plain,
negate(add(c,negate(add(A,negate(negate(A)))))) = negate(negate(A)),
inference(paramod,[status(thm)],[c_1,c_186]) ).
cnf(c_91,plain,
negate(negate(add(A,negate(negate(A))))) = negate(negate(A)),
inference(paramod,[status(thm)],[c_59,c_187]) ).
cnf(c_188,plain,
negate(add(c,negate(add(A,negate(negate(A)))))) = A,
inference(paramod,[status(thm)],[c_89,c_3]) ).
cnf(c_189,plain,
negate(negate(add(A,negate(negate(A))))) = A,
inference(paramod,[status(thm)],[c_59,c_188]) ).
cnf(c_95,plain,
negate(negate(A)) = A,
inference(paramod,[status(thm)],[c_91,c_189]) ).
cnf(c_190,plain,
negate(A) = add(negate(add(B,A)),negate(add(negate(B),A))),
inference(paramod,[status(thm)],[c_35,c_95]) ).
cnf(c_172,plain,
add(negate(add(A,B)),negate(add(negate(A),B))) = negate(B),
inference(copy,[status(thm)],[c_190]) ).
cnf(c_191,plain,
negate(negate(b)) != b,
inference(paramod,[status(thm)],[c_172,c_7]) ).
cnf(c_192,plain,
b != b,
inference(paramod,[status(thm)],[c_95,c_191]) ).
cnf(c_173,plain,
$false,
inference(copy,[status(thm)],[c_192]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ROB004-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 06:13:17 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 2360658 was started by sandbox2 on n014,
% 0.09/0.37 % Sat Sep 26 06:13:17 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.09/0.39
% 0.09/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.39
% 0.09/0.39 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.09/0.39 % Length of proof is 23.
% 0.09/0.39 % Level of proof is 9.
% 0.09/0.39 % Maximum clause weight is 15.000.
% 0.09/0.39 % Given clauses 38.
% 0.09/0.39
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------