%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN180-1 : 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 : n001.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 09:37:14 AM UTC 2026
% Result : Unsatisfiable 0.97s 0.53s
% Output : CNFRefutation 0.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 21
% Syntax : Number of formulae : 63 ( 26 unt; 0 def)
% Number of atoms : 132 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 150 ( 81 ~; 69 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 18 ( 17 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 95 ( 25 sgn 33 !; 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(axiom_34,axiom,
n0(c,d),
file('theBenchmark.p',axiom_34) ).
cnf(c_3,plain,
n0(c,d),
inference(clausify,[status(thm)],[axiom_34]) ).
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_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]) ).
fof(rule_066,axiom,
! [VAR_0,VAR_1] :
( ~ n0(VAR_1,VAR_0)
| p1(VAR_0,VAR_0,VAR_0) ),
file('theBenchmark.p',rule_066) ).
cnf(c_17,plain,
( ~ n0(B,A)
| p1(A,A,A) ),
inference(clausify,[status(thm)],[rule_066]) ).
fof(rule_092,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ p0(VAR_3,VAR_0)
| ~ n0(VAR_2,VAR_1)
| q1(VAR_0,VAR_1,VAR_0) ),
file('theBenchmark.p',rule_092) ).
cnf(c_21,plain,
( ~ p0(D,A)
| ~ n0(C,B)
| q1(A,B,A) ),
inference(clausify,[status(thm)],[rule_092]) ).
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_137,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ p1(VAR_1,VAR_2,VAR_0)
| n2(VAR_0) ),
file('theBenchmark.p',rule_137) ).
cnf(c_46,plain,
( ~ p1(B,C,A)
| n2(A) ),
inference(clausify,[status(thm)],[rule_137]) ).
fof(rule_210,axiom,
! [VAR_0] :
( ~ n2(VAR_0)
| k3(VAR_0,VAR_0,VAR_0) ),
file('theBenchmark.p',rule_210) ).
cnf(c_48,plain,
( ~ n2(A)
| k3(A,A,A) ),
inference(clausify,[status(thm)],[rule_210]) ).
cnf(c_191,plain,
( ~ p1(B,C,A)
| k3(A,A,A) ),
inference(resolve,[status(thm)],[c_48,c_46]) ).
cnf(c_230,plain,
( ~ p0(B,A)
| q1(A,d,A) ),
inference(resolve,[status(thm)],[c_21,c_3]) ).
cnf(c_238,plain,
p1(a,a,a),
inference(resolve,[status(thm)],[c_17,c_2]) ).
cnf(c_256,plain,
l1(e,e),
inference(resolve,[status(thm)],[c_10,c_4]) ).
fof(prove_this,axiom,
~ q4(a,e),
file('theBenchmark.p',prove_this) ).
cnf(c_264,plain,
~ q4(a,e),
inference(clausify,[status(thm)],[prove_this]) ).
fof(rule_295,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( ~ m3(VAR_3,VAR_4,VAR_3)
| ~ q2(VAR_3,VAR_1,VAR_0)
| ~ k3(VAR_2,VAR_2,VAR_0)
| q4(VAR_0,VAR_1) ),
file('theBenchmark.p',rule_295) ).
cnf(c_276,plain,
( ~ m3(D,E,D)
| ~ q2(D,B,A)
| ~ k3(C,C,A)
| q4(A,B) ),
inference(clausify,[status(thm)],[rule_295]) ).
fof(rule_238,axiom,
! [VAR_0] :
( ~ p2(VAR_0,VAR_0,VAR_0)
| m3(VAR_0,VAR_0,VAR_0) ),
file('theBenchmark.p',rule_238) ).
cnf(c_307,plain,
( ~ p2(A,A,A)
| m3(A,A,A) ),
inference(clausify,[status(thm)],[rule_238]) ).
fof(rule_186,axiom,
! [VAR_0,VAR_1] :
( ~ l1(VAR_1,VAR_0)
| q2(VAR_0,VAR_0,VAR_1) ),
file('theBenchmark.p',rule_186) ).
cnf(c_324,plain,
( ~ l1(B,A)
| q2(A,A,B) ),
inference(clausify,[status(thm)],[rule_186]) ).
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_005,axiom,
! [VAR_0,VAR_1] :
( ~ m0(VAR_1,VAR_1,VAR_0)
| m1(VAR_0,VAR_1,VAR_0) ),
file('theBenchmark.p',rule_005) ).
cnf(c_459,plain,
( ~ m0(B,B,A)
| m1(A,B,A) ),
inference(clausify,[status(thm)],[rule_005]) ).
fof(axiom_28,axiom,
k0(e),
file('theBenchmark.p',axiom_28) ).
cnf(c_469,plain,
k0(e),
inference(clausify,[status(thm)],[axiom_28]) ).
fof(axiom_17,axiom,
! [VAR_0] : q0(VAR_0,d),
file('theBenchmark.p',axiom_17) ).
cnf(c_479,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_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_1,axiom,
s0(d),
file('theBenchmark.p',axiom_1) ).
cnf(c_487,plain,
s0(d),
inference(clausify,[status(thm)],[axiom_1]) ).
cnf(c_493,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_534,plain,
k3(a,a,a),
inference(resolve,[status(thm)],[c_191,c_238]) ).
cnf(c_543,plain,
( ~ m3(B,C,B)
| ~ q2(B,e,a)
| ~ k3(A,A,a) ),
inference(resolve,[status(thm)],[c_276,c_264]) ).
cnf(c_546,plain,
q2(e,e,e),
inference(resolve,[status(thm)],[c_324,c_256]) ).
cnf(c_622,plain,
q1(A,d,A),
inference(resolve,[status(thm)],[c_230,c_481]) ).
cnf(c_804,plain,
( ~ m3(A,B,A)
| ~ q2(A,e,a) ),
inference(resolve,[status(thm)],[c_534,c_543]) ).
cnf(c_813,plain,
( ~ p2(A,A,A)
| ~ q2(A,e,a) ),
inference(resolve,[status(thm)],[c_804,c_307]) ).
cnf(c_842,plain,
( ~ m1(A,A,A)
| ~ q2(A,e,a) ),
inference(resolve,[status(thm)],[c_813,c_334]) ).
cnf(c_865,plain,
( ~ m0(A,A,A)
| ~ q2(A,e,a) ),
inference(resolve,[status(thm)],[c_842,c_459]) ).
cnf(c_873,plain,
~ q2(a,e,a),
inference(resolve,[status(thm)],[c_865,c_483]) ).
cnf(c_879,plain,
( ~ q2(B,B,B)
| ~ k0(B)
| ~ m0(C,D,A)
| q2(A,B,A)
| ~ q1(d,d,d)
| ~ s0(d) ),
inference(resolve,[status(thm)],[c_493,c_479]) ).
cnf(c_880,plain,
( ~ q2(B,B,B)
| ~ k0(B)
| ~ m0(C,D,A)
| q2(A,B,A)
| ~ q1(d,d,d) ),
inference(resolve,[status(thm)],[c_879,c_487]) ).
cnf(c_881,plain,
( ~ q2(e,e,e)
| ~ k0(e)
| ~ m0(A,B,a)
| ~ q1(d,d,d) ),
inference(resolve,[status(thm)],[c_880,c_873]) ).
cnf(c_882,plain,
( ~ q2(e,e,e)
| ~ k0(e)
| ~ q1(d,d,d) ),
inference(resolve,[status(thm)],[c_881,c_483]) ).
cnf(c_883,plain,
( ~ q2(e,e,e)
| ~ q1(d,d,d) ),
inference(resolve,[status(thm)],[c_882,c_469]) ).
cnf(c_877,plain,
~ q1(d,d,d),
inference(resolve,[status(thm)],[c_883,c_546]) ).
cnf(c_878,plain,
$false,
inference(resolve,[status(thm)],[c_877,c_622]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN180-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 17:24:43 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 2322859 was started by sandbox on n001,
% 0.10/0.38 % Sat Sep 26 17:24:43 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 0.97/0.53
% 0.97/0.53 % SZS status Unsatisfiable for theBenchmark
% 0.97/0.53
% 0.97/0.53 % Proof 1 at 0.13 (+ 0.01) seconds.
% 0.97/0.53 % Length of proof is 37.
% 0.97/0.53 % Level of proof is 9.
% 0.97/0.53 % Maximum clause weight is 25.000.
% 0.97/0.53 % Given clauses 442.
% 0.97/0.53
% 0.97/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------