%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN250-1 : 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 : n006.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 09:37:23 AM UTC 2026
% Result : Unsatisfiable 0.80s 0.51s
% Output : CNFRefutation 0.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 12
% Syntax : Number of formulae : 36 ( 19 unt; 0 def)
% Number of atoms : 68 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 70 ( 38 ~; 32 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 47 ( 12 sgn 16 !; 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_37,axiom,
n0(b,a),
file('theBenchmark.p',axiom_37) ).
cnf(c_2,plain,
n0(b,a),
inference(clausify,[status(thm)],[axiom_37]) ).
cnf(c_263,plain,
k1(a),
inference(resolve,[status(thm)],[c_1,c_2]) ).
fof(prove_this,axiom,
~ m1(e,a,a),
file('theBenchmark.p',prove_this) ).
cnf(c_264,plain,
~ m1(e,a,a),
inference(clausify,[status(thm)],[prove_this]) ).
fof(rule_034,axiom,
! [VAR_0,VAR_1] :
( ~ q0(VAR_0,VAR_0)
| ~ k1(VAR_1)
| ~ k1(a)
| m1(VAR_0,VAR_1,VAR_1) ),
file('theBenchmark.p',rule_034) ).
cnf(c_445,plain,
( ~ q0(A,A)
| ~ k1(B)
| ~ k1(a)
| m1(A,B,B) ),
inference(clausify,[status(thm)],[rule_034]) ).
cnf(c_446,plain,
( ~ q0(A,A)
| ~ k1(B)
| m1(A,B,B) ),
inference(resolve,[status(thm)],[c_263,c_445]) ).
fof(rule_024,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ m1(VAR_1,c,VAR_1)
| ~ q0(VAR_0,VAR_1)
| ~ m0(a,VAR_2,a)
| m1(VAR_0,a,VAR_1) ),
file('theBenchmark.p',rule_024) ).
cnf(c_456,plain,
( ~ m1(B,c,B)
| ~ q0(A,B)
| ~ m0(a,C,a)
| m1(A,a,B) ),
inference(clausify,[status(thm)],[rule_024]) ).
fof(rule_016,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ m1(VAR_2,VAR_3,VAR_1)
| ~ m1(VAR_2,VAR_1,VAR_0)
| m1(VAR_0,VAR_1,VAR_1) ),
file('theBenchmark.p',rule_016) ).
cnf(c_462,plain,
( ~ m1(C,D,B)
| ~ m1(C,B,A)
| m1(A,B,B) ),
inference(clausify,[status(thm)],[rule_016]) ).
fof(rule_007,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ r0(VAR_0)
| ~ p0(VAR_2,VAR_1)
| m1(VAR_0,VAR_1,VAR_0) ),
file('theBenchmark.p',rule_007) ).
cnf(c_466,plain,
( ~ r0(A)
| ~ p0(C,B)
| m1(A,B,A) ),
inference(clausify,[status(thm)],[rule_007]) ).
fof(axiom_21,axiom,
q0(b,e),
file('theBenchmark.p',axiom_21) ).
cnf(c_483,plain,
q0(b,e),
inference(clausify,[status(thm)],[axiom_21]) ).
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_13,axiom,
r0(e),
file('theBenchmark.p',axiom_13) ).
cnf(c_490,plain,
r0(e),
inference(clausify,[status(thm)],[axiom_13]) ).
fof(axiom_12,axiom,
! [VAR_0] : m0(a,VAR_0,a),
file('theBenchmark.p',axiom_12) ).
cnf(c_491,plain,
m0(a,A,a),
inference(clausify,[status(thm)],[axiom_12]) ).
fof(axiom_6,axiom,
q0(b,b),
file('theBenchmark.p',axiom_6) ).
cnf(c_493,plain,
q0(b,b),
inference(clausify,[status(thm)],[axiom_6]) ).
cnf(c_622,plain,
( ~ m1(B,c,B)
| ~ q0(A,B)
| m1(A,a,B) ),
inference(resolve,[status(thm)],[c_491,c_456]) ).
cnf(c_686,plain,
( ~ m1(A,B,a)
| ~ m1(A,a,e) ),
inference(resolve,[status(thm)],[c_462,c_264]) ).
cnf(c_919,plain,
( ~ r0(A)
| m1(A,B,A) ),
inference(resolve,[status(thm)],[c_466,c_489]) ).
cnf(c_782,plain,
m1(e,A,e),
inference(resolve,[status(thm)],[c_919,c_490]) ).
cnf(c_920,plain,
( ~ q0(A,A)
| m1(A,a,a) ),
inference(resolve,[status(thm)],[c_446,c_263]) ).
cnf(c_790,plain,
m1(b,a,a),
inference(resolve,[status(thm)],[c_920,c_493]) ).
cnf(c_921,plain,
( ~ m1(e,c,e)
| ~ q0(A,e)
| ~ m1(A,B,a) ),
inference(resolve,[status(thm)],[c_686,c_622]) ).
cnf(c_858,plain,
( ~ q0(A,e)
| ~ m1(A,B,a) ),
inference(resolve,[status(thm)],[c_782,c_921]) ).
cnf(c_917,plain,
~ m1(b,A,a),
inference(resolve,[status(thm)],[c_858,c_483]) ).
cnf(c_918,plain,
$false,
inference(resolve,[status(thm)],[c_917,c_790]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN250-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n006.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 17:26:10 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.37 % Process 1765445 was started by sandbox2 on n006,
% 0.08/0.37 % Sat Sep 26 17:26:10 2026
% 0.08/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.38
% 0.08/0.38 % From the command line: assign(max_seconds, 300).
% 0.80/0.51
% 0.80/0.51 % SZS status Unsatisfiable for theBenchmark
% 0.80/0.51
% 0.80/0.51 % Proof 1 at 0.11 (+ 0.01) seconds.
% 0.80/0.51 % Length of proof is 21.
% 0.80/0.51 % Level of proof is 4.
% 0.80/0.51 % Maximum clause weight is 20.000.
% 0.80/0.51 % Given clauses 358.
% 0.80/0.51
% 0.80/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------