%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN561-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 09:38:50 AM UTC 2026
% Result : Unsatisfiable 0.18s 0.49s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 28 ( 18 unt; 0 def)
% Number of atoms : 45 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 43 ( 26 ~; 17 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p2_1,axiom,
! [VAR_0] : p2(VAR_0,VAR_0),
file('theBenchmark.p',p2_1) ).
cnf(c_1,plain,
p2(A,A),
inference(clausify,[status(thm)],[p2_1]) ).
fof(p9_2,axiom,
p9(c14,c10),
file('theBenchmark.p',p9_2) ).
cnf(c_2,plain,
p9(c14,c10),
inference(clausify,[status(thm)],[p9_2]) ).
fof(p8_3,axiom,
p8(c11,c14),
file('theBenchmark.p',p8_3) ).
cnf(c_3,plain,
p8(c11,c14),
inference(clausify,[status(thm)],[p8_3]) ).
fof(p2_4,axiom,
p2(f7(c10,c14),c15),
file('theBenchmark.p',p2_4) ).
cnf(c_4,plain,
p2(f7(c10,c14),c15),
inference(clausify,[status(thm)],[p2_4]) ).
fof(p2_5,axiom,
p2(f6(c15,c11),c16),
file('theBenchmark.p',p2_5) ).
cnf(c_5,plain,
p2(f6(c15,c11),c16),
inference(clausify,[status(thm)],[p2_5]) ).
fof(p2_6,axiom,
p2(f3(f4(f5(c12)),c13),c16),
file('theBenchmark.p',p2_6) ).
cnf(c_6,plain,
p2(f3(f4(f5(c12)),c13),c16),
inference(clausify,[status(thm)],[p2_6]) ).
fof(p2_9,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ p2(VAR_2,VAR_1)
| ~ p2(VAR_2,VAR_0)
| p2(VAR_0,VAR_1) ),
file('theBenchmark.p',p2_9) ).
cnf(c_9,plain,
( ~ p2(C,B)
| ~ p2(C,A)
| p2(A,B) ),
inference(clausify,[status(thm)],[p2_9]) ).
fof(not_p9_15,axiom,
! [VAR_0,VAR_1] :
( ~ p2(f6(VAR_1,c11),f3(f4(f5(c12)),c13))
| ~ p2(f7(c10,VAR_0),VAR_1)
| ~ p8(c11,VAR_0)
| ~ p9(VAR_0,c10) ),
file('theBenchmark.p',not_p9_15) ).
cnf(c_15,plain,
( ~ p2(f6(B,c11),f3(f4(f5(c12)),c13))
| ~ p2(f7(c10,A),B)
| ~ p8(c11,A)
| ~ p9(A,c10) ),
inference(clausify,[status(thm)],[not_p9_15]) ).
cnf(c_149,plain,
( ~ p2(f3(f4(f5(c12)),c13),A)
| p2(c16,A) ),
inference(resolve,[status(thm)],[c_9,c_6]) ).
cnf(c_22,plain,
p2(c16,f3(f4(f5(c12)),c13)),
inference(resolve,[status(thm)],[c_149,c_1]) ).
cnf(c_150,plain,
( ~ p2(f6(c15,c11),A)
| p2(c16,A) ),
inference(resolve,[status(thm)],[c_9,c_5]) ).
cnf(c_23,plain,
p2(c16,f6(c15,c11)),
inference(resolve,[status(thm)],[c_150,c_1]) ).
cnf(c_151,plain,
( ~ p2(f6(c15,c11),f3(f4(f5(c12)),c13))
| ~ p8(c11,c14)
| ~ p9(c14,c10) ),
inference(resolve,[status(thm)],[c_15,c_4]) ).
cnf(c_152,plain,
( ~ p2(f6(c15,c11),f3(f4(f5(c12)),c13))
| ~ p8(c11,c14) ),
inference(resolve,[status(thm)],[c_2,c_151]) ).
cnf(c_75,plain,
~ p2(f6(c15,c11),f3(f4(f5(c12)),c13)),
inference(resolve,[status(thm)],[c_3,c_152]) ).
cnf(c_153,plain,
( ~ p2(A,f3(f4(f5(c12)),c13))
| ~ p2(A,f6(c15,c11)) ),
inference(resolve,[status(thm)],[c_9,c_75]) ).
cnf(c_110,plain,
~ p2(f3(f4(f5(c12)),c13),f6(c15,c11)),
inference(resolve,[status(thm)],[c_153,c_1]) ).
cnf(c_154,plain,
( ~ p2(A,f6(c15,c11))
| ~ p2(A,f3(f4(f5(c12)),c13)) ),
inference(resolve,[status(thm)],[c_9,c_110]) ).
cnf(c_155,plain,
~ p2(c16,f3(f4(f5(c12)),c13)),
inference(resolve,[status(thm)],[c_154,c_23]) ).
cnf(c_148,plain,
$false,
inference(resolve,[status(thm)],[c_22,c_155]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN561-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n013.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Sat Sep 26 18:13:06 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.45 % Process 3339601 was started by sandbox on n013,
% 0.18/0.45 % Sat Sep 26 18:13:06 2026
% 0.18/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.46
% 0.18/0.46 % From the command line: assign(max_seconds, 300).
% 0.18/0.49
% 0.18/0.49 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.49
% 0.18/0.49 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.18/0.49 % Length of proof is 13.
% 0.18/0.49 % Level of proof is 3.
% 0.18/0.49 % Maximum clause weight is 20.000.
% 0.18/0.49 % Given clauses 21.
% 0.18/0.49
% 0.18/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------