%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL109-5 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 07:58:00 AM UTC 2026
% Result : Unsatisfiable 0.18s 0.50s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 31 ( 25 unt; 0 def)
% Number of atoms : 37 ( 23 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 10 ~; 6 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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; 3 con; 0-2 aty)
% Number of variables : 47 ( 4 sgn 15 !; 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(big_V_definition,axiom,
! [VAR_0,VAR_1] : big_V(VAR_0,VAR_1) = implies(implies(VAR_0,VAR_1),VAR_1),
file('theBenchmark.p',big_V_definition) ).
cnf(c_5,plain,
big_V(A,B) = implies(implies(A,B),B),
inference(clausify,[status(thm)],[big_V_definition]) ).
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(lemma_1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ordered(implies(VAR_0,VAR_2),implies(VAR_1,VAR_2))
| ~ ordered(VAR_0,VAR_1) ),
file('theBenchmark.p',lemma_1) ).
cnf(c_10,plain,
( ordered(implies(A,C),implies(B,C))
| ~ ordered(A,B) ),
inference(clausify,[status(thm)],[lemma_1]) ).
fof(prove_mv_4,axiom,
big_V(implies(x,y),implies(y,x)) != truth,
file('theBenchmark.p',prove_mv_4) ).
cnf(c_21,plain,
big_V(implies(x,y),implies(y,x)) != truth,
inference(clausify,[status(thm)],[prove_mv_4]) ).
cnf(c_22,plain,
implies(implies(implies(x,y),implies(y,x)),implies(y,x)) != truth,
inference(paramod,[status(thm)],[c_5,c_21]) ).
cnf(c_214,plain,
implies(A,implies(implies(A,B),implies(truth,B))) = truth,
inference(paramod,[status(thm)],[c_1,c_2]) ).
cnf(c_23,plain,
implies(A,implies(implies(A,B),B)) = truth,
inference(paramod,[status(thm)],[c_1,c_214]) ).
cnf(c_215,plain,
implies(A,A) = implies(implies(A,truth),truth),
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_29,plain,
implies(implies(A,truth),truth) = implies(A,A),
inference(copy,[status(thm)],[c_215]) ).
cnf(c_89,plain,
~ ordered(implies(implies(x,y),implies(y,x)),implies(y,x)),
inference(resolve,[status(thm)],[c_8,c_22]) ).
cnf(c_90,plain,
ordered(A,implies(implies(A,B),B)),
inference(resolve,[status(thm)],[c_9,c_23]) ).
cnf(c_216,plain,
truth = implies(implies(truth,A),A),
inference(paramod,[status(thm)],[c_23,c_1]) ).
cnf(c_217,plain,
truth = implies(A,A),
inference(paramod,[status(thm)],[c_1,c_216]) ).
cnf(c_91,plain,
implies(A,A) = truth,
inference(copy,[status(thm)],[c_217]) ).
cnf(c_105,plain,
implies(implies(A,truth),truth) = truth,
inference(paramod,[status(thm)],[c_91,c_29]) ).
cnf(c_187,plain,
ordered(A,truth),
inference(paramod,[status(thm)],[c_105,c_90]) ).
cnf(c_218,plain,
ordered(implies(A,B),implies(truth,B)),
inference(resolve,[status(thm)],[c_10,c_187]) ).
cnf(c_212,plain,
ordered(implies(A,B),B),
inference(paramod,[status(thm)],[c_1,c_218]) ).
cnf(c_213,plain,
$false,
inference(resolve,[status(thm)],[c_212,c_89]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL109-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n003.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Fri Sep 25 21:53:54 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.44 % Process 1191300 was started by sandbox2 on n003,
% 0.18/0.44 % Fri Sep 25 21:53:54 2026
% 0.18/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.45
% 0.18/0.45 % From the command line: assign(max_seconds, 300).
% 0.18/0.50
% 0.18/0.50 % Assigning unary symbol not kb_weight 0 and highest precedence (9).
% 0.18/0.50
% 0.18/0.50 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.50
% 0.18/0.50 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.18/0.50 % Length of proof is 18.
% 0.18/0.50 % Level of proof is 6.
% 0.18/0.50 % Maximum clause weight is 41.000.
% 0.18/0.50 % Given clauses 32.
% 0.18/0.50
% 0.18/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------