%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL198-3 : 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 : n010.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 07:58:16 AM UTC 2026
% Result : Unsatisfiable 5.24s 1.19s
% Output : CNFRefutation 5.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 59 ( 42 unt; 0 def)
% Number of atoms : 79 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 47 ( 27 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 115 ( 11 sgn 16 !; 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(implies(or(not(p),implies(p,q)),implies(p,q))),
file('theBenchmark.p',prove_this) ).
cnf(c_12,plain,
~ theorem(implies(or(not(p),implies(p,q)),implies(p,q))),
inference(clausify,[status(thm)],[prove_this]) ).
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_13,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_14,plain,
implies(A,B) = or(not(A),B),
inference(clausify,[status(thm)],[implies_definition]) ).
cnf(c_15,plain,
( ~ theorem(B)
| ~ theorem(or(not(B),A))
| theorem(A) ),
inference(paramod,[status(thm)],[c_14,c_13]) ).
cnf(c_2453,plain,
~ theorem(implies(or(not(p),or(not(p),q)),implies(p,q))),
inference(paramod,[status(thm)],[c_14,c_12]) ).
cnf(c_2454,plain,
~ theorem(implies(or(not(p),or(not(p),q)),or(not(p),q))),
inference(paramod,[status(thm)],[c_14,c_2453]) ).
cnf(c_16,plain,
~ theorem(or(not(or(not(p),or(not(p),q))),or(not(p),q))),
inference(paramod,[status(thm)],[c_14,c_2454]) ).
cnf(c_2455,plain,
theorem(implies(or(not(A),B),implies(or(C,A),or(C,B)))),
inference(paramod,[status(thm)],[c_14,c_11]) ).
cnf(c_2456,plain,
theorem(implies(or(not(A),B),or(not(or(C,A)),or(C,B)))),
inference(paramod,[status(thm)],[c_14,c_2455]) ).
cnf(c_17,plain,
theorem(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B)))),
inference(paramod,[status(thm)],[c_14,c_2456]) ).
cnf(c_18,plain,
theorem(or(not(or(A,or(B,C))),or(B,or(A,C)))),
inference(paramod,[status(thm)],[c_14,c_10]) ).
cnf(c_19,plain,
theorem(or(not(or(A,B)),or(B,A))),
inference(paramod,[status(thm)],[c_14,c_9]) ).
cnf(c_20,plain,
theorem(or(not(A),or(B,A))),
inference(paramod,[status(thm)],[c_14,c_8]) ).
cnf(c_21,plain,
theorem(or(not(or(A,A)),A)),
inference(paramod,[status(thm)],[c_14,c_7]) ).
cnf(c_2457,plain,
( ~ theorem(or(B,or(A,C)))
| theorem(or(A,or(B,C))) ),
inference(resolve,[status(thm)],[c_15,c_18]) ).
cnf(c_27,plain,
theorem(or(not(or(A,B)),or(not(or(not(B),C)),or(A,C)))),
inference(resolve,[status(thm)],[c_2457,c_17]) ).
cnf(c_2458,plain,
( ~ theorem(or(not(B),C))
| theorem(or(not(or(A,B)),or(A,C))) ),
inference(resolve,[status(thm)],[c_15,c_17]) ).
cnf(c_32,plain,
theorem(or(not(or(A,or(B,C))),or(A,or(C,B)))),
inference(resolve,[status(thm)],[c_2458,c_19]) ).
cnf(c_2459,plain,
( ~ theorem(or(B,or(A,C)))
| theorem(or(A,or(B,C))) ),
inference(resolve,[status(thm)],[c_15,c_18]) ).
cnf(c_39,plain,
theorem(or(A,or(not(B),B))),
inference(resolve,[status(thm)],[c_2459,c_20]) ).
cnf(c_2460,plain,
( ~ theorem(or(not(B),C))
| theorem(or(not(or(A,B)),or(A,C))) ),
inference(resolve,[status(thm)],[c_15,c_17]) ).
cnf(c_49,plain,
theorem(or(not(or(A,or(B,B))),or(A,B))),
inference(resolve,[status(thm)],[c_2460,c_21]) ).
cnf(c_2461,plain,
( ~ theorem(B)
| theorem(or(not(A),A)) ),
inference(resolve,[status(thm)],[c_15,c_39]) ).
cnf(c_127,plain,
theorem(or(not(A),A)),
inference(resolve,[status(thm)],[c_2461,c_39]) ).
cnf(c_2462,plain,
( ~ theorem(or(B,A))
| theorem(or(A,B)) ),
inference(resolve,[status(thm)],[c_15,c_19]) ).
cnf(c_137,plain,
theorem(or(A,not(A))),
inference(resolve,[status(thm)],[c_2462,c_127]) ).
cnf(c_2463,plain,
( ~ theorem(B)
| theorem(or(A,B)) ),
inference(resolve,[status(thm)],[c_15,c_20]) ).
cnf(c_158,plain,
theorem(or(A,or(B,not(B)))),
inference(resolve,[status(thm)],[c_2463,c_137]) ).
cnf(c_2464,plain,
( ~ theorem(or(B,or(A,C)))
| theorem(or(A,or(B,C))) ),
inference(resolve,[status(thm)],[c_15,c_18]) ).
cnf(c_332,plain,
theorem(or(A,or(B,not(A)))),
inference(resolve,[status(thm)],[c_2464,c_158]) ).
cnf(c_2465,plain,
( ~ theorem(or(A,or(C,B)))
| theorem(or(A,or(B,C))) ),
inference(resolve,[status(thm)],[c_15,c_32]) ).
cnf(c_746,plain,
theorem(or(A,or(not(A),B))),
inference(resolve,[status(thm)],[c_2465,c_332]) ).
cnf(c_2466,plain,
( ~ theorem(or(B,A))
| theorem(or(A,B)) ),
inference(resolve,[status(thm)],[c_15,c_19]) ).
cnf(c_1047,plain,
theorem(or(or(not(A),B),A)),
inference(resolve,[status(thm)],[c_2466,c_746]) ).
cnf(c_2467,plain,
( ~ theorem(or(C,A))
| theorem(or(not(or(not(A),B)),or(C,B))) ),
inference(resolve,[status(thm)],[c_15,c_27]) ).
cnf(c_1106,plain,
theorem(or(not(or(not(A),B)),or(or(not(A),C),B))),
inference(resolve,[status(thm)],[c_2467,c_1047]) ).
cnf(c_2468,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_15,c_16]) ).
cnf(c_2451,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_2468,c_49]) ).
cnf(c_2452,plain,
$false,
inference(resolve,[status(thm)],[c_2451,c_1106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL198-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n010.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Fri Sep 25 22:00:30 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 1799204 was started by sandbox2 on n010,
% 0.18/0.44 % Fri Sep 25 22:00:30 2026
% 0.18/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.44
% 0.18/0.44 % From the command line: assign(max_seconds, 300).
% 5.24/1.19
% 5.24/1.19 % SZS status Unsatisfiable for theBenchmark
% 5.24/1.19
% 5.24/1.19 % Proof 1 at 0.62 (+ 0.11) seconds.
% 5.24/1.19 % Length of proof is 34.
% 5.24/1.19 % Level of proof is 11.
% 5.24/1.19 % Maximum clause weight is 69.000.
% 5.24/1.19 % Given clauses 89.
% 5.24/1.19
% 5.24/1.19 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------