%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ROB005-1 : 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 1.78s 0.64s
% Output : CNFRefutation 1.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 5
% Syntax : Number of formulae : 67 ( 67 unt; 0 def)
% Number of atoms : 67 ( 66 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 ( 3 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 : 66 ( 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(idempotence,axiom,
add(c,c) = c,
file('theBenchmark.p',idempotence) ).
cnf(c_4,plain,
add(c,c) = c,
inference(clausify,[status(thm)],[idempotence]) ).
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_1028,plain,
add(add(A,B),C) = add(B,add(A,C)),
inference(paramod,[status(thm)],[c_1,c_2]) ).
cnf(c_7,plain,
add(A,add(B,C)) = add(B,add(A,C)),
inference(paramod,[status(thm)],[c_2,c_1028]) ).
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_1029,plain,
negate(add(negate(add(A,add(negate(add(B,C)),negate(add(B,negate(C)))))),negate(add(A,B)))) = A,
inference(paramod,[status(thm)],[c_3,c_3]) ).
cnf(c_12,plain,
negate(add(negate(add(A,B)),negate(add(A,add(negate(add(B,C)),negate(add(B,negate(C)))))))) = A,
inference(paramod,[status(thm)],[c_1,c_1029]) ).
cnf(c_1030,plain,
add(c,A) = add(c,add(c,A)),
inference(paramod,[status(thm)],[c_4,c_2]) ).
cnf(c_14,plain,
add(c,add(c,A)) = add(c,A),
inference(copy,[status(thm)],[c_1030]) ).
cnf(c_16,plain,
negate(add(negate(c),negate(add(c,negate(c))))) = c,
inference(paramod,[status(thm)],[c_4,c_3]) ).
cnf(c_1031,plain,
negate(add(negate(add(A,add(negate(c),negate(add(c,negate(c)))))),negate(add(A,c)))) = A,
inference(paramod,[status(thm)],[c_16,c_3]) ).
cnf(c_23,plain,
negate(add(negate(add(A,c)),negate(add(A,add(negate(c),negate(add(c,negate(c)))))))) = A,
inference(paramod,[status(thm)],[c_1,c_1031]) ).
cnf(c_1032,plain,
negate(add(negate(add(negate(c),add(c,negate(c)))),c)) = negate(c),
inference(paramod,[status(thm)],[c_16,c_3]) ).
cnf(c_1033,plain,
negate(add(negate(add(c,add(negate(c),negate(c)))),c)) = negate(c),
inference(paramod,[status(thm)],[c_7,c_1032]) ).
cnf(c_24,plain,
negate(add(c,negate(add(c,add(negate(c),negate(c)))))) = negate(c),
inference(paramod,[status(thm)],[c_1,c_1033]) ).
cnf(c_25,plain,
negate(add(negate(add(A,B)),negate(add(negate(A),B)))) = B,
inference(paramod,[status(thm)],[c_1,c_8]) ).
cnf(c_1034,plain,
negate(add(negate(add(c,A)),negate(add(add(c,A),negate(c))))) = add(c,A),
inference(paramod,[status(thm)],[c_14,c_8]) ).
cnf(c_35,plain,
negate(add(negate(add(c,A)),negate(add(c,add(A,negate(c)))))) = add(c,A),
inference(paramod,[status(thm)],[c_2,c_1034]) ).
cnf(c_1035,plain,
negate(add(negate(add(add(negate(c),negate(add(c,negate(c)))),A)),negate(add(c,A)))) = A,
inference(paramod,[status(thm)],[c_16,c_25]) ).
cnf(c_1036,plain,
negate(add(negate(add(negate(c),add(negate(add(c,negate(c))),A))),negate(add(c,A)))) = A,
inference(paramod,[status(thm)],[c_2,c_1035]) ).
cnf(c_73,plain,
negate(add(negate(add(c,A)),negate(add(negate(c),add(negate(add(c,negate(c))),A))))) = A,
inference(paramod,[status(thm)],[c_1,c_1036]) ).
cnf(c_1037,plain,
negate(add(negate(add(c,add(c,add(negate(c),negate(c))))),negate(c))) = c,
inference(paramod,[status(thm)],[c_24,c_3]) ).
cnf(c_1038,plain,
negate(add(negate(add(c,add(negate(c),negate(c)))),negate(c))) = c,
inference(paramod,[status(thm)],[c_14,c_1037]) ).
cnf(c_144,plain,
negate(add(negate(c),negate(add(c,add(negate(c),negate(c)))))) = c,
inference(paramod,[status(thm)],[c_1,c_1038]) ).
cnf(c_1039,plain,
negate(add(negate(c),negate(add(negate(add(c,add(negate(c),negate(c)))),negate(c))))) = negate(add(c,add(negate(c),negate(c)))),
inference(paramod,[status(thm)],[c_24,c_8]) ).
cnf(c_1040,plain,
negate(add(negate(c),negate(add(negate(c),negate(add(c,add(negate(c),negate(c)))))))) = negate(add(c,add(negate(c),negate(c)))),
inference(paramod,[status(thm)],[c_1,c_1039]) ).
cnf(c_1041,plain,
negate(add(negate(c),c)) = negate(add(c,add(negate(c),negate(c)))),
inference(paramod,[status(thm)],[c_144,c_1040]) ).
cnf(c_1042,plain,
negate(add(c,negate(c))) = negate(add(c,add(negate(c),negate(c)))),
inference(paramod,[status(thm)],[c_1,c_1041]) ).
cnf(c_145,plain,
negate(add(c,add(negate(c),negate(c)))) = negate(add(c,negate(c))),
inference(copy,[status(thm)],[c_1042]) ).
cnf(c_154,plain,
negate(add(c,negate(add(c,negate(c))))) = negate(c),
inference(paramod,[status(thm)],[c_145,c_24]) ).
cnf(c_1043,plain,
negate(add(negate(c),negate(add(c,add(negate(add(c,negate(c))),negate(c)))))) = add(c,negate(add(c,negate(c)))),
inference(paramod,[status(thm)],[c_154,c_35]) ).
cnf(c_533,plain,
negate(add(negate(c),negate(add(c,add(negate(c),negate(add(c,negate(c)))))))) = add(c,negate(add(c,negate(c)))),
inference(paramod,[status(thm)],[c_1,c_1043]) ).
cnf(c_1044,plain,
negate(add(negate(c),negate(add(c,add(negate(c),negate(add(c,negate(c)))))))) = c,
inference(paramod,[status(thm)],[c_4,c_23]) ).
cnf(c_646,plain,
add(c,negate(add(c,negate(c)))) = c,
inference(paramod,[status(thm)],[c_533,c_1044]) ).
cnf(c_1045,plain,
add(c,A) = add(c,add(negate(add(c,negate(c))),A)),
inference(paramod,[status(thm)],[c_646,c_2]) ).
cnf(c_667,plain,
add(c,add(negate(add(c,negate(c))),A)) = add(c,A),
inference(copy,[status(thm)],[c_1045]) ).
cnf(c_1046,plain,
negate(add(negate(add(c,A)),negate(add(add(negate(add(c,negate(c))),A),negate(c))))) = add(negate(add(c,negate(c))),A),
inference(paramod,[status(thm)],[c_667,c_8]) ).
cnf(c_1047,plain,
negate(add(negate(add(c,A)),negate(add(negate(c),add(negate(add(c,negate(c))),A))))) = add(negate(add(c,negate(c))),A),
inference(paramod,[status(thm)],[c_1,c_1046]) ).
cnf(c_1048,plain,
A = add(negate(add(c,negate(c))),A),
inference(paramod,[status(thm)],[c_73,c_1047]) ).
cnf(c_676,plain,
add(negate(add(c,negate(c))),A) = A,
inference(copy,[status(thm)],[c_1048]) ).
cnf(c_1049,plain,
negate(add(negate(A),negate(add(negate(add(c,negate(c))),add(negate(add(A,B)),negate(add(A,negate(B)))))))) = negate(add(c,negate(c))),
inference(paramod,[status(thm)],[c_676,c_12]) ).
cnf(c_1050,plain,
negate(add(negate(A),negate(add(negate(add(A,B)),negate(add(A,negate(B))))))) = negate(add(c,negate(c))),
inference(paramod,[status(thm)],[c_676,c_1049]) ).
cnf(c_1051,plain,
negate(add(negate(A),A)) = negate(add(c,negate(c))),
inference(paramod,[status(thm)],[c_3,c_1050]) ).
cnf(c_1052,plain,
negate(add(A,negate(A))) = negate(add(c,negate(c))),
inference(paramod,[status(thm)],[c_1,c_1051]) ).
cnf(c_703,plain,
negate(add(c,negate(c))) = negate(add(A,negate(A))),
inference(copy,[status(thm)],[c_1052]) ).
cnf(c_1053,plain,
negate(add(negate(add(c,negate(c))),negate(add(A,negate(negate(A)))))) = A,
inference(paramod,[status(thm)],[c_703,c_3]) ).
cnf(c_865,plain,
negate(negate(add(A,negate(negate(A))))) = A,
inference(paramod,[status(thm)],[c_676,c_1053]) ).
cnf(c_1054,plain,
negate(add(negate(add(negate(negate(A)),A)),negate(add(c,negate(c))))) = negate(negate(A)),
inference(paramod,[status(thm)],[c_703,c_9]) ).
cnf(c_1055,plain,
negate(add(negate(add(A,negate(negate(A)))),negate(add(c,negate(c))))) = negate(negate(A)),
inference(paramod,[status(thm)],[c_1,c_1054]) ).
cnf(c_1056,plain,
negate(add(negate(add(c,negate(c))),negate(add(A,negate(negate(A)))))) = negate(negate(A)),
inference(paramod,[status(thm)],[c_1,c_1055]) ).
cnf(c_1057,plain,
negate(negate(add(A,negate(negate(A))))) = negate(negate(A)),
inference(paramod,[status(thm)],[c_676,c_1056]) ).
cnf(c_1058,plain,
A = negate(negate(A)),
inference(paramod,[status(thm)],[c_865,c_1057]) ).
cnf(c_873,plain,
negate(negate(A)) = A,
inference(copy,[status(thm)],[c_1058]) ).
cnf(c_1059,plain,
negate(A) = add(negate(add(B,A)),negate(add(negate(B),A))),
inference(paramod,[status(thm)],[c_25,c_873]) ).
cnf(c_1012,plain,
add(negate(add(A,B)),negate(add(negate(A),B))) = negate(B),
inference(copy,[status(thm)],[c_1059]) ).
cnf(c_1060,plain,
negate(negate(b)) != b,
inference(paramod,[status(thm)],[c_1012,c_5]) ).
cnf(c_1061,plain,
b != b,
inference(paramod,[status(thm)],[c_873,c_1060]) ).
cnf(c_1027,plain,
$false,
inference(copy,[status(thm)],[c_1061]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ROB005-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n003.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 06:14:53 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.02/0.37 % Process 2205031 was started by sandbox on n003,
% 0.02/0.37 % Sat Sep 26 06:14:53 2026
% 0.02/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.02/0.37
% 0.02/0.37 % From the command line: assign(max_seconds, 300).
% 1.78/0.64
% 1.78/0.64 % SZS status Unsatisfiable for theBenchmark
% 1.78/0.64
% 1.78/0.64 % Proof 1 at 0.21 (+ 0.05) seconds.
% 1.78/0.64 % Length of proof is 28.
% 1.78/0.64 % Level of proof is 14.
% 1.78/0.64 % Maximum clause weight is 23.000.
% 1.78/0.64 % Given clauses 48.
% 1.78/0.64
% 1.78/0.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------