%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL337-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 07:58:37 AM UTC 2026
% Result : Unsatisfiable 20.05s 8.31s
% Output : CNFRefutation 20.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of formulae : 75 ( 54 unt; 0 def)
% Number of atoms : 99 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 65 ( 41 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 139 ( 15 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rule_1,axiom,
! [VAR_0] :
( ~ axiom(VAR_0)
| theorem(VAR_0) ),
file('theBenchmark.p',rule_1) ).
cnf(c_1,plain,
( ~ axiom(A)
| theorem(A) ),
inference(clausify,[status(thm)],[rule_1]) ).
fof(axiom_1_6,axiom,
! [VAR_0,VAR_1,VAR_2] : axiom(implies(implies(VAR_0,VAR_1),implies(or(VAR_2,VAR_0),or(VAR_2,VAR_1)))),
file('theBenchmark.p',axiom_1_6) ).
cnf(c_2,plain,
axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))),
inference(clausify,[status(thm)],[axiom_1_6]) ).
fof(axiom_1_5,axiom,
! [VAR_0,VAR_1,VAR_2] : axiom(implies(or(VAR_0,or(VAR_1,VAR_2)),or(VAR_1,or(VAR_0,VAR_2)))),
file('theBenchmark.p',axiom_1_5) ).
cnf(c_3,plain,
axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(clausify,[status(thm)],[axiom_1_5]) ).
fof(axiom_1_4,axiom,
! [VAR_0,VAR_1] : axiom(implies(or(VAR_0,VAR_1),or(VAR_1,VAR_0))),
file('theBenchmark.p',axiom_1_4) ).
cnf(c_4,plain,
axiom(implies(or(A,B),or(B,A))),
inference(clausify,[status(thm)],[axiom_1_4]) ).
fof(axiom_1_3,axiom,
! [VAR_0,VAR_1] : axiom(implies(VAR_0,or(VAR_1,VAR_0))),
file('theBenchmark.p',axiom_1_3) ).
cnf(c_5,plain,
axiom(implies(A,or(B,A))),
inference(clausify,[status(thm)],[axiom_1_3]) ).
fof(axiom_1_2,axiom,
! [VAR_0] : axiom(implies(or(VAR_0,VAR_0),VAR_0)),
file('theBenchmark.p',axiom_1_2) ).
cnf(c_6,plain,
axiom(implies(or(A,A),A)),
inference(clausify,[status(thm)],[axiom_1_2]) ).
cnf(c_7,plain,
theorem(implies(or(A,A),A)),
inference(resolve,[status(thm)],[c_1,c_6]) ).
cnf(c_8,plain,
theorem(implies(A,or(B,A))),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_9,plain,
theorem(implies(or(A,B),or(B,A))),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_10,plain,
theorem(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_11,plain,
theorem(implies(implies(A,B),implies(or(C,A),or(C,B)))),
inference(resolve,[status(thm)],[c_1,c_2]) ).
fof(prove_this,axiom,
~ theorem(equivalent(implies(p,implies(p,q)),implies(p,q))),
file('theBenchmark.p',prove_this) ).
cnf(c_12,plain,
~ theorem(equivalent(implies(p,implies(p,q)),implies(p,q))),
inference(clausify,[status(thm)],[prove_this]) ).
fof(equivalent_defn,axiom,
! [VAR_0,VAR_1] : equivalent(VAR_0,VAR_1) = and(implies(VAR_0,VAR_1),implies(VAR_1,VAR_0)),
file('theBenchmark.p',equivalent_defn) ).
cnf(c_13,plain,
equivalent(A,B) = and(implies(A,B),implies(B,A)),
inference(clausify,[status(thm)],[equivalent_defn]) ).
fof(and_defn,axiom,
! [VAR_0,VAR_1] : and(VAR_0,VAR_1) = not(or(not(VAR_0),not(VAR_1))),
file('theBenchmark.p',and_defn) ).
cnf(c_14,plain,
and(A,B) = not(or(not(A),not(B))),
inference(clausify,[status(thm)],[and_defn]) ).
fof(rule_2,axiom,
! [VAR_0,VAR_1] :
( ~ theorem(VAR_1)
| ~ theorem(implies(VAR_1,VAR_0))
| theorem(VAR_0) ),
file('theBenchmark.p',rule_2) ).
cnf(c_15,plain,
( ~ theorem(B)
| ~ theorem(implies(B,A))
| theorem(A) ),
inference(clausify,[status(thm)],[rule_2]) ).
fof(implies_definition,axiom,
! [VAR_0,VAR_1] : implies(VAR_0,VAR_1) = or(not(VAR_0),VAR_1),
file('theBenchmark.p',implies_definition) ).
cnf(c_16,plain,
implies(A,B) = or(not(A),B),
inference(clausify,[status(thm)],[implies_definition]) ).
cnf(c_6386,plain,
~ theorem(equivalent(implies(p,or(not(p),q)),implies(p,q))),
inference(paramod,[status(thm)],[c_16,c_12]) ).
cnf(c_6387,plain,
~ theorem(equivalent(or(not(p),or(not(p),q)),implies(p,q))),
inference(paramod,[status(thm)],[c_16,c_6386]) ).
cnf(c_6388,plain,
~ theorem(equivalent(or(not(p),or(not(p),q)),or(not(p),q))),
inference(paramod,[status(thm)],[c_16,c_6387]) ).
cnf(c_6389,plain,
~ theorem(and(implies(or(not(p),or(not(p),q)),or(not(p),q)),implies(or(not(p),q),or(not(p),or(not(p),q))))),
inference(paramod,[status(thm)],[c_13,c_6388]) ).
cnf(c_6390,plain,
~ theorem(and(or(not(or(not(p),or(not(p),q))),or(not(p),q)),implies(or(not(p),q),or(not(p),or(not(p),q))))),
inference(paramod,[status(thm)],[c_16,c_6389]) ).
cnf(c_6391,plain,
~ theorem(and(or(not(or(not(p),or(not(p),q))),or(not(p),q)),or(not(or(not(p),q)),or(not(p),or(not(p),q))))),
inference(paramod,[status(thm)],[c_16,c_6390]) ).
cnf(c_17,plain,
~ theorem(not(or(not(or(not(or(not(p),or(not(p),q))),or(not(p),q))),not(or(not(or(not(p),q)),or(not(p),or(not(p),q))))))),
inference(paramod,[status(thm)],[c_14,c_6391]) ).
cnf(c_19,plain,
( ~ theorem(B)
| ~ theorem(or(not(B),A))
| theorem(A) ),
inference(paramod,[status(thm)],[c_16,c_15]) ).
cnf(c_6392,plain,
theorem(implies(or(not(A),B),implies(or(C,A),or(C,B)))),
inference(paramod,[status(thm)],[c_16,c_11]) ).
cnf(c_6393,plain,
theorem(implies(or(not(A),B),or(not(or(C,A)),or(C,B)))),
inference(paramod,[status(thm)],[c_16,c_6392]) ).
cnf(c_20,plain,
theorem(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B)))),
inference(paramod,[status(thm)],[c_16,c_6393]) ).
cnf(c_21,plain,
theorem(or(not(or(A,or(B,C))),or(B,or(A,C)))),
inference(paramod,[status(thm)],[c_16,c_10]) ).
cnf(c_22,plain,
theorem(or(not(or(A,B)),or(B,A))),
inference(paramod,[status(thm)],[c_16,c_9]) ).
cnf(c_23,plain,
theorem(or(not(A),or(B,A))),
inference(paramod,[status(thm)],[c_16,c_8]) ).
cnf(c_24,plain,
theorem(or(not(or(A,A)),A)),
inference(paramod,[status(thm)],[c_16,c_7]) ).
cnf(c_6394,plain,
( ~ theorem(or(B,or(A,C)))
| theorem(or(A,or(B,C))) ),
inference(resolve,[status(thm)],[c_19,c_21]) ).
cnf(c_29,plain,
theorem(or(not(or(A,B)),or(not(or(not(B),C)),or(A,C)))),
inference(resolve,[status(thm)],[c_6394,c_20]) ).
cnf(c_6395,plain,
( ~ theorem(or(not(B),C))
| theorem(or(not(or(A,B)),or(A,C))) ),
inference(resolve,[status(thm)],[c_19,c_20]) ).
cnf(c_33,plain,
theorem(or(not(or(A,or(B,C))),or(A,or(C,B)))),
inference(resolve,[status(thm)],[c_6395,c_22]) ).
cnf(c_6396,plain,
( ~ theorem(or(B,or(A,C)))
| theorem(or(A,or(B,C))) ),
inference(resolve,[status(thm)],[c_19,c_21]) ).
cnf(c_39,plain,
theorem(or(A,or(not(B),B))),
inference(resolve,[status(thm)],[c_6396,c_23]) ).
cnf(c_6397,plain,
( ~ theorem(A)
| ~ theorem(or(not(A),not(or(not(or(not(or(not(p),or(not(p),q))),or(not(p),q))),not(or(not(or(not(p),q)),or(not(p),or(not(p),q)))))))) ),
inference(resolve,[status(thm)],[c_19,c_17]) ).
cnf(c_44,plain,
~ theorem(or(not(or(not(A),or(B,A))),not(or(not(or(not(or(not(p),or(not(p),q))),or(not(p),q))),not(or(not(or(not(p),q)),or(not(p),or(not(p),q)))))))),
inference(resolve,[status(thm)],[c_6397,c_23]) ).
cnf(c_6398,plain,
( ~ theorem(or(not(B),C))
| theorem(or(not(or(A,B)),or(A,C))) ),
inference(resolve,[status(thm)],[c_19,c_20]) ).
cnf(c_48,plain,
theorem(or(not(or(A,or(B,B))),or(A,B))),
inference(resolve,[status(thm)],[c_6398,c_24]) ).
cnf(c_6399,plain,
( ~ theorem(A)
| ~ theorem(or(not(A),or(not(or(not(B),or(C,B))),not(or(not(or(not(or(not(p),or(not(p),q))),or(not(p),q))),not(or(not(or(not(p),q)),or(not(p),or(not(p),q))))))))) ),
inference(resolve,[status(thm)],[c_19,c_44]) ).
cnf(c_69,plain,
~ theorem(or(not(or(not(or(not(or(not(p),or(not(p),q))),or(not(p),q))),not(or(not(or(not(p),q)),or(not(p),or(not(p),q)))))),not(or(not(A),or(B,A))))),
inference(resolve,[status(thm)],[c_6399,c_22]) ).
cnf(c_6400,plain,
( ~ theorem(B)
| theorem(or(not(A),A)) ),
inference(resolve,[status(thm)],[c_19,c_39]) ).
cnf(c_98,plain,
theorem(or(not(A),A)),
inference(resolve,[status(thm)],[c_6400,c_39]) ).
cnf(c_6401,plain,
( ~ theorem(or(B,A))
| theorem(or(A,B)) ),
inference(resolve,[status(thm)],[c_19,c_22]) ).
cnf(c_106,plain,
theorem(or(A,not(A))),
inference(resolve,[status(thm)],[c_6401,c_98]) ).
cnf(c_6402,plain,
( ~ theorem(or(B,or(A,C)))
| theorem(or(A,or(B,C))) ),
inference(resolve,[status(thm)],[c_19,c_21]) ).
cnf(c_107,plain,
theorem(or(A,or(not(or(A,B)),B))),
inference(resolve,[status(thm)],[c_6402,c_98]) ).
cnf(c_6403,plain,
( ~ theorem(B)
| theorem(or(A,B)) ),
inference(resolve,[status(thm)],[c_19,c_23]) ).
cnf(c_114,plain,
theorem(or(A,or(B,not(B)))),
inference(resolve,[status(thm)],[c_6403,c_106]) ).
cnf(c_6404,plain,
( ~ theorem(or(B,or(A,C)))
| theorem(or(A,or(B,C))) ),
inference(resolve,[status(thm)],[c_19,c_21]) ).
cnf(c_242,plain,
theorem(or(A,or(B,not(A)))),
inference(resolve,[status(thm)],[c_6404,c_114]) ).
cnf(c_6405,plain,
( ~ theorem(A)
| ~ theorem(or(not(A),or(not(or(not(or(not(or(not(p),or(not(p),q))),or(not(p),q))),not(or(not(or(not(p),q)),or(not(p),or(not(p),q)))))),not(or(not(B),or(C,B)))))) ),
inference(resolve,[status(thm)],[c_19,c_69]) ).
cnf(c_961,plain,
~ theorem(or(not(or(not(p),or(not(p),q))),or(not(p),q))),
inference(resolve,[status(thm)],[c_6405,c_107]) ).
cnf(c_6406,plain,
( ~ theorem(or(A,or(C,B)))
| theorem(or(A,or(B,C))) ),
inference(resolve,[status(thm)],[c_19,c_33]) ).
cnf(c_1292,plain,
theorem(or(A,or(not(A),B))),
inference(resolve,[status(thm)],[c_6406,c_242]) ).
cnf(c_6407,plain,
( ~ theorem(or(B,A))
| theorem(or(A,B)) ),
inference(resolve,[status(thm)],[c_19,c_22]) ).
cnf(c_1485,plain,
theorem(or(or(not(A),B),A)),
inference(resolve,[status(thm)],[c_6407,c_1292]) ).
cnf(c_6408,plain,
( ~ theorem(or(C,A))
| theorem(or(not(or(not(A),B)),or(C,B))) ),
inference(resolve,[status(thm)],[c_19,c_29]) ).
cnf(c_1636,plain,
theorem(or(not(or(not(A),B)),or(or(not(A),C),B))),
inference(resolve,[status(thm)],[c_6408,c_1485]) ).
cnf(c_6409,plain,
( ~ theorem(A)
| ~ theorem(or(not(A),or(not(or(not(p),or(not(p),q))),or(not(p),q)))) ),
inference(resolve,[status(thm)],[c_19,c_961]) ).
cnf(c_6384,plain,
~ theorem(or(not(or(not(p),or(not(p),q))),or(or(not(p),q),or(not(p),q)))),
inference(resolve,[status(thm)],[c_6409,c_48]) ).
cnf(c_6385,plain,
$false,
inference(resolve,[status(thm)],[c_6384,c_1636]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL337-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/5.67 % Computer : n005.cluster.edu
% 0.20/5.67 % Model : x86_64 x86_64
% 0.20/5.67 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/5.67 % Memory : 8046.5625MB
% 0.20/5.67 % OS : Linux 6.8.0-71-generic
% 0.20/5.67 % CPULimit : 300
% 0.20/5.67 % WCLimit : 300
% 0.20/5.67 % DateTime : Fri Sep 25 22:16:37 UTC 2026
% 0.20/5.67 % CPUTime :
% 0.20/5.68 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.20/5.68 % Process 403668 was started by sandbox2 on n005,
% 0.20/5.68 % Fri Sep 25 22:16:37 2026
% 0.20/5.68 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.20/5.68
% 0.20/5.68 % From the command line: assign(max_seconds, 300).
% 20.05/8.31
% 20.05/8.31 % SZS status Unsatisfiable for theBenchmark
% 20.05/8.31
% 20.05/8.31 % Proof 1 at 2.31 (+ 0.28) seconds.
% 20.05/8.31 % Length of proof is 40.
% 20.05/8.31 % Level of proof is 11.
% 20.05/8.31 % Maximum clause weight is 39.000.
% 20.05/8.31 % Given clauses 146.
% 20.05/8.31
% 20.05/8.31 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------