%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL143-1 : 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 : n002.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 07:58:05 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.38s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 17 ( 13 unt; 0 def)
% Number of atoms : 21 ( 12 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 7 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 18 ( 0 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(partial_order_definition1,axiom,
! [VAR_0,VAR_1] :
( implies(VAR_0,VAR_1) = truth
| ~ ordered(VAR_0,VAR_1) ),
file('theBenchmark.p',partial_order_definition1) ).
cnf(c_8,plain,
( implies(A,B) = truth
| ~ ordered(A,B) ),
inference(clausify,[status(thm)],[partial_order_definition1]) ).
fof(partial_order_definition2,axiom,
! [VAR_0,VAR_1] :
( ordered(VAR_0,VAR_1)
| implies(VAR_0,VAR_1) != truth ),
file('theBenchmark.p',partial_order_definition2) ).
cnf(c_9,plain,
( ordered(A,B)
| implies(A,B) != truth ),
inference(clausify,[status(thm)],[partial_order_definition2]) ).
fof(antecedent,axiom,
ordered(x,y),
file('theBenchmark.p',antecedent) ).
cnf(c_10,plain,
ordered(x,y),
inference(clausify,[status(thm)],[antecedent]) ).
fof(prove_wajsberg_theorem,axiom,
~ ordered(implies(z,x),implies(z,y)),
file('theBenchmark.p',prove_wajsberg_theorem) ).
cnf(c_11,plain,
~ ordered(implies(z,x),implies(z,y)),
inference(clausify,[status(thm)],[prove_wajsberg_theorem]) ).
cnf(c_40,plain,
implies(x,y) = truth,
inference(resolve,[status(thm)],[c_8,c_10]) ).
cnf(c_41,plain,
implies(implies(z,x),implies(z,y)) != truth,
inference(resolve,[status(thm)],[c_9,c_11]) ).
cnf(c_55,plain,
implies(implies(A,x),implies(truth,implies(A,y))) = truth,
inference(paramod,[status(thm)],[c_40,c_2]) ).
cnf(c_53,plain,
implies(implies(A,x),implies(A,y)) = truth,
inference(paramod,[status(thm)],[c_1,c_55]) ).
cnf(c_54,plain,
$false,
inference(resolve,[status(thm)],[c_53,c_41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL143-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n002.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 21:57:35 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 81961 was started by sandbox on n002,
% 0.10/0.36 % Fri Sep 25 21:57:35 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.36
% 0.10/0.36 % From the command line: assign(max_seconds, 300).
% 0.10/0.38
% 0.10/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.38
% 0.10/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/0.38 % Length of proof is 10.
% 0.10/0.38 % Level of proof is 3.
% 0.10/0.38 % Maximum clause weight is 13.000.
% 0.10/0.38 % Given clauses 14.
% 0.10/0.38
% 0.10/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------