%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN171-1 : 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 : n009.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 09:37:13 AM UTC 2026
% Result : Unsatisfiable 0.23s 0.68s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 30
% Syntax : Number of formulae : 95 ( 35 unt; 0 def)
% Number of atoms : 201 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 229 ( 123 ~; 106 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 132 ( 29 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_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_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_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_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]) ).
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_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_191,plain,
( ~ p1(B,C,A)
| k3(A,A,A) ),
inference(resolve,[status(thm)],[c_48,c_46]) ).
cnf(c_234,plain,
p1(b,b,b),
inference(resolve,[status(thm)],[c_17,c_6]) ).
cnf(c_258,plain,
l1(a,a),
inference(resolve,[status(thm)],[c_10,c_2]) ).
cnf(c_259,plain,
k1(b),
inference(resolve,[status(thm)],[c_1,c_6]) ).
cnf(c_262,plain,
k1(d),
inference(resolve,[status(thm)],[c_1,c_3]) ).
fof(prove_this,axiom,
~ p4(d,a,a),
file('theBenchmark.p',prove_this) ).
cnf(c_264,plain,
~ p4(d,a,a),
inference(clausify,[status(thm)],[prove_this]) ).
fof(rule_288,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ p4(VAR_2,VAR_2,VAR_3)
| ~ r3(VAR_1,VAR_1,VAR_0)
| p4(VAR_0,VAR_1,VAR_1) ),
file('theBenchmark.p',rule_288) ).
cnf(c_281,plain,
( ~ p4(C,C,D)
| ~ r3(B,B,A)
| p4(A,B,B) ),
inference(clausify,[status(thm)],[rule_288]) ).
fof(rule_287,axiom,
! [VAR_0,VAR_1] :
( ~ k3(VAR_0,VAR_0,VAR_1)
| p4(VAR_0,VAR_1,VAR_0) ),
file('theBenchmark.p',rule_287) ).
cnf(c_282,plain,
( ~ k3(A,A,B)
| p4(A,B,A) ),
inference(clausify,[status(thm)],[rule_287]) ).
fof(rule_268,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ r3(VAR_1,VAR_3,VAR_3)
| ~ m3(VAR_2,b,VAR_0)
| ~ m2(VAR_1)
| r3(VAR_0,VAR_0,VAR_1) ),
file('theBenchmark.p',rule_268) ).
cnf(c_293,plain,
( ~ r3(B,D,D)
| ~ m3(C,b,A)
| ~ m2(B)
| r3(A,A,B) ),
inference(clausify,[status(thm)],[rule_268]) ).
fof(rule_267,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ p2(VAR_0,VAR_2,VAR_1)
| r3(VAR_0,VAR_1,VAR_0) ),
file('theBenchmark.p',rule_267) ).
cnf(c_294,plain,
( ~ p2(A,C,B)
| r3(A,B,A) ),
inference(clausify,[status(thm)],[rule_267]) ).
fof(rule_170,axiom,
! [VAR_0] :
( ~ n1(VAR_0,e,e)
| p2(VAR_0,e,VAR_0) ),
file('theBenchmark.p',rule_170) ).
cnf(c_339,plain,
( ~ n1(A,e,e)
| p2(A,e,A) ),
inference(clausify,[status(thm)],[rule_170]) ).
fof(rule_135,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ l1(VAR_1,VAR_2)
| ~ s0(VAR_0)
| m2(VAR_0) ),
file('theBenchmark.p',rule_135) ).
cnf(c_368,plain,
( ~ l1(B,C)
| ~ s0(A)
| m2(A) ),
inference(clausify,[status(thm)],[rule_135]) ).
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_040,axiom,
! [VAR_0,VAR_1] :
( ~ k1(VAR_0)
| ~ m0(VAR_0,VAR_1,e)
| n1(VAR_0,e,e) ),
file('theBenchmark.p',rule_040) ).
cnf(c_440,plain,
( ~ k1(A)
| ~ m0(A,B,e)
| n1(A,e,e) ),
inference(clausify,[status(thm)],[rule_040]) ).
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_32,axiom,
k0(b),
file('theBenchmark.p',axiom_32) ).
cnf(c_474,plain,
k0(b),
inference(clausify,[status(thm)],[axiom_32]) ).
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_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_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_1046,plain,
( ~ m0(e,d,A)
| q1(e,A,A) ),
inference(resolve,[status(thm)],[c_485,c_390]) ).
cnf(c_606,plain,
q1(e,A,A),
inference(resolve,[status(thm)],[c_485,c_1046]) ).
cnf(c_654,plain,
k3(b,b,b),
inference(resolve,[status(thm)],[c_234,c_191]) ).
cnf(c_671,plain,
( ~ p4(A,A,B)
| ~ r3(a,a,d) ),
inference(resolve,[status(thm)],[c_281,c_264]) ).
cnf(c_699,plain,
( ~ s0(A)
| m2(A) ),
inference(resolve,[status(thm)],[c_368,c_258]) ).
cnf(c_1047,plain,
( ~ k0(A)
| m1(c,A,c) ),
inference(resolve,[status(thm)],[c_458,c_480]) ).
cnf(c_759,plain,
m1(c,b,c),
inference(resolve,[status(thm)],[c_1047,c_474]) ).
cnf(c_788,plain,
q1(A,A,A),
inference(resolve,[status(thm)],[c_485,c_380]) ).
cnf(c_1048,plain,
( ~ k1(A)
| n1(A,e,e) ),
inference(resolve,[status(thm)],[c_440,c_485]) ).
cnf(c_793,plain,
n1(d,e,e),
inference(resolve,[status(thm)],[c_1048,c_262]) ).
cnf(c_880,plain,
k2(A,A),
inference(resolve,[status(thm)],[c_606,c_373]) ).
cnf(c_919,plain,
( ~ k3(A,A,A)
| ~ r3(a,a,d) ),
inference(resolve,[status(thm)],[c_671,c_282]) ).
cnf(c_928,plain,
~ r3(a,a,d),
inference(resolve,[status(thm)],[c_919,c_654]) ).
cnf(c_930,plain,
( ~ r3(d,B,B)
| ~ m3(A,b,a)
| ~ m2(d) ),
inference(resolve,[status(thm)],[c_928,c_293]) ).
cnf(c_942,plain,
( ~ p2(d,B,d)
| ~ m3(A,b,a)
| ~ m2(d) ),
inference(resolve,[status(thm)],[c_930,c_294]) ).
cnf(c_1049,plain,
( ~ n1(d,e,e)
| ~ m3(A,b,a)
| ~ m2(d) ),
inference(resolve,[status(thm)],[c_942,c_339]) ).
cnf(c_988,plain,
( ~ m3(A,b,a)
| ~ m2(d) ),
inference(resolve,[status(thm)],[c_793,c_1049]) ).
cnf(c_1050,plain,
( ~ k2(c,b)
| ~ l0(a)
| ~ q1(d,A,d)
| ~ q0(a,A)
| ~ m2(d) ),
inference(resolve,[status(thm)],[c_988,c_527]) ).
cnf(c_1009,plain,
( ~ k2(c,b)
| ~ q1(d,A,d)
| ~ q0(a,A)
| ~ m2(d) ),
inference(resolve,[status(thm)],[c_484,c_1050]) ).
cnf(c_1033,plain,
m2(d),
inference(resolve,[status(thm)],[c_699,c_495]) ).
cnf(c_1037,plain,
( ~ k2(c,b)
| ~ q1(d,A,d)
| ~ q0(a,A) ),
inference(resolve,[status(thm)],[c_1033,c_1009]) ).
cnf(c_1051,plain,
( ~ k2(c,b)
| ~ q1(d,d,d) ),
inference(resolve,[status(thm)],[c_1037,c_487]) ).
cnf(c_1041,plain,
~ k2(c,b),
inference(resolve,[status(thm)],[c_788,c_1051]) ).
cnf(c_1052,plain,
( ~ k2(B,b)
| ~ k1(B)
| ~ m1(A,b,c) ),
inference(resolve,[status(thm)],[c_375,c_1041]) ).
cnf(c_1053,plain,
( ~ k2(b,b)
| ~ m1(A,b,c) ),
inference(resolve,[status(thm)],[c_1052,c_259]) ).
cnf(c_1044,plain,
~ m1(A,b,c),
inference(resolve,[status(thm)],[c_1053,c_880]) ).
cnf(c_1045,plain,
$false,
inference(resolve,[status(thm)],[c_1044,c_759]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN171-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.45 % Computer : n009.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Sat Sep 26 17:18:15 UTC 2026
% 0.20/0.45 % CPUTime :
% 0.20/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.20/0.46 % Process 702415 was started by sandbox2 on n009,
% 0.20/0.46 % Sat Sep 26 17:18:15 2026
% 0.20/0.46 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.20/0.48
% 0.20/0.48 % From the command line: assign(max_seconds, 300).
% 0.23/0.68
% 0.23/0.68 % SZS status Unsatisfiable for theBenchmark
% 0.23/0.68
% 0.23/0.68 % Proof 1 at 0.17 (+ 0.02) seconds.
% 0.23/0.68 % Length of proof is 57.
% 0.23/0.68 % Level of proof is 11.
% 0.23/0.68 % Maximum clause weight is 21.000.
% 0.23/0.68 % Given clauses 361.
% 0.23/0.68
% 0.23/0.68 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------