%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN037-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 09:36:48 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 53
% Number of leaves : 22
% Syntax : Number of formulae : 117 ( 6 unt; 0 def)
% Number of atoms : 379 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 376 ( 114 ~; 262 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 4 prp; 0-1 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-1 aty)
% Number of variables : 90 ( 54 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clause_1,axiom,
! [VAR_0] :
( ~ p(fy(VAR_0))
| ~ p(VAR_0)
| ~ m3
| ~ m1 ),
file('theBenchmark.p',clause_1) ).
cnf(c_1,plain,
( ~ p(fy(A))
| ~ p(A)
| ~ m3
| ~ m1 ),
inference(clausify,[status(thm)],[clause_1]) ).
fof(clause_2,axiom,
! [VAR_0] :
( p(fy(VAR_0))
| p(VAR_0)
| ~ m3
| ~ m1 ),
file('theBenchmark.p',clause_2) ).
cnf(c_2,plain,
( p(fy(A))
| p(A)
| ~ m3
| ~ m1 ),
inference(clausify,[status(thm)],[clause_2]) ).
fof(clause_3,axiom,
! [VAR_0] :
( p(VAR_0)
| m3
| ~ p(cx)
| ~ m1 ),
file('theBenchmark.p',clause_3) ).
cnf(c_3,plain,
( p(A)
| m3
| ~ p(cx)
| ~ m1 ),
inference(clausify,[status(thm)],[clause_3]) ).
fof(clause_4,axiom,
! [VAR_0] :
( p(cx)
| m3
| ~ p(VAR_0)
| ~ m1 ),
file('theBenchmark.p',clause_4) ).
cnf(c_4,plain,
( p(cx)
| m3
| ~ p(A)
| ~ m1 ),
inference(clausify,[status(thm)],[clause_4]) ).
fof(clause_5,axiom,
! [VAR_0] :
( q(VAR_0)
| ~ q(cw)
| ~ m3
| ~ m2 ),
file('theBenchmark.p',clause_5) ).
cnf(c_5,plain,
( q(A)
| ~ q(cw)
| ~ m3
| ~ m2 ),
inference(clausify,[status(thm)],[clause_5]) ).
fof(clause_6,axiom,
! [VAR_0] :
( q(cw)
| ~ q(VAR_0)
| ~ m3
| ~ m2 ),
file('theBenchmark.p',clause_6) ).
cnf(c_6,plain,
( q(cw)
| ~ q(A)
| ~ m3
| ~ m2 ),
inference(clausify,[status(thm)],[clause_6]) ).
fof(clause_7,axiom,
! [VAR_0] :
( m3
| ~ q(fz5(VAR_0))
| ~ q(VAR_0)
| ~ m2 ),
file('theBenchmark.p',clause_7) ).
cnf(c_7,plain,
( m3
| ~ q(fz5(A))
| ~ q(A)
| ~ m2 ),
inference(clausify,[status(thm)],[clause_7]) ).
fof(clause_8,axiom,
! [VAR_0] :
( q(fz5(VAR_0))
| q(VAR_0)
| m3
| ~ m2 ),
file('theBenchmark.p',clause_8) ).
cnf(c_8,plain,
( q(fz5(A))
| q(A)
| m3
| ~ m2 ),
inference(clausify,[status(thm)],[clause_8]) ).
fof(clause_9,axiom,
! [VAR_0] :
( p(VAR_0)
| m1
| ~ p(cx)
| ~ m3 ),
file('theBenchmark.p',clause_9) ).
cnf(c_9,plain,
( p(A)
| m1
| ~ p(cx)
| ~ m3 ),
inference(clausify,[status(thm)],[clause_9]) ).
fof(clause_10,axiom,
! [VAR_0] :
( p(cx)
| m1
| ~ p(VAR_0)
| ~ m3 ),
file('theBenchmark.p',clause_10) ).
cnf(c_10,plain,
( p(cx)
| m1
| ~ p(A)
| ~ m3 ),
inference(clausify,[status(thm)],[clause_10]) ).
fof(clause_11,axiom,
! [VAR_0] :
( m2
| ~ q(fz2(VAR_0))
| ~ q(VAR_0)
| ~ m3 ),
file('theBenchmark.p',clause_11) ).
cnf(c_11,plain,
( m2
| ~ q(fz2(A))
| ~ q(A)
| ~ m3 ),
inference(clausify,[status(thm)],[clause_11]) ).
fof(clause_12,axiom,
! [VAR_0] :
( q(fz2(VAR_0))
| q(VAR_0)
| m2
| ~ m3 ),
file('theBenchmark.p',clause_12) ).
cnf(c_12,plain,
( q(fz2(A))
| q(A)
| m2
| ~ m3 ),
inference(clausify,[status(thm)],[clause_12]) ).
fof(clause_13,axiom,
! [VAR_0] :
( m3
| m1
| ~ p(fy3(VAR_0))
| ~ p(VAR_0) ),
file('theBenchmark.p',clause_13) ).
cnf(c_13,plain,
( m3
| m1
| ~ p(fy3(A))
| ~ p(A) ),
inference(clausify,[status(thm)],[clause_13]) ).
fof(clause_14,axiom,
! [VAR_0] :
( q(VAR_0)
| m3
| m2
| ~ q(cw) ),
file('theBenchmark.p',clause_14) ).
cnf(c_14,plain,
( q(A)
| m3
| m2
| ~ q(cw) ),
inference(clausify,[status(thm)],[clause_14]) ).
fof(clause_15,axiom,
! [VAR_0] :
( q(cw)
| m3
| m2
| ~ q(VAR_0) ),
file('theBenchmark.p',clause_15) ).
cnf(c_15,plain,
( q(cw)
| m3
| m2
| ~ q(A) ),
inference(clausify,[status(thm)],[clause_15]) ).
fof(clause_16,axiom,
! [VAR_0] :
( p(fy3(VAR_0))
| p(VAR_0)
| m3
| m1 ),
file('theBenchmark.p',clause_16) ).
cnf(c_16,plain,
( p(fy3(A))
| p(A)
| m3
| m1 ),
inference(clausify,[status(thm)],[clause_16]) ).
fof(clause_17,axiom,
! [VAR_0,VAR_1] :
( q(VAR_1)
| ~ q(VAR_0)
| ~ m1 ),
file('theBenchmark.p',clause_17) ).
cnf(c_17,plain,
( q(B)
| ~ q(A)
| ~ m1 ),
inference(clausify,[status(thm)],[clause_17]) ).
fof(clause_18,axiom,
! [VAR_0,VAR_1] :
( p(VAR_1)
| ~ p(VAR_0)
| ~ m2 ),
file('theBenchmark.p',clause_18) ).
cnf(c_18,plain,
( p(B)
| ~ p(A)
| ~ m2 ),
inference(clausify,[status(thm)],[clause_18]) ).
fof(clause_19,axiom,
( m2
| ~ p(cvv) ),
file('theBenchmark.p',clause_19) ).
cnf(c_19,plain,
( m2
| ~ p(cvv) ),
inference(clausify,[status(thm)],[clause_19]) ).
fof(clause_20,axiom,
( m1
| ~ q(cuu) ),
file('theBenchmark.p',clause_20) ).
cnf(c_20,plain,
( m1
| ~ q(cuu) ),
inference(clausify,[status(thm)],[clause_20]) ).
fof(clause_21,axiom,
( p(cv)
| m2 ),
file('theBenchmark.p',clause_21) ).
cnf(c_21,plain,
( p(cv)
| m2 ),
inference(clausify,[status(thm)],[clause_21]) ).
fof(clause_22,axiom,
( q(cu)
| m1 ),
file('theBenchmark.p',clause_22) ).
cnf(c_22,plain,
( q(cu)
| m1 ),
inference(clausify,[status(thm)],[clause_22]) ).
cnf(c_23,plain,
( p(B)
| m3
| m1
| p(A)
| ~ m2 ),
inference(resolve,[status(thm)],[c_18,c_16]) ).
cnf(c_24,plain,
( m3
| m1
| p(A)
| ~ m2 ),
inference(factor,[status(thm)],[c_23]) ).
cnf(c_25,plain,
( p(cx)
| m1
| ~ m3
| m2 ),
inference(resolve,[status(thm)],[c_21,c_10]) ).
cnf(c_26,plain,
( p(cx)
| m3
| ~ m1
| m2 ),
inference(resolve,[status(thm)],[c_21,c_4]) ).
cnf(c_27,plain,
( q(cw)
| m3
| m2
| m1 ),
inference(resolve,[status(thm)],[c_22,c_15]) ).
cnf(c_28,plain,
( q(cw)
| ~ m3
| ~ m2
| m1 ),
inference(resolve,[status(thm)],[c_22,c_6]) ).
cnf(c_74,plain,
( q(A)
| m3
| m2
| m3
| m2
| m1 ),
inference(resolve,[status(thm)],[c_27,c_14]) ).
cnf(c_75,plain,
( q(A)
| m3
| m3
| m2
| m1 ),
inference(copy,[status(thm)],[c_74]) ).
cnf(c_29,plain,
( q(A)
| m3
| m2
| m1 ),
inference(copy,[status(thm)],[c_75]) ).
cnf(c_76,plain,
( m1
| m3
| m2
| m1 ),
inference(resolve,[status(thm)],[c_29,c_20]) ).
cnf(c_30,plain,
( m3
| m2
| m1 ),
inference(copy,[status(thm)],[c_76]) ).
cnf(c_77,plain,
( p(cx)
| m3
| m2
| m3
| m2 ),
inference(resolve,[status(thm)],[c_30,c_26]) ).
cnf(c_78,plain,
( p(cx)
| m3
| m3
| m2 ),
inference(copy,[status(thm)],[c_77]) ).
cnf(c_31,plain,
( p(cx)
| m3
| m2 ),
inference(copy,[status(thm)],[c_78]) ).
cnf(c_79,plain,
( p(A)
| m3
| ~ m1
| m3
| m2 ),
inference(resolve,[status(thm)],[c_31,c_3]) ).
cnf(c_32,plain,
( p(A)
| ~ m1
| m3
| m2 ),
inference(copy,[status(thm)],[c_79]) ).
cnf(c_80,plain,
( m3
| m2
| p(A)
| m3
| m2 ),
inference(resolve,[status(thm)],[c_32,c_30]) ).
cnf(c_81,plain,
( m3
| p(A)
| m3
| m2 ),
inference(copy,[status(thm)],[c_80]) ).
cnf(c_33,plain,
( p(A)
| m3
| m2 ),
inference(copy,[status(thm)],[c_81]) ).
cnf(c_82,plain,
( m2
| m3
| m2 ),
inference(resolve,[status(thm)],[c_33,c_19]) ).
cnf(c_34,plain,
( m3
| m2 ),
inference(copy,[status(thm)],[c_82]) ).
cnf(c_83,plain,
( m3
| m1
| p(A)
| m3 ),
inference(resolve,[status(thm)],[c_34,c_24]) ).
cnf(c_35,plain,
( m1
| p(A)
| m3 ),
inference(copy,[status(thm)],[c_83]) ).
cnf(c_84,plain,
( q(fz5(A))
| q(A)
| m3
| m3 ),
inference(resolve,[status(thm)],[c_34,c_8]) ).
cnf(c_36,plain,
( q(fz5(A))
| q(A)
| m3 ),
inference(copy,[status(thm)],[c_84]) ).
cnf(c_85,plain,
( m3
| m1
| ~ p(A)
| m1
| m3 ),
inference(resolve,[status(thm)],[c_35,c_13]) ).
cnf(c_86,plain,
( m3
| ~ p(A)
| m1
| m3 ),
inference(copy,[status(thm)],[c_85]) ).
cnf(c_37,plain,
( ~ p(A)
| m1
| m3 ),
inference(copy,[status(thm)],[c_86]) ).
cnf(c_87,plain,
( m1
| m3
| m1
| m3 ),
inference(resolve,[status(thm)],[c_37,c_35]) ).
cnf(c_88,plain,
( m1
| m1
| m3 ),
inference(copy,[status(thm)],[c_87]) ).
cnf(c_38,plain,
( m1
| m3 ),
inference(copy,[status(thm)],[c_88]) ).
cnf(c_39,plain,
( q(B)
| ~ m1
| q(A)
| m3 ),
inference(resolve,[status(thm)],[c_36,c_17]) ).
cnf(c_40,plain,
( ~ m1
| q(A)
| m3 ),
inference(factor,[status(thm)],[c_39]) ).
cnf(c_89,plain,
( m3
| q(A)
| m3 ),
inference(resolve,[status(thm)],[c_40,c_38]) ).
cnf(c_41,plain,
( q(A)
| m3 ),
inference(copy,[status(thm)],[c_89]) ).
cnf(c_90,plain,
( m3
| ~ q(A)
| ~ m2
| m3 ),
inference(resolve,[status(thm)],[c_41,c_7]) ).
cnf(c_42,plain,
( ~ q(A)
| ~ m2
| m3 ),
inference(copy,[status(thm)],[c_90]) ).
cnf(c_91,plain,
( m3
| ~ m2
| m3 ),
inference(resolve,[status(thm)],[c_42,c_41]) ).
cnf(c_43,plain,
( ~ m2
| m3 ),
inference(copy,[status(thm)],[c_91]) ).
cnf(c_92,plain,
( m3
| m3 ),
inference(resolve,[status(thm)],[c_43,c_34]) ).
cnf(c_44,plain,
m3,
inference(copy,[status(thm)],[c_92]) ).
cnf(c_45,plain,
( q(cw)
| ~ m2
| m1 ),
inference(resolve,[status(thm)],[c_44,c_28]) ).
cnf(c_46,plain,
( p(cx)
| m1
| m2 ),
inference(resolve,[status(thm)],[c_44,c_25]) ).
cnf(c_47,plain,
( q(fz2(A))
| q(A)
| m2 ),
inference(resolve,[status(thm)],[c_44,c_12]) ).
cnf(c_48,plain,
( m2
| ~ q(fz2(A))
| ~ q(A) ),
inference(resolve,[status(thm)],[c_44,c_11]) ).
cnf(c_50,plain,
( p(A)
| m1
| ~ p(cx) ),
inference(resolve,[status(thm)],[c_44,c_9]) ).
cnf(c_52,plain,
( q(A)
| ~ q(cw)
| ~ m2 ),
inference(resolve,[status(thm)],[c_44,c_5]) ).
cnf(c_53,plain,
( p(fy(A))
| p(A)
| ~ m1 ),
inference(resolve,[status(thm)],[c_44,c_2]) ).
cnf(c_54,plain,
( ~ p(fy(A))
| ~ p(A)
| ~ m1 ),
inference(resolve,[status(thm)],[c_44,c_1]) ).
cnf(c_93,plain,
( m1
| m2
| p(A)
| m1 ),
inference(resolve,[status(thm)],[c_50,c_46]) ).
cnf(c_55,plain,
( m2
| p(A)
| m1 ),
inference(copy,[status(thm)],[c_93]) ).
cnf(c_94,plain,
( m2
| m2
| m1 ),
inference(resolve,[status(thm)],[c_55,c_19]) ).
cnf(c_56,plain,
( m2
| m1 ),
inference(copy,[status(thm)],[c_94]) ).
cnf(c_57,plain,
( q(B)
| ~ m1
| q(A)
| m2 ),
inference(resolve,[status(thm)],[c_47,c_17]) ).
cnf(c_58,plain,
( ~ m1
| q(A)
| m2 ),
inference(factor,[status(thm)],[c_57]) ).
cnf(c_95,plain,
( m2
| q(A)
| m2 ),
inference(resolve,[status(thm)],[c_58,c_56]) ).
cnf(c_59,plain,
( q(A)
| m2 ),
inference(copy,[status(thm)],[c_95]) ).
cnf(c_96,plain,
( m2
| m2
| ~ q(A) ),
inference(resolve,[status(thm)],[c_48,c_59]) ).
cnf(c_60,plain,
( m2
| ~ q(A) ),
inference(copy,[status(thm)],[c_96]) ).
cnf(c_97,plain,
( m2
| m2 ),
inference(resolve,[status(thm)],[c_60,c_59]) ).
cnf(c_61,plain,
m2,
inference(copy,[status(thm)],[c_97]) ).
cnf(c_62,plain,
( q(A)
| ~ q(cw) ),
inference(resolve,[status(thm)],[c_61,c_52]) ).
cnf(c_64,plain,
( q(cw)
| m1 ),
inference(resolve,[status(thm)],[c_61,c_45]) ).
cnf(c_65,plain,
( p(B)
| ~ p(A) ),
inference(resolve,[status(thm)],[c_61,c_18]) ).
cnf(c_66,plain,
( m1
| q(A) ),
inference(resolve,[status(thm)],[c_62,c_64]) ).
cnf(c_98,plain,
( m1
| m1 ),
inference(resolve,[status(thm)],[c_66,c_20]) ).
cnf(c_67,plain,
m1,
inference(copy,[status(thm)],[c_98]) ).
cnf(c_68,plain,
( ~ p(fy(A))
| ~ p(A) ),
inference(resolve,[status(thm)],[c_67,c_54]) ).
cnf(c_69,plain,
( p(fy(A))
| p(A) ),
inference(resolve,[status(thm)],[c_67,c_53]) ).
cnf(c_71,plain,
( p(B)
| p(A) ),
inference(resolve,[status(thm)],[c_69,c_65]) ).
cnf(c_72,plain,
p(A),
inference(factor,[status(thm)],[c_71]) ).
cnf(c_99,plain,
~ p(fy(A)),
inference(resolve,[status(thm)],[c_72,c_68]) ).
cnf(c_73,plain,
$false,
inference(resolve,[status(thm)],[c_72,c_99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN037-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n026.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 17:08:25 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.13/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.36 % Process 1523082 was started by sandbox2 on n026,
% 0.13/0.36 % Sat Sep 26 17:08:25 2026
% 0.13/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.37
% 0.13/0.37 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.37
% 0.13/0.37 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.13/0.37 % Length of proof is 69.
% 0.13/0.37 % Level of proof is 27.
% 0.13/0.37 % Maximum clause weight is 7.000.
% 0.13/0.37 % Given clauses 65.
% 0.13/0.37
% 0.13/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------