%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN270-1 : TPTP v9.3.1. Released v1.1.0.
% 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 09:37:26 AM UTC 2026
% Result : Unsatisfiable 0.75s 0.51s
% Output : CNFRefutation 0.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 14
% Syntax : Number of formulae : 44 ( 20 unt; 0 def)
% Number of atoms : 80 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 87 ( 51 ~; 36 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 52 ( 7 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_37,axiom,
n0(b,a),
file('theBenchmark.p',axiom_37) ).
cnf(c_2,plain,
n0(b,a),
inference(clausify,[status(thm)],[axiom_37]) ).
fof(rule_002,axiom,
! [VAR_0,VAR_1] :
( ~ n0(VAR_1,VAR_0)
| l1(VAR_0,VAR_0) ),
file('theBenchmark.p',rule_002) ).
cnf(c_10,plain,
( ~ n0(B,A)
| l1(A,A) ),
inference(clausify,[status(thm)],[rule_002]) ).
cnf(c_258,plain,
l1(a,a),
inference(resolve,[status(thm)],[c_10,c_2]) ).
fof(prove_this,axiom,
~ p4(b,b,c),
file('theBenchmark.p',prove_this) ).
cnf(c_264,plain,
~ p4(b,b,c),
inference(clausify,[status(thm)],[prove_this]) ).
fof(rule_285,axiom,
! [VAR_0,VAR_1] :
( ~ r3(VAR_1,VAR_0,VAR_1)
| ~ r0(VAR_0)
| p4(VAR_0,VAR_0,VAR_1) ),
file('theBenchmark.p',rule_285) ).
cnf(c_283,plain,
( ~ r3(B,A,B)
| ~ r0(A)
| p4(A,A,B) ),
inference(clausify,[status(thm)],[rule_285]) ).
fof(rule_267,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ p2(VAR_0,VAR_2,VAR_1)
| r3(VAR_0,VAR_1,VAR_0) ),
file('theBenchmark.p',rule_267) ).
cnf(c_293,plain,
( ~ p2(A,C,B)
| r3(A,B,A) ),
inference(clausify,[status(thm)],[rule_267]) ).
fof(rule_176,axiom,
! [VAR_0,VAR_1] :
( ~ m1(VAR_1,VAR_0,VAR_1)
| p2(VAR_0,VAR_1,VAR_0) ),
file('theBenchmark.p',rule_176) ).
cnf(c_334,plain,
( ~ m1(B,A,B)
| p2(A,B,A) ),
inference(clausify,[status(thm)],[rule_176]) ).
fof(rule_146,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ p2(VAR_0,VAR_1,VAR_0)
| ~ l1(VAR_2,VAR_3)
| ~ p1(VAR_0,VAR_2,VAR_3)
| p2(VAR_0,VAR_1,VAR_1) ),
file('theBenchmark.p',rule_146) ).
cnf(c_356,plain,
( ~ p2(A,B,A)
| ~ l1(C,D)
| ~ p1(A,C,D)
| p2(A,B,B) ),
inference(clausify,[status(thm)],[rule_146]) ).
fof(rule_085,axiom,
! [VAR_0,VAR_1] :
( ~ p0(VAR_1,VAR_0)
| p1(VAR_0,VAR_0,VAR_0) ),
file('theBenchmark.p',rule_085) ).
cnf(c_399,plain,
( ~ p0(B,A)
| p1(A,A,A) ),
inference(clausify,[status(thm)],[rule_085]) ).
fof(rule_082,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ p1(VAR_2,VAR_0,VAR_3)
| ~ m0(VAR_2,VAR_0,VAR_3)
| p1(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',rule_082) ).
cnf(c_402,plain,
( ~ p1(C,A,D)
| ~ m0(C,A,D)
| p1(A,B,C) ),
inference(clausify,[status(thm)],[rule_082]) ).
fof(rule_035,axiom,
! [VAR_0,VAR_1] :
( ~ l0(VAR_1)
| ~ r0(VAR_0)
| m1(VAR_0,VAR_1,VAR_0) ),
file('theBenchmark.p',rule_035) ).
cnf(c_437,plain,
( ~ l0(B)
| ~ r0(A)
| m1(A,B,A) ),
inference(clausify,[status(thm)],[rule_035]) ).
fof(axiom_24,axiom,
l0(c),
file('theBenchmark.p',axiom_24) ).
cnf(c_472,plain,
l0(c),
inference(clausify,[status(thm)],[axiom_24]) ).
fof(axiom_14,axiom,
! [VAR_0] : p0(b,VAR_0),
file('theBenchmark.p',axiom_14) ).
cnf(c_481,plain,
p0(b,A),
inference(clausify,[status(thm)],[axiom_14]) ).
fof(axiom_12,axiom,
! [VAR_0] : m0(a,VAR_0,a),
file('theBenchmark.p',axiom_12) ).
cnf(c_483,plain,
m0(a,A,a),
inference(clausify,[status(thm)],[axiom_12]) ).
fof(axiom_9,axiom,
r0(b),
file('theBenchmark.p',axiom_9) ).
cnf(c_484,plain,
r0(b),
inference(clausify,[status(thm)],[axiom_9]) ).
cnf(c_613,plain,
p1(A,A,A),
inference(resolve,[status(thm)],[c_399,c_481]) ).
cnf(c_799,plain,
( ~ r3(c,b,c)
| ~ r0(b) ),
inference(resolve,[status(thm)],[c_283,c_264]) ).
cnf(c_632,plain,
~ r3(c,b,c),
inference(resolve,[status(thm)],[c_799,c_484]) ).
cnf(c_641,plain,
~ p2(c,A,b),
inference(resolve,[status(thm)],[c_632,c_293]) ).
cnf(c_643,plain,
( ~ p2(c,b,c)
| ~ l1(A,B)
| ~ p1(c,A,B) ),
inference(resolve,[status(thm)],[c_641,c_356]) ).
cnf(c_685,plain,
( ~ p2(c,b,c)
| ~ p1(c,a,a) ),
inference(resolve,[status(thm)],[c_643,c_258]) ).
cnf(c_691,plain,
( ~ m1(b,c,b)
| ~ p1(c,a,a) ),
inference(resolve,[status(thm)],[c_685,c_334]) ).
cnf(c_760,plain,
( ~ l0(c)
| ~ r0(b)
| ~ p1(c,a,a) ),
inference(resolve,[status(thm)],[c_691,c_437]) ).
cnf(c_800,plain,
( ~ l0(c)
| ~ p1(c,a,a) ),
inference(resolve,[status(thm)],[c_760,c_484]) ).
cnf(c_787,plain,
~ p1(c,a,a),
inference(resolve,[status(thm)],[c_800,c_472]) ).
cnf(c_801,plain,
( ~ p1(a,c,A)
| ~ m0(a,c,A) ),
inference(resolve,[status(thm)],[c_402,c_787]) ).
cnf(c_793,plain,
~ p1(a,c,a),
inference(resolve,[status(thm)],[c_801,c_483]) ).
cnf(c_802,plain,
( ~ p1(a,a,A)
| ~ m0(a,a,A) ),
inference(resolve,[status(thm)],[c_402,c_793]) ).
cnf(c_797,plain,
~ p1(a,a,a),
inference(resolve,[status(thm)],[c_802,c_483]) ).
cnf(c_798,plain,
$false,
inference(resolve,[status(thm)],[c_797,c_613]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN270-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n003.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 : Sat Sep 26 17:29:55 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 3402184 was started by sandbox2 on n003,
% 0.10/0.36 % Sat Sep 26 17:29:55 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.75/0.51
% 0.75/0.51 % SZS status Unsatisfiable for theBenchmark
% 0.75/0.51
% 0.75/0.51 % Proof 1 at 0.11 (+ 0.02) seconds.
% 0.75/0.51 % Length of proof is 26.
% 0.75/0.51 % Level of proof is 10.
% 0.75/0.51 % Maximum clause weight is 15.000.
% 0.75/0.51 % Given clauses 454.
% 0.75/0.51
% 0.75/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------