%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWX206-1 : 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 : n016.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 09:16:20 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 21 ( 21 unt; 0 def)
% Number of atoms : 21 ( 20 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 14 ( 1 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom,axiom,
! [VAR_0] : impl(btrue,VAR_0) = VAR_0,
file('theBenchmark.p',axiom) ).
cnf(c_1,plain,
impl(btrue,A) = A,
inference(clausify,[status(thm)],[axiom]) ).
fof(axiom_002,axiom,
! [VAR_0] : x2(z,VAR_0) = VAR_0,
file('theBenchmark.p',axiom_002) ).
cnf(c_3,plain,
x2(z,A) = A,
inference(clausify,[status(thm)],[axiom_002]) ).
fof(axiom_004,axiom,
! [VAR_0] : plus_not_idem(VAR_0) = impl(eq(x2(VAR_0,VAR_0),VAR_0),eq2(btrue,bfalse)),
file('theBenchmark.p',axiom_004) ).
cnf(c_6,plain,
plus_not_idem(A) = impl(eq(x2(A,A),A),eq2(btrue,bfalse)),
inference(clausify,[status(thm)],[axiom_004]) ).
fof(axiom_006,axiom,
eq2(btrue,bfalse) = bfalse,
file('theBenchmark.p',axiom_006) ).
cnf(c_8,plain,
eq2(btrue,bfalse) = bfalse,
inference(clausify,[status(thm)],[axiom_006]) ).
fof(axiom_010,axiom,
! [VAR_0] : eq(VAR_0,VAR_0) = btrue,
file('theBenchmark.p',axiom_010) ).
cnf(c_12,plain,
eq(A,A) = btrue,
inference(clausify,[status(thm)],[axiom_010]) ).
fof(axiom_011,axiom,
! [VAR_0] : eq2(VAR_0,VAR_0) = btrue,
file('theBenchmark.p',axiom_011) ).
cnf(c_13,plain,
eq2(A,A) = btrue,
inference(clausify,[status(thm)],[axiom_011]) ).
fof(goal,axiom,
! [VAR_0] : eq2(plus_not_idem(VAR_0),bfalse) != btrue,
file('theBenchmark.p',goal) ).
cnf(c_14,plain,
eq2(plus_not_idem(A),bfalse) != btrue,
inference(clausify,[status(thm)],[goal]) ).
cnf(c_23,plain,
eq2(impl(eq(x2(A,A),A),eq2(btrue,bfalse)),bfalse) != btrue,
inference(paramod,[status(thm)],[c_6,c_14]) ).
cnf(c_15,plain,
eq2(impl(eq(x2(A,A),A),bfalse),bfalse) != btrue,
inference(paramod,[status(thm)],[c_8,c_23]) ).
cnf(c_24,plain,
eq2(impl(eq(z,z),bfalse),bfalse) != btrue,
inference(paramod,[status(thm)],[c_3,c_15]) ).
cnf(c_25,plain,
eq2(impl(btrue,bfalse),bfalse) != btrue,
inference(paramod,[status(thm)],[c_12,c_24]) ).
cnf(c_26,plain,
eq2(bfalse,bfalse) != btrue,
inference(paramod,[status(thm)],[c_1,c_25]) ).
cnf(c_27,plain,
btrue != btrue,
inference(paramod,[status(thm)],[c_13,c_26]) ).
cnf(c_22,plain,
$false,
inference(copy,[status(thm)],[c_27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX206-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.05/0.37 % Computer : n016.cluster.edu
% 0.05/0.37 % Model : x86_64 x86_64
% 0.05/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.37 % Memory : 8046.5625MB
% 0.05/0.37 % OS : Linux 6.8.0-71-generic
% 0.05/0.37 % CPULimit : 300
% 0.05/0.37 % WCLimit : 300
% 0.05/0.37 % DateTime : Sat Sep 26 17:00:16 UTC 2026
% 0.05/0.37 % CPUTime :
% 0.05/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.05/0.37 % Process 1340344 was started by sandbox on n016,
% 0.05/0.37 % Sat Sep 26 17:00:16 2026
% 0.05/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.05/0.37
% 0.05/0.37 % From the command line: assign(max_seconds, 300).
% 0.10/0.39
% 0.10/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.39
% 0.10/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/0.39 % Length of proof is 9.
% 0.10/0.39 % Level of proof is 2.
% 0.10/0.39 % Maximum clause weight is 12.000.
% 0.10/0.39 % Given clauses 12.
% 0.10/0.39
% 0.10/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------