%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL132-1 : 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 : n026.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 07:58:04 AM UTC 2026
% Result : Unsatisfiable 0.10s 5.45s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 12 unt; 0 def)
% Number of atoms : 12 ( 11 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 15 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(wajsberg_1,axiom,
! [VAR_0] : implies(truth,VAR_0) = VAR_0,
file('theBenchmark.p',wajsberg_1) ).
cnf(c_1,plain,
implies(truth,A) = A,
inference(clausify,[status(thm)],[wajsberg_1]) ).
fof(wajsberg_2,axiom,
! [VAR_0,VAR_1,VAR_2] : implies(implies(VAR_0,VAR_1),implies(implies(VAR_1,VAR_2),implies(VAR_0,VAR_2))) = truth,
file('theBenchmark.p',wajsberg_2) ).
cnf(c_2,plain,
implies(implies(A,B),implies(implies(B,C),implies(A,C))) = truth,
inference(clausify,[status(thm)],[wajsberg_2]) ).
fof(prove_wajsberg_lemma,axiom,
implies(x,x) != truth,
file('theBenchmark.p',prove_wajsberg_lemma) ).
cnf(c_5,plain,
implies(x,x) != truth,
inference(clausify,[status(thm)],[prove_wajsberg_lemma]) ).
cnf(c_30,plain,
implies(A,implies(implies(A,B),implies(truth,B))) = truth,
inference(paramod,[status(thm)],[c_1,c_2]) ).
cnf(c_6,plain,
implies(A,implies(implies(A,B),B)) = truth,
inference(paramod,[status(thm)],[c_1,c_30]) ).
cnf(c_31,plain,
truth = implies(implies(truth,A),A),
inference(paramod,[status(thm)],[c_6,c_1]) ).
cnf(c_32,plain,
truth = implies(A,A),
inference(paramod,[status(thm)],[c_1,c_31]) ).
cnf(c_28,plain,
implies(A,A) = truth,
inference(copy,[status(thm)],[c_32]) ).
cnf(c_29,plain,
$false,
inference(resolve,[status(thm)],[c_28,c_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL132-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.43 % Computer : n026.cluster.edu
% 0.10/5.43 % Model : x86_64 x86_64
% 0.10/5.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.43 % Memory : 8046.5625MB
% 0.10/5.43 % OS : Linux 6.8.0-71-generic
% 0.10/5.43 % CPULimit : 300
% 0.10/5.43 % WCLimit : 300
% 0.10/5.43 % DateTime : Fri Sep 25 21:57:15 UTC 2026
% 0.10/5.43 % CPUTime :
% 0.10/5.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.44 % Process 3559581 was started by sandbox on n026,
% 0.10/5.44 % Fri Sep 25 21:57:15 2026
% 0.10/5.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/5.44
% 0.10/5.44 % From the command line: assign(max_seconds, 300).
% 0.10/5.45
% 0.10/5.45 % SZS status Unsatisfiable for theBenchmark
% 0.10/5.45
% 0.10/5.45 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/5.45 % Length of proof is 6.
% 0.10/5.45 % Level of proof is 3.
% 0.10/5.45 % Maximum clause weight is 13.000.
% 0.10/5.45 % Given clauses 6.
% 0.10/5.45
% 0.10/5.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------