%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN202-1 : 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 : n020.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 09:37:17 AM UTC 2026
% Result : Unsatisfiable 2.73s 0.88s
% Output : CNFRefutation 2.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 16
% Syntax : Number of formulae : 49 ( 23 unt; 0 def)
% Number of atoms : 106 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 119 ( 62 ~; 57 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 15 ( 14 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 76 ( 20 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rule_124,axiom,
! [VAR_0,VAR_1] :
( ~ q1(d,VAR_1,d)
| ~ s0(d)
| ~ q0(VAR_0,VAR_1)
| r1(VAR_0) ),
file('theBenchmark.p',rule_124) ).
cnf(c_31,plain,
( ~ q1(d,B,d)
| ~ s0(d)
| ~ q0(A,B)
| r1(A) ),
inference(clausify,[status(thm)],[rule_124]) ).
fof(rule_187,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ q2(VAR_1,VAR_1,VAR_1)
| ~ k0(VAR_1)
| ~ m0(VAR_2,VAR_3,VAR_0)
| ~ r1(VAR_1)
| q2(VAR_0,VAR_1,VAR_0) ),
file('theBenchmark.p',rule_187) ).
cnf(c_38,plain,
( ~ q2(B,B,B)
| ~ k0(B)
| ~ m0(C,D,A)
| ~ r1(B)
| q2(A,B,A) ),
inference(clausify,[status(thm)],[rule_187]) ).
fof(rule_189,axiom,
! [VAR_0] :
( ~ s1(b)
| ~ q2(b,VAR_0,b)
| s2(VAR_0) ),
file('theBenchmark.p',rule_189) ).
cnf(c_78,plain,
( ~ s1(b)
| ~ q2(b,A,b)
| s2(A) ),
inference(clausify,[status(thm)],[rule_189]) ).
fof(prove_this,axiom,
~ s2(e),
file('theBenchmark.p',prove_this) ).
cnf(c_91,plain,
~ s2(e),
inference(clausify,[status(thm)],[prove_this]) ).
cnf(c_139,plain,
( ~ s1(b)
| ~ q2(b,e,b) ),
inference(resolve,[status(thm)],[c_91,c_78]) ).
fof(rule_181,axiom,
! [VAR_0] :
( ~ p1(VAR_0,VAR_0,VAR_0)
| q2(VAR_0,VAR_0,VAR_0) ),
file('theBenchmark.p',rule_181) ).
cnf(c_330,plain,
( ~ p1(A,A,A)
| q2(A,A,A) ),
inference(clausify,[status(thm)],[rule_181]) ).
fof(rule_125,axiom,
! [VAR_0] :
( ~ p0(VAR_0,VAR_0)
| s1(VAR_0) ),
file('theBenchmark.p',rule_125) ).
cnf(c_377,plain,
( ~ p0(A,A)
| s1(A) ),
inference(clausify,[status(thm)],[rule_125]) ).
fof(rule_113,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ m1(VAR_0,VAR_1,VAR_1)
| ~ r0(VAR_2)
| q1(VAR_0,VAR_0,VAR_1) ),
file('theBenchmark.p',rule_113) ).
cnf(c_385,plain,
( ~ m1(A,B,B)
| ~ r0(C)
| q1(A,A,B) ),
inference(clausify,[status(thm)],[rule_113]) ).
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_406,plain,
( ~ p0(B,A)
| p1(A,A,A) ),
inference(clausify,[status(thm)],[rule_085]) ).
fof(rule_015,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ m0(VAR_1,VAR_1,VAR_0)
| ~ l0(VAR_2)
| m1(VAR_0,VAR_1,VAR_1) ),
file('theBenchmark.p',rule_015) ).
cnf(c_463,plain,
( ~ m0(B,B,A)
| ~ l0(C)
| m1(A,B,B) ),
inference(clausify,[status(thm)],[rule_015]) ).
fof(axiom_28,axiom,
k0(e),
file('theBenchmark.p',axiom_28) ).
cnf(c_477,plain,
k0(e),
inference(clausify,[status(thm)],[axiom_28]) ).
fof(axiom_20,axiom,
l0(a),
file('theBenchmark.p',axiom_20) ).
cnf(c_484,plain,
l0(a),
inference(clausify,[status(thm)],[axiom_20]) ).
fof(axiom_19,axiom,
! [VAR_0,VAR_1] : m0(VAR_0,d,VAR_1),
file('theBenchmark.p',axiom_19) ).
cnf(c_485,plain,
m0(A,d,B),
inference(clausify,[status(thm)],[axiom_19]) ).
fof(axiom_17,axiom,
! [VAR_0] : q0(VAR_0,d),
file('theBenchmark.p',axiom_17) ).
cnf(c_487,plain,
q0(A,d),
inference(clausify,[status(thm)],[axiom_17]) ).
fof(axiom_14,axiom,
! [VAR_0] : p0(b,VAR_0),
file('theBenchmark.p',axiom_14) ).
cnf(c_489,plain,
p0(b,A),
inference(clausify,[status(thm)],[axiom_14]) ).
fof(axiom_9,axiom,
r0(b),
file('theBenchmark.p',axiom_9) ).
cnf(c_492,plain,
r0(b),
inference(clausify,[status(thm)],[axiom_9]) ).
fof(axiom_1,axiom,
s0(d),
file('theBenchmark.p',axiom_1) ).
cnf(c_495,plain,
s0(d),
inference(clausify,[status(thm)],[axiom_1]) ).
cnf(c_506,plain,
( ~ q2(A,A,A)
| ~ k0(A)
| ~ m0(D,E,C)
| q2(C,A,C)
| ~ q1(d,B,d)
| ~ s0(d)
| ~ q0(A,B) ),
inference(resolve,[status(thm)],[c_31,c_38]) ).
cnf(c_507,plain,
( ~ q2(A,A,A)
| ~ k0(A)
| ~ m0(D,E,C)
| q2(C,A,C)
| ~ q1(d,B,d)
| ~ q0(A,B) ),
inference(resolve,[status(thm)],[c_495,c_506]) ).
cnf(c_1643,plain,
( ~ q2(b,e,b)
| ~ p0(b,b) ),
inference(resolve,[status(thm)],[c_377,c_139]) ).
cnf(c_678,plain,
~ q2(b,e,b),
inference(resolve,[status(thm)],[c_489,c_1643]) ).
cnf(c_1644,plain,
( ~ m0(B,B,A)
| m1(A,B,B) ),
inference(resolve,[status(thm)],[c_463,c_484]) ).
cnf(c_765,plain,
m1(A,d,d),
inference(resolve,[status(thm)],[c_1644,c_485]) ).
cnf(c_803,plain,
p1(A,A,A),
inference(resolve,[status(thm)],[c_489,c_406]) ).
cnf(c_820,plain,
q2(A,A,A),
inference(resolve,[status(thm)],[c_803,c_330]) ).
cnf(c_837,plain,
( ~ k0(A)
| ~ m0(D,E,C)
| q2(C,A,C)
| ~ q1(d,B,d)
| ~ q0(A,B) ),
inference(resolve,[status(thm)],[c_820,c_507]) ).
cnf(c_1645,plain,
( ~ m1(A,B,B)
| q1(A,A,B) ),
inference(resolve,[status(thm)],[c_385,c_492]) ).
cnf(c_1105,plain,
q1(A,A,d),
inference(resolve,[status(thm)],[c_1645,c_765]) ).
cnf(c_1646,plain,
( ~ k0(B)
| ~ m0(C,D,A)
| q2(A,B,A)
| ~ q1(d,d,d) ),
inference(resolve,[status(thm)],[c_837,c_487]) ).
cnf(c_1647,plain,
( ~ k0(B)
| ~ m0(C,D,A)
| q2(A,B,A) ),
inference(resolve,[status(thm)],[c_1646,c_1105]) ).
cnf(c_1648,plain,
( ~ k0(B)
| q2(A,B,A) ),
inference(resolve,[status(thm)],[c_1647,c_485]) ).
cnf(c_1641,plain,
q2(A,e,A),
inference(resolve,[status(thm)],[c_1648,c_477]) ).
cnf(c_1642,plain,
$false,
inference(resolve,[status(thm)],[c_1641,c_678]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN202-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n020.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sat Sep 26 17:22:04 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 2111835 was started by sandbox2 on n020,
% 0.17/0.44 % Sat Sep 26 17:22:04 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.46
% 0.17/0.46 % From the command line: assign(max_seconds, 300).
% 2.73/0.88
% 2.73/0.88 % given #500 (T,wt=9): 818 q1(b,b,a). [hyper(388,b,489,a,c,471,a,d,260,a)].
% 2.73/0.88
% 2.73/0.88 % SZS status Unsatisfiable for theBenchmark
% 2.73/0.88
% 2.73/0.88 % Proof 1 at 0.31 (+ 0.10) seconds.
% 2.73/0.88 % Length of proof is 27.
% 2.73/0.88 % Level of proof is 5.
% 2.73/0.88 % Maximum clause weight is 26.000.
% 2.73/0.88 % Given clauses 745.
% 2.73/0.88
% 2.73/0.88 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------