%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWX190-1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 09:16:17 AM UTC 2026
% Result : Unsatisfiable 0.16s 5.83s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 29 ( 29 unt; 0 def)
% Number of atoms : 29 ( 28 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 16 ( 16 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 34 ( 7 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_043,axiom,
! [VAR_0] : d(n(VAR_0)) = n(z),
file('theBenchmark.p',axiom_043) ).
cnf(c_57,plain,
d(n(A)) = n(z),
inference(clausify,[status(thm)],[axiom_043]) ).
fof(axiom_044,axiom,
! [VAR_0,VAR_1] : d(x(VAR_0,VAR_1)) = x(d(VAR_0),d(VAR_1)),
file('theBenchmark.p',axiom_044) ).
cnf(c_58,plain,
d(x(A,B)) = x(d(A),d(B)),
inference(clausify,[status(thm)],[axiom_044]) ).
fof(axiom_052,axiom,
! [VAR_0] : opt(x(n(z),VAR_0)) = VAR_0,
file('theBenchmark.p',axiom_052) ).
cnf(c_67,plain,
opt(x(n(z),A)) = A,
inference(clausify,[status(thm)],[axiom_052]) ).
fof(axiom_063,axiom,
! [VAR_0] : prop4(VAR_0) = eq2(opt(d(VAR_0)),opt(d(opt(VAR_0)))),
file('theBenchmark.p',axiom_063) ).
cnf(c_85,plain,
prop4(A) = eq2(opt(d(A)),opt(d(opt(A)))),
inference(clausify,[status(thm)],[axiom_063]) ).
fof(axiom_074,axiom,
! [VAR_0,VAR_1,VAR_2] : eq2(x(VAR_0,VAR_1),n(VAR_2)) = bfalse,
file('theBenchmark.p',axiom_074) ).
cnf(c_97,plain,
eq2(x(A,B),n(C)) = bfalse,
inference(clausify,[status(thm)],[axiom_074]) ).
fof(axiom_088,axiom,
! [VAR_0] : eq3(VAR_0,VAR_0) = btrue,
file('theBenchmark.p',axiom_088) ).
cnf(c_115,plain,
eq3(A,A) = btrue,
inference(clausify,[status(thm)],[axiom_088]) ).
fof(goal,axiom,
! [VAR_0] : eq3(prop4(VAR_0),bfalse) != btrue,
file('theBenchmark.p',goal) ).
cnf(c_116,plain,
eq3(prop4(A),bfalse) != btrue,
inference(clausify,[status(thm)],[goal]) ).
cnf(c_117,plain,
eq3(eq2(opt(d(A)),opt(d(opt(A)))),bfalse) != btrue,
inference(paramod,[status(thm)],[c_85,c_116]) ).
cnf(c_297,plain,
eq3(eq2(opt(d(x(n(z),A))),opt(d(A))),bfalse) != btrue,
inference(paramod,[status(thm)],[c_67,c_117]) ).
cnf(c_298,plain,
eq3(eq2(opt(x(d(n(z)),d(A))),opt(d(A))),bfalse) != btrue,
inference(paramod,[status(thm)],[c_58,c_297]) ).
cnf(c_299,plain,
eq3(eq2(opt(x(n(z),d(A))),opt(d(A))),bfalse) != btrue,
inference(paramod,[status(thm)],[c_57,c_298]) ).
cnf(c_254,plain,
eq3(eq2(d(A),opt(d(A))),bfalse) != btrue,
inference(paramod,[status(thm)],[c_67,c_299]) ).
cnf(c_300,plain,
eq3(eq2(x(d(A),d(B)),opt(d(x(A,B)))),bfalse) != btrue,
inference(paramod,[status(thm)],[c_58,c_254]) ).
cnf(c_276,plain,
eq3(eq2(x(d(A),d(B)),opt(x(d(A),d(B)))),bfalse) != btrue,
inference(paramod,[status(thm)],[c_58,c_300]) ).
cnf(c_301,plain,
eq3(eq2(x(n(z),d(A)),opt(x(d(n(B)),d(A)))),bfalse) != btrue,
inference(paramod,[status(thm)],[c_57,c_276]) ).
cnf(c_302,plain,
eq3(eq2(x(n(z),d(A)),opt(x(n(z),d(A)))),bfalse) != btrue,
inference(paramod,[status(thm)],[c_57,c_301]) ).
cnf(c_288,plain,
eq3(eq2(x(n(z),d(A)),d(A)),bfalse) != btrue,
inference(paramod,[status(thm)],[c_67,c_302]) ).
cnf(c_303,plain,
eq3(eq2(x(n(z),n(z)),d(n(A))),bfalse) != btrue,
inference(paramod,[status(thm)],[c_57,c_288]) ).
cnf(c_304,plain,
eq3(eq2(x(n(z),n(z)),n(z)),bfalse) != btrue,
inference(paramod,[status(thm)],[c_57,c_303]) ).
cnf(c_305,plain,
eq3(bfalse,bfalse) != btrue,
inference(paramod,[status(thm)],[c_97,c_304]) ).
cnf(c_306,plain,
btrue != btrue,
inference(paramod,[status(thm)],[c_115,c_305]) ).
cnf(c_296,plain,
$false,
inference(copy,[status(thm)],[c_306]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX190-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.77 % Computer : n019.cluster.edu
% 0.10/5.77 % Model : x86_64 x86_64
% 0.10/5.77 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.77 % Memory : 8046.5625MB
% 0.10/5.77 % OS : Linux 6.8.0-71-generic
% 0.10/5.77 % CPULimit : 300
% 0.10/5.77 % WCLimit : 300
% 0.10/5.77 % DateTime : Sat Sep 26 16:54:10 UTC 2026
% 0.10/5.77 % CPUTime :
% 0.10/5.77 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.77 % Process 1778760 was started by sandbox on n019,
% 0.10/5.77 % Sat Sep 26 16:54:10 2026
% 0.10/5.77 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/5.78
% 0.10/5.78 % From the command line: assign(max_seconds, 300).
% 0.16/5.83
% 0.16/5.83 % SZS status Unsatisfiable for theBenchmark
% 0.16/5.83
% 0.16/5.83 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.16/5.83 % Length of proof is 12.
% 0.16/5.83 % Level of proof is 5.
% 0.16/5.83 % Maximum clause weight is 16.000.
% 0.16/5.83 % Given clauses 102.
% 0.16/5.83
% 0.16/5.83 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------