%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL133-1 : 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 : n004.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 0.15s 5.40s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 27 unt; 0 def)
% Number of atoms : 27 ( 26 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 34 ( 2 sgn 8 !; 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(wajsberg_3,axiom,
! [VAR_0,VAR_1] : implies(implies(VAR_0,VAR_1),VAR_1) = implies(implies(VAR_1,VAR_0),VAR_0),
file('theBenchmark.p',wajsberg_3) ).
cnf(c_3,plain,
implies(implies(A,B),B) = implies(implies(B,A),A),
inference(clausify,[status(thm)],[wajsberg_3]) ).
fof(lemma_antecedent,axiom,
! [VAR_0,VAR_1] : implies(VAR_0,VAR_1) = implies(VAR_1,VAR_0),
file('theBenchmark.p',lemma_antecedent) ).
cnf(c_5,plain,
implies(A,B) = implies(B,A),
inference(clausify,[status(thm)],[lemma_antecedent]) ).
fof(prove_wajsberg_lemma,axiom,
x != y,
file('theBenchmark.p',prove_wajsberg_lemma) ).
cnf(c_6,plain,
x != y,
inference(clausify,[status(thm)],[prove_wajsberg_lemma]) ).
cnf(c_7,plain,
y != x,
inference(copy,[status(thm)],[c_6]) ).
cnf(c_48,plain,
implies(B,implies(A,B)) = implies(implies(B,A),A),
inference(paramod,[status(thm)],[c_5,c_3]) ).
cnf(c_8,plain,
implies(A,implies(B,A)) = implies(B,implies(A,B)),
inference(paramod,[status(thm)],[c_5,c_48]) ).
cnf(c_49,plain,
implies(A,implies(implies(A,B),implies(truth,B))) = truth,
inference(paramod,[status(thm)],[c_1,c_2]) ).
cnf(c_50,plain,
implies(A,implies(implies(A,B),B)) = truth,
inference(paramod,[status(thm)],[c_1,c_49]) ).
cnf(c_9,plain,
implies(A,implies(B,implies(A,B))) = truth,
inference(paramod,[status(thm)],[c_5,c_50]) ).
cnf(c_21,plain,
implies(A,truth) = A,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_51,plain,
implies(A,implies(truth,A)) = implies(A,truth),
inference(paramod,[status(thm)],[c_8,c_1]) ).
cnf(c_52,plain,
implies(A,A) = implies(A,truth),
inference(paramod,[status(thm)],[c_1,c_51]) ).
cnf(c_28,plain,
implies(A,A) = A,
inference(paramod,[status(thm)],[c_21,c_52]) ).
cnf(c_53,plain,
truth = implies(A,implies(truth,A)),
inference(paramod,[status(thm)],[c_9,c_1]) ).
cnf(c_54,plain,
truth = implies(A,A),
inference(paramod,[status(thm)],[c_1,c_53]) ).
cnf(c_38,plain,
truth = A,
inference(paramod,[status(thm)],[c_28,c_54]) ).
cnf(c_55,plain,
truth != x,
inference(paramod,[status(thm)],[c_38,c_7]) ).
cnf(c_46,plain,
x != truth,
inference(copy,[status(thm)],[c_55]) ).
cnf(c_56,plain,
A = truth,
inference(copy,[status(thm)],[c_38]) ).
cnf(c_47,plain,
$false,
inference(resolve,[status(thm)],[c_46,c_56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL133-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.38 % Computer : n004.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Fri Sep 25 21:54:26 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.38 % Process 50781 was started by sandbox on n004,
% 0.11/5.38 % Fri Sep 25 21:54:26 2026
% 0.11/5.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/5.38
% 0.11/5.38 % From the command line: assign(max_seconds, 300).
% 0.15/5.40
% 0.15/5.40 % SZS status Unsatisfiable for theBenchmark
% 0.15/5.40
% 0.15/5.40 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.15/5.40 % Length of proof is 13.
% 0.15/5.40 % Level of proof is 5.
% 0.15/5.40 % Maximum clause weight is 13.000.
% 0.15/5.40 % Given clauses 8.
% 0.15/5.40
% 0.15/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------