%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ROB014-2 : 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 : 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 08:26:57 AM UTC 2026
% Result : Unsatisfiable 0.20s 0.47s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 34 unt; 0 def)
% Number of atoms : 38 ( 37 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 17 ( 15 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 12 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 11 !; 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(one_times_x,axiom,
! [VAR_0] : multiply(one,VAR_0) = VAR_0,
file('theBenchmark.p',one_times_x) ).
cnf(c_4,plain,
multiply(one,A) = A,
inference(clausify,[status(thm)],[one_times_x]) ).
fof(lemma_3_2,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_0 = VAR_1
| negate(add(VAR_0,negate(add(VAR_1,VAR_2)))) != negate(add(VAR_1,negate(add(VAR_0,VAR_2)))) ),
file('theBenchmark.p',lemma_3_2) ).
cnf(c_8,plain,
( A = B
| negate(add(A,negate(add(B,C)))) != negate(add(B,negate(add(A,C)))) ),
inference(clausify,[status(thm)],[lemma_3_2]) ).
fof(condition,axiom,
negate(add(negate(e),negate(add(d,negate(e))))) = d,
file('theBenchmark.p',condition) ).
cnf(c_10,plain,
negate(add(negate(e),negate(add(d,negate(e))))) = d,
inference(clausify,[status(thm)],[condition]) ).
fof(prove_base_step,axiom,
negate(add(e,multiply(one,add(d,negate(add(d,negate(e))))))) != negate(e),
file('theBenchmark.p',prove_base_step) ).
cnf(c_11,plain,
negate(add(e,multiply(one,add(d,negate(add(d,negate(e))))))) != negate(e),
inference(clausify,[status(thm)],[prove_base_step]) ).
cnf(c_12,plain,
negate(add(e,add(d,negate(add(d,negate(e)))))) != negate(e),
inference(paramod,[status(thm)],[c_4,c_11]) ).
cnf(c_117,plain,
add(add(A,B),C) = add(B,add(A,C)),
inference(paramod,[status(thm)],[c_1,c_2]) ).
cnf(c_14,plain,
add(A,add(B,C)) = add(B,add(A,C)),
inference(paramod,[status(thm)],[c_2,c_117]) ).
cnf(c_15,plain,
negate(add(d,add(e,negate(add(d,negate(e)))))) != negate(e),
inference(paramod,[status(thm)],[c_14,c_12]) ).
cnf(c_17,plain,
negate(add(negate(add(A,B)),negate(add(negate(B),A)))) = A,
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_118,plain,
negate(add(negate(add(d,add(e,negate(add(d,negate(e)))))),negate(add(negate(e),A)))) != negate(add(negate(e),negate(add(negate(add(d,add(e,negate(add(d,negate(e)))))),A)))),
inference(resolve,[status(thm)],[c_8,c_15]) ).
cnf(c_48,plain,
negate(add(negate(e),negate(add(negate(add(d,add(e,negate(add(d,negate(e)))))),A)))) != negate(add(negate(add(d,add(e,negate(add(d,negate(e)))))),negate(add(negate(e),A)))),
inference(copy,[status(thm)],[c_118]) ).
cnf(c_119,plain,
negate(add(negate(add(negate(add(A,negate(B))),add(A,B))),A)) = negate(add(A,negate(B))),
inference(paramod,[status(thm)],[c_3,c_17]) ).
cnf(c_120,plain,
negate(add(negate(add(add(A,B),negate(add(A,negate(B))))),A)) = negate(add(A,negate(B))),
inference(paramod,[status(thm)],[c_1,c_119]) ).
cnf(c_121,plain,
negate(add(negate(add(A,add(B,negate(add(A,negate(B)))))),A)) = negate(add(A,negate(B))),
inference(paramod,[status(thm)],[c_2,c_120]) ).
cnf(c_104,plain,
negate(add(A,negate(add(A,add(B,negate(add(A,negate(B)))))))) = negate(add(A,negate(B))),
inference(paramod,[status(thm)],[c_1,c_121]) ).
cnf(c_122,plain,
negate(add(negate(add(negate(add(d,negate(e))),e)),d)) = negate(add(d,negate(e))),
inference(paramod,[status(thm)],[c_10,c_17]) ).
cnf(c_123,plain,
negate(add(negate(add(e,negate(add(d,negate(e))))),d)) = negate(add(d,negate(e))),
inference(paramod,[status(thm)],[c_1,c_122]) ).
cnf(c_110,plain,
negate(add(d,negate(add(e,negate(add(d,negate(e))))))) = negate(add(d,negate(e))),
inference(paramod,[status(thm)],[c_1,c_123]) ).
cnf(c_124,plain,
negate(add(negate(e),d)) != negate(add(negate(add(d,add(e,negate(add(d,negate(e)))))),negate(add(negate(e),negate(add(negate(add(e,negate(add(d,negate(e))))),d)))))),
inference(paramod,[status(thm)],[c_17,c_48]) ).
cnf(c_125,plain,
negate(add(d,negate(e))) != negate(add(negate(add(d,add(e,negate(add(d,negate(e)))))),negate(add(negate(e),negate(add(negate(add(e,negate(add(d,negate(e))))),d)))))),
inference(paramod,[status(thm)],[c_1,c_124]) ).
cnf(c_126,plain,
negate(add(d,negate(e))) != negate(add(negate(add(d,add(e,negate(add(d,negate(e)))))),negate(add(negate(e),negate(add(d,negate(add(e,negate(add(d,negate(e))))))))))),
inference(paramod,[status(thm)],[c_1,c_125]) ).
cnf(c_127,plain,
negate(add(d,negate(e))) != negate(add(negate(add(d,add(e,negate(add(d,negate(e)))))),negate(add(negate(e),negate(add(d,negate(e))))))),
inference(paramod,[status(thm)],[c_110,c_126]) ).
cnf(c_128,plain,
negate(add(d,negate(e))) != negate(add(negate(add(d,add(e,negate(add(d,negate(e)))))),d)),
inference(paramod,[status(thm)],[c_10,c_127]) ).
cnf(c_129,plain,
negate(add(d,negate(e))) != negate(add(d,negate(add(d,add(e,negate(add(d,negate(e)))))))),
inference(paramod,[status(thm)],[c_1,c_128]) ).
cnf(c_130,plain,
negate(add(d,negate(e))) != negate(add(d,negate(e))),
inference(paramod,[status(thm)],[c_104,c_129]) ).
cnf(c_116,plain,
$false,
inference(copy,[status(thm)],[c_130]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ROB014-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.43 % Computer : n017.cluster.edu
% 0.20/0.43 % Model : x86_64 x86_64
% 0.20/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.43 % Memory : 8046.5625MB
% 0.20/0.43 % OS : Linux 6.8.0-71-generic
% 0.20/0.43 % CPULimit : 300
% 0.20/0.43 % WCLimit : 300
% 0.20/0.43 % DateTime : Sat Sep 26 06:10:19 UTC 2026
% 0.20/0.43 % CPUTime :
% 0.20/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.20/0.43 % Process 26994 was started by sandbox2 on n017,
% 0.20/0.43 % Sat Sep 26 06:10:19 2026
% 0.20/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.20/0.44
% 0.20/0.44 % From the command line: assign(max_seconds, 300).
% 0.20/0.47
% 0.20/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.20/0.47
% 0.20/0.47 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.20/0.47 % Length of proof is 15.
% 0.20/0.47 % Level of proof is 4.
% 0.20/0.47 % Maximum clause weight is 100.000.
% 0.20/0.47 % Given clauses 23.
% 0.20/0.47
% 0.20/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------