%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ROB011-1 : 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 08:26:57 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.38s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 25 ( 25 unt; 0 def)
% Number of atoms : 25 ( 24 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 10 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 32 ( 0 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(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(condition,axiom,
negate(add(a,negate(b))) = c,
file('theBenchmark.p',condition) ).
cnf(c_8,plain,
negate(add(a,negate(b))) = c,
inference(clausify,[status(thm)],[condition]) ).
cnf(c_9,plain,
c = negate(add(a,negate(b))),
inference(copy,[status(thm)],[c_8]) ).
fof(prove_base_step,axiom,
negate(add(a,negate(add(b,multiply(one,add(a,c)))))) != c,
file('theBenchmark.p',prove_base_step) ).
cnf(c_10,plain,
negate(add(a,negate(add(b,multiply(one,add(a,c)))))) != c,
inference(clausify,[status(thm)],[prove_base_step]) ).
cnf(c_58,plain,
negate(add(a,negate(add(b,multiply(one,add(a,negate(add(a,negate(b))))))))) != c,
inference(paramod,[status(thm)],[c_9,c_10]) ).
cnf(c_59,plain,
negate(add(a,negate(add(b,add(a,negate(add(a,negate(b)))))))) != c,
inference(paramod,[status(thm)],[c_4,c_58]) ).
cnf(c_11,plain,
negate(add(a,negate(add(b,add(a,negate(add(a,negate(b)))))))) != negate(add(a,negate(b))),
inference(paramod,[status(thm)],[c_9,c_59]) ).
cnf(c_60,plain,
add(add(A,B),C) = add(B,add(A,C)),
inference(paramod,[status(thm)],[c_1,c_2]) ).
cnf(c_13,plain,
add(A,add(B,C)) = add(B,add(A,C)),
inference(paramod,[status(thm)],[c_2,c_60]) ).
cnf(c_14,plain,
negate(add(a,negate(add(a,add(b,negate(add(a,negate(b)))))))) != negate(add(a,negate(b))),
inference(paramod,[status(thm)],[c_13,c_11]) ).
cnf(c_16,plain,
negate(add(negate(add(A,B)),negate(add(negate(B),A)))) = A,
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_61,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_16]) ).
cnf(c_62,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_61]) ).
cnf(c_63,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_62]) ).
cnf(c_56,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_63]) ).
cnf(c_57,plain,
$false,
inference(resolve,[status(thm)],[c_56,c_14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ROB011-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % 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 06:14:33 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 2361896 was started by sandbox2 on n014,
% 0.09/0.37 % Sat Sep 26 06:14:33 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).
% 0.09/0.38
% 0.09/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.38
% 0.09/0.38 % Proof 1 at 0.00 (+ 0.01) seconds.
% 0.09/0.38 % Length of proof is 13.
% 0.09/0.38 % Level of proof is 4.
% 0.09/0.38 % Maximum clause weight is 19.000.
% 0.09/0.38 % Given clauses 20.
% 0.09/0.38
% 0.09/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------