%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN128-1 : 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 : n018.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 09:37:06 AM UTC 2026
% Result : Unsatisfiable 0.64s 0.51s
% Output : CNFRefutation 0.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 27
% Syntax : Number of formulae : 87 ( 32 unt; 0 def)
% Number of atoms : 184 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 210 ( 113 ~; 97 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 23 ( 22 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 168 ( 49 sgn 49 !; 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_26,axiom,
n0(d,c),
file('theBenchmark.p',axiom_26) ).
cnf(c_5,plain,
n0(d,c),
inference(clausify,[status(thm)],[axiom_26]) ).
fof(axiom_15,axiom,
n0(a,b),
file('theBenchmark.p',axiom_15) ).
cnf(c_6,plain,
n0(a,b),
inference(clausify,[status(thm)],[axiom_15]) ).
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_296,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ q4(VAR_1,VAR_2)
| ~ l4(VAR_1)
| ~ r1(VAR_0)
| q4(VAR_0,VAR_0) ),
file('theBenchmark.p',rule_296) ).
cnf(c_42,plain,
( ~ q4(B,C)
| ~ l4(B)
| ~ r1(A)
| q4(A,A) ),
inference(clausify,[status(thm)],[rule_296]) ).
fof(rule_302,axiom,
! [VAR_0,VAR_1] :
( ~ k1(VAR_0)
| ~ q4(VAR_1,VAR_1)
| l5(VAR_0) ),
file('theBenchmark.p',rule_302) ).
cnf(c_129,plain,
( ~ k1(A)
| ~ q4(B,B)
| l5(A) ),
inference(clausify,[status(thm)],[rule_302]) ).
fof(prove_this,axiom,
~ l5(c),
file('theBenchmark.p',prove_this) ).
cnf(c_130,plain,
~ l5(c),
inference(clausify,[status(thm)],[prove_this]) ).
cnf(c_228,plain,
( ~ p0(B,A)
| q1(A,b,A) ),
inference(resolve,[status(thm)],[c_21,c_6]) ).
cnf(c_236,plain,
p1(c,c,c),
inference(resolve,[status(thm)],[c_17,c_5]) ).
cnf(c_261,plain,
k1(c),
inference(resolve,[status(thm)],[c_1,c_5]) ).
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_277,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ p3(VAR_1,VAR_2,VAR_0)
| l4(VAR_0) ),
file('theBenchmark.p',rule_277) ).
cnf(c_289,plain,
( ~ p3(B,C,A)
| l4(A) ),
inference(clausify,[status(thm)],[rule_277]) ).
fof(rule_241,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ k2(VAR_1,VAR_2)
| ~ q2(VAR_3,d,VAR_0)
| p3(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',rule_241) ).
cnf(c_306,plain,
( ~ k2(B,C)
| ~ q2(D,d,A)
| p3(A,B,C) ),
inference(clausify,[status(thm)],[rule_241]) ).
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_308,plain,
( ~ p2(A,A,A)
| m3(A,A,A) ),
inference(clausify,[status(thm)],[rule_238]) ).
fof(rule_206,axiom,
! [VAR_0,VAR_1] :
( ~ p2(VAR_1,VAR_0,VAR_0)
| k3(VAR_0,VAR_1,VAR_0) ),
file('theBenchmark.p',rule_206) ).
cnf(c_317,plain,
( ~ p2(B,A,A)
| k3(A,B,A) ),
inference(clausify,[status(thm)],[rule_206]) ).
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_325,plain,
( ~ l1(B,A)
| q2(A,A,B) ),
inference(clausify,[status(thm)],[rule_186]) ).
fof(rule_177,axiom,
! [VAR_0,VAR_1] :
( ~ p1(VAR_0,VAR_0,VAR_0)
| ~ k0(VAR_1)
| q2(VAR_0,VAR_1,VAR_1) ),
file('theBenchmark.p',rule_177) ).
cnf(c_334,plain,
( ~ p1(A,A,A)
| ~ k0(B)
| q2(A,B,B) ),
inference(clausify,[status(thm)],[rule_177]) ).
fof(rule_153,axiom,
! [VAR_0] :
( ~ n1(d,d,VAR_0)
| p2(VAR_0,VAR_0,VAR_0) ),
file('theBenchmark.p',rule_153) ).
cnf(c_353,plain,
( ~ n1(d,d,A)
| p2(A,A,A) ),
inference(clausify,[status(thm)],[rule_153]) ).
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_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_059,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ m0(VAR_1,VAR_2,VAR_0)
| ~ m0(VAR_2,VAR_3,VAR_3)
| n1(VAR_0,VAR_0,VAR_1) ),
file('theBenchmark.p',rule_059) ).
cnf(c_424,plain,
( ~ m0(B,C,A)
| ~ m0(C,D,D)
| n1(A,A,B) ),
inference(clausify,[status(thm)],[rule_059]) ).
fof(rule_003,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ m0(VAR_1,VAR_0,VAR_2)
| ~ r0(VAR_3)
| ~ p0(VAR_2,VAR_0)
| l1(VAR_0,VAR_1) ),
file('theBenchmark.p',rule_003) ).
cnf(c_469,plain,
( ~ m0(B,A,C)
| ~ r0(D)
| ~ p0(C,A)
| l1(A,B) ),
inference(clausify,[status(thm)],[rule_003]) ).
fof(axiom_32,axiom,
k0(b),
file('theBenchmark.p',axiom_32) ).
cnf(c_474,plain,
k0(b),
inference(clausify,[status(thm)],[axiom_32]) ).
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_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_6,axiom,
q0(b,b),
file('theBenchmark.p',axiom_6) ).
cnf(c_493,plain,
q0(b,b),
inference(clausify,[status(thm)],[axiom_6]) ).
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_510,plain,
( ~ q4(C,D)
| ~ l4(C)
| q4(A,A)
| ~ q1(d,B,d)
| ~ s0(d)
| ~ q0(A,B) ),
inference(resolve,[status(thm)],[c_31,c_42]) ).
cnf(c_511,plain,
( ~ q4(C,D)
| ~ l4(C)
| q4(A,A)
| ~ q1(d,B,d)
| ~ q0(A,B) ),
inference(resolve,[status(thm)],[c_495,c_510]) ).
cnf(c_551,plain,
( ~ k1(c)
| ~ q4(A,A) ),
inference(resolve,[status(thm)],[c_129,c_130]) ).
cnf(c_552,plain,
~ q4(A,A),
inference(resolve,[status(thm)],[c_261,c_551]) ).
cnf(c_937,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_937]) ).
cnf(c_626,plain,
( ~ q4(C,D)
| ~ l4(C)
| ~ q1(d,B,d)
| ~ q0(A,B) ),
inference(resolve,[status(thm)],[c_552,c_511]) ).
cnf(c_938,plain,
( ~ p1(A,A,A)
| q2(A,b,b) ),
inference(resolve,[status(thm)],[c_334,c_474]) ).
cnf(c_665,plain,
q2(c,b,b),
inference(resolve,[status(thm)],[c_938,c_236]) ).
cnf(c_939,plain,
( ~ m0(B,C,A)
| n1(A,A,B) ),
inference(resolve,[status(thm)],[c_424,c_485]) ).
cnf(c_696,plain,
n1(A,A,B),
inference(resolve,[status(thm)],[c_939,c_485]) ).
cnf(c_699,plain,
p2(A,A,A),
inference(resolve,[status(thm)],[c_696,c_353]) ).
cnf(c_703,plain,
m3(A,A,A),
inference(resolve,[status(thm)],[c_699,c_308]) ).
cnf(c_729,plain,
q1(A,b,A),
inference(resolve,[status(thm)],[c_228,c_489]) ).
cnf(c_940,plain,
( ~ m0(B,A,b)
| ~ r0(C)
| l1(A,B) ),
inference(resolve,[status(thm)],[c_469,c_489]) ).
cnf(c_941,plain,
( ~ m0(B,A,b)
| l1(A,B) ),
inference(resolve,[status(thm)],[c_940,c_490]) ).
cnf(c_744,plain,
l1(d,A),
inference(resolve,[status(thm)],[c_941,c_485]) ).
cnf(c_762,plain,
k2(A,A),
inference(resolve,[status(thm)],[c_373,c_583]) ).
cnf(c_942,plain,
( ~ q4(A,B)
| ~ l4(A)
| ~ q1(d,b,d) ),
inference(resolve,[status(thm)],[c_626,c_493]) ).
cnf(c_768,plain,
( ~ q4(A,B)
| ~ l4(A) ),
inference(resolve,[status(thm)],[c_729,c_942]) ).
cnf(c_774,plain,
( ~ p3(C,D,A)
| ~ q4(A,B) ),
inference(resolve,[status(thm)],[c_768,c_289]) ).
cnf(c_781,plain,
( ~ k2(E,A)
| ~ q2(C,d,D)
| ~ q4(A,B) ),
inference(resolve,[status(thm)],[c_774,c_306]) ).
cnf(c_909,plain,
( ~ q2(C,d,D)
| ~ q4(A,B) ),
inference(resolve,[status(thm)],[c_781,c_762]) ).
cnf(c_912,plain,
( ~ l1(C,d)
| ~ q4(A,B) ),
inference(resolve,[status(thm)],[c_909,c_325]) ).
cnf(c_914,plain,
~ q4(A,B),
inference(resolve,[status(thm)],[c_912,c_744]) ).
cnf(c_915,plain,
( ~ m3(C,E,C)
| ~ q2(C,D,B)
| ~ k3(A,A,B) ),
inference(resolve,[status(thm)],[c_914,c_276]) ).
cnf(c_943,plain,
( ~ p2(C,C,C)
| ~ m3(A,D,A)
| ~ q2(A,B,C) ),
inference(resolve,[status(thm)],[c_915,c_317]) ).
cnf(c_922,plain,
( ~ m3(A,D,A)
| ~ q2(A,B,C) ),
inference(resolve,[status(thm)],[c_699,c_943]) ).
cnf(c_935,plain,
~ m3(c,A,c),
inference(resolve,[status(thm)],[c_922,c_665]) ).
cnf(c_936,plain,
$false,
inference(resolve,[status(thm)],[c_935,c_703]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN128-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n018.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 17:15:07 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 970098 was started by sandbox2 on n018,
% 0.09/0.36 % Sat Sep 26 17:15:07 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 0.64/0.51
% 0.64/0.51 % SZS status Unsatisfiable for theBenchmark
% 0.64/0.51
% 0.64/0.51 % Proof 1 at 0.11 (+ 0.01) seconds.
% 0.64/0.51 % Length of proof is 53.
% 0.64/0.51 % Level of proof is 13.
% 0.64/0.51 % Maximum clause weight is 15.000.
% 0.64/0.51 % Given clauses 374.
% 0.64/0.51
% 0.64/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------