%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN138-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 09:37:08 AM UTC 2026
% Result : Unsatisfiable 0.97s 0.51s
% Output : CNFRefutation 0.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 16
% Syntax : Number of formulae : 50 ( 22 unt; 0 def)
% Number of atoms : 108 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 125 ( 67 ~; 58 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 63 ( 11 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rule_001,axiom,
! [VAR_0,VAR_1] :
( ~ n0(VAR_1,VAR_0)
| k1(VAR_0) ),
file('theBenchmark.p',rule_001) ).
cnf(c_1,plain,
( ~ n0(B,A)
| k1(A) ),
inference(clausify,[status(thm)],[rule_001]) ).
fof(axiom_30,axiom,
n0(e,e),
file('theBenchmark.p',axiom_30) ).
cnf(c_4,plain,
n0(e,e),
inference(clausify,[status(thm)],[axiom_30]) ).
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_188,axiom,
! [VAR_0] :
( ~ l0(VAR_0)
| ~ r1(VAR_0)
| r2(VAR_0) ),
file('theBenchmark.p',rule_188) ).
cnf(c_39,plain,
( ~ l0(A)
| ~ r1(A)
| r2(A) ),
inference(clausify,[status(thm)],[rule_188]) ).
cnf(c_59,plain,
( ~ l0(A)
| r2(A)
| ~ q1(d,B,d)
| ~ s0(d)
| ~ q0(A,B) ),
inference(resolve,[status(thm)],[c_31,c_39]) ).
fof(rule_231,axiom,
! [VAR_0,VAR_1] :
( ~ k2(c,VAR_1)
| ~ r2(VAR_0)
| m3(VAR_0,VAR_1,VAR_0) ),
file('theBenchmark.p',rule_231) ).
cnf(c_68,plain,
( ~ k2(c,B)
| ~ r2(A)
| m3(A,B,A) ),
inference(clausify,[status(thm)],[rule_231]) ).
cnf(c_261,plain,
k1(e),
inference(resolve,[status(thm)],[c_1,c_4]) ).
fof(prove_this,axiom,
~ m3(c,e,c),
file('theBenchmark.p',prove_this) ).
cnf(c_264,plain,
~ m3(c,e,c),
inference(clausify,[status(thm)],[prove_this]) ).
fof(rule_129,axiom,
! [VAR_0,VAR_1] :
( ~ q1(VAR_1,VAR_0,VAR_0)
| k2(VAR_0,VAR_0) ),
file('theBenchmark.p',rule_129) ).
cnf(c_373,plain,
( ~ q1(B,A,A)
| k2(A,A) ),
inference(clausify,[status(thm)],[rule_129]) ).
fof(rule_127,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ k2(VAR_3,VAR_1)
| ~ k1(VAR_3)
| ~ m1(VAR_2,VAR_1,VAR_0)
| k2(VAR_0,VAR_1) ),
file('theBenchmark.p',rule_127) ).
cnf(c_375,plain,
( ~ k2(D,B)
| ~ k1(D)
| ~ m1(C,B,A)
| k2(A,B) ),
inference(clausify,[status(thm)],[rule_127]) ).
fof(rule_121,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ m0(VAR_1,VAR_2,VAR_0)
| q1(VAR_0,VAR_0,VAR_0) ),
file('theBenchmark.p',rule_121) ).
cnf(c_380,plain,
( ~ m0(B,C,A)
| q1(A,A,A) ),
inference(clausify,[status(thm)],[rule_121]) ).
fof(rule_107,axiom,
! [VAR_0] :
( ~ m0(e,d,VAR_0)
| ~ m0(VAR_0,d,VAR_0)
| q1(e,VAR_0,VAR_0) ),
file('theBenchmark.p',rule_107) ).
cnf(c_390,plain,
( ~ m0(e,d,A)
| ~ m0(A,d,A)
| q1(e,A,A) ),
inference(clausify,[status(thm)],[rule_107]) ).
fof(rule_021,axiom,
! [VAR_0,VAR_1] :
( ~ k0(VAR_1)
| ~ l0(VAR_0)
| m1(VAR_0,VAR_1,VAR_0) ),
file('theBenchmark.p',rule_021) ).
cnf(c_458,plain,
( ~ k0(B)
| ~ l0(A)
| m1(A,B,A) ),
inference(clausify,[status(thm)],[rule_021]) ).
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_24,axiom,
l0(c),
file('theBenchmark.p',axiom_24) ).
cnf(c_480,plain,
l0(c),
inference(clausify,[status(thm)],[axiom_24]) ).
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_1,axiom,
s0(d),
file('theBenchmark.p',axiom_1) ).
cnf(c_495,plain,
s0(d),
inference(clausify,[status(thm)],[axiom_1]) ).
cnf(c_526,plain,
( ~ k2(c,C)
| m3(A,C,A)
| ~ l0(A)
| ~ q1(d,B,d)
| ~ s0(d)
| ~ q0(A,B) ),
inference(resolve,[status(thm)],[c_59,c_68]) ).
cnf(c_527,plain,
( ~ k2(c,C)
| m3(A,C,A)
| ~ l0(A)
| ~ q1(d,B,d)
| ~ q0(A,B) ),
inference(resolve,[status(thm)],[c_495,c_526]) ).
cnf(c_841,plain,
( ~ m0(e,d,A)
| q1(e,A,A) ),
inference(resolve,[status(thm)],[c_485,c_390]) ).
cnf(c_583,plain,
q1(e,A,A),
inference(resolve,[status(thm)],[c_485,c_841]) ).
cnf(c_842,plain,
( ~ k0(A)
| m1(c,A,c) ),
inference(resolve,[status(thm)],[c_458,c_480]) ).
cnf(c_680,plain,
m1(c,e,c),
inference(resolve,[status(thm)],[c_842,c_477]) ).
cnf(c_697,plain,
q1(A,A,A),
inference(resolve,[status(thm)],[c_380,c_485]) ).
cnf(c_843,plain,
( ~ k2(c,e)
| ~ l0(c)
| ~ q1(d,A,d)
| ~ q0(c,A) ),
inference(resolve,[status(thm)],[c_527,c_264]) ).
cnf(c_761,plain,
( ~ k2(c,e)
| ~ q1(d,A,d)
| ~ q0(c,A) ),
inference(resolve,[status(thm)],[c_480,c_843]) ).
cnf(c_764,plain,
k2(A,A),
inference(resolve,[status(thm)],[c_373,c_583]) ).
cnf(c_844,plain,
( ~ k2(c,e)
| ~ q1(d,d,d) ),
inference(resolve,[status(thm)],[c_761,c_487]) ).
cnf(c_834,plain,
~ k2(c,e),
inference(resolve,[status(thm)],[c_697,c_844]) ).
cnf(c_845,plain,
( ~ k2(B,e)
| ~ k1(B)
| ~ m1(A,e,c) ),
inference(resolve,[status(thm)],[c_375,c_834]) ).
cnf(c_846,plain,
( ~ k2(e,e)
| ~ m1(A,e,c) ),
inference(resolve,[status(thm)],[c_845,c_261]) ).
cnf(c_839,plain,
~ m1(A,e,c),
inference(resolve,[status(thm)],[c_846,c_764]) ).
cnf(c_840,plain,
$false,
inference(resolve,[status(thm)],[c_839,c_680]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN138-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n002.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sat Sep 26 17:17:38 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 2286098 was started by sandbox on n002,
% 0.11/0.37 % Sat Sep 26 17:17:38 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 0.97/0.51
% 0.97/0.51 % SZS status Unsatisfiable for theBenchmark
% 0.97/0.51
% 0.97/0.51 % Proof 1 at 0.11 (+ 0.01) seconds.
% 0.97/0.51 % Length of proof is 28.
% 0.97/0.51 % Level of proof is 7.
% 0.97/0.51 % Maximum clause weight is 21.000.
% 0.97/0.51 % Given clauses 339.
% 0.97/0.51
% 0.97/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------