%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYO613-1 : TPTP v9.3.1. Released v7.1.0.
% 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 09:51:06 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 3
% Syntax : Number of formulae : 29 ( 6 unt; 0 def)
% Number of atoms : 304 ( 0 equ)
% Maximal formula atoms : 23 ( 10 avg)
% Number of connectives : 574 ( 299 ~; 275 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 36 ( 12 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 237 ( 34 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sos_01,axiom,
! [VAR_0] : le(VAR_0,VAR_0),
file('theBenchmark.p',sos_01) ).
cnf(c_1,plain,
le(A,A),
inference(clausify,[status(thm)],[sos_01]) ).
fof(sos_04,axiom,
! [VAR_0] : eq(f(VAR_0),a0),
file('theBenchmark.p',sos_04) ).
cnf(c_4,plain,
eq(f(A),a0),
inference(clausify,[status(thm)],[sos_04]) ).
fof(sos_05,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6,VAR_7,VAR_8,VAR_9,VAR_10,VAR_11] :
( ~ le(s(VAR_10),VAR_11)
| ~ le(s(VAR_9),VAR_10)
| ~ le(s(VAR_8),VAR_9)
| ~ le(s(VAR_7),VAR_8)
| ~ le(s(VAR_6),VAR_7)
| ~ le(s(VAR_5),VAR_6)
| ~ le(s(VAR_4),VAR_5)
| ~ le(s(VAR_3),VAR_4)
| ~ le(s(VAR_2),VAR_3)
| ~ le(s(VAR_1),VAR_2)
| ~ le(s(VAR_0),VAR_1)
| ~ eq(f(VAR_11),a0)
| ~ eq(f(VAR_10),a0)
| ~ eq(f(VAR_9),a0)
| ~ eq(f(VAR_8),a0)
| ~ eq(f(VAR_7),a0)
| ~ eq(f(VAR_6),a0)
| ~ eq(f(VAR_5),a0)
| ~ eq(f(VAR_4),a0)
| ~ eq(f(VAR_3),a0)
| ~ eq(f(VAR_2),a0)
| ~ eq(f(VAR_1),a0)
| ~ eq(f(VAR_0),a0) ),
file('theBenchmark.p',sos_05) ).
cnf(c_5,plain,
( ~ le(s(V10),V11)
| ~ le(s(V9),V10)
| ~ le(s(V8),V9)
| ~ le(s(V7),V8)
| ~ le(s(V6),V7)
| ~ le(s(F),V6)
| ~ le(s(E),F)
| ~ le(s(D),E)
| ~ le(s(C),D)
| ~ le(s(B),C)
| ~ le(s(A),B)
| ~ eq(f(V11),a0)
| ~ eq(f(V10),a0)
| ~ eq(f(V9),a0)
| ~ eq(f(V8),a0)
| ~ eq(f(V7),a0)
| ~ eq(f(V6),a0)
| ~ eq(f(F),a0)
| ~ eq(f(E),a0)
| ~ eq(f(D),a0)
| ~ eq(f(C),a0)
| ~ eq(f(B),a0)
| ~ eq(f(A),a0) ),
inference(clausify,[status(thm)],[sos_05]) ).
cnf(c_10,plain,
( ~ le(s(V9),V10)
| ~ le(s(V8),V9)
| ~ le(s(V7),V8)
| ~ le(s(V6),V7)
| ~ le(s(F),V6)
| ~ le(s(E),F)
| ~ le(s(D),E)
| ~ le(s(C),D)
| ~ le(s(B),C)
| ~ le(s(A),B)
| ~ le(s(V11),A)
| ~ eq(f(V10),a0)
| ~ eq(f(V9),a0)
| ~ eq(f(V8),a0)
| ~ eq(f(V7),a0)
| ~ eq(f(V6),a0)
| ~ eq(f(F),a0)
| ~ eq(f(E),a0)
| ~ eq(f(D),a0)
| ~ eq(f(C),a0)
| ~ eq(f(B),a0)
| ~ eq(f(A),a0) ),
inference(resolve,[status(thm)],[c_4,c_5]) ).
cnf(c_11,plain,
( ~ le(s(V8),V9)
| ~ le(s(V7),V8)
| ~ le(s(V6),V7)
| ~ le(s(F),V6)
| ~ le(s(E),F)
| ~ le(s(D),E)
| ~ le(s(C),D)
| ~ le(s(B),C)
| ~ le(s(A),B)
| ~ le(s(V11),A)
| ~ le(s(V10),V11)
| ~ eq(f(V9),a0)
| ~ eq(f(V8),a0)
| ~ eq(f(V7),a0)
| ~ eq(f(V6),a0)
| ~ eq(f(F),a0)
| ~ eq(f(E),a0)
| ~ eq(f(D),a0)
| ~ eq(f(C),a0)
| ~ eq(f(B),a0)
| ~ eq(f(A),a0) ),
inference(resolve,[status(thm)],[c_4,c_10]) ).
cnf(c_12,plain,
( ~ le(s(V7),V8)
| ~ le(s(V6),V7)
| ~ le(s(F),V6)
| ~ le(s(E),F)
| ~ le(s(D),E)
| ~ le(s(C),D)
| ~ le(s(B),C)
| ~ le(s(A),B)
| ~ le(s(V11),A)
| ~ le(s(V10),V11)
| ~ le(s(V9),V10)
| ~ eq(f(V8),a0)
| ~ eq(f(V7),a0)
| ~ eq(f(V6),a0)
| ~ eq(f(F),a0)
| ~ eq(f(E),a0)
| ~ eq(f(D),a0)
| ~ eq(f(C),a0)
| ~ eq(f(B),a0)
| ~ eq(f(A),a0) ),
inference(resolve,[status(thm)],[c_4,c_11]) ).
cnf(c_13,plain,
( ~ le(s(V6),V7)
| ~ le(s(F),V6)
| ~ le(s(E),F)
| ~ le(s(D),E)
| ~ le(s(C),D)
| ~ le(s(B),C)
| ~ le(s(A),B)
| ~ le(s(V11),A)
| ~ le(s(V10),V11)
| ~ le(s(V9),V10)
| ~ le(s(V8),V9)
| ~ eq(f(V7),a0)
| ~ eq(f(V6),a0)
| ~ eq(f(F),a0)
| ~ eq(f(E),a0)
| ~ eq(f(D),a0)
| ~ eq(f(C),a0)
| ~ eq(f(B),a0)
| ~ eq(f(A),a0) ),
inference(resolve,[status(thm)],[c_4,c_12]) ).
cnf(c_14,plain,
( ~ le(s(F),V6)
| ~ le(s(E),F)
| ~ le(s(D),E)
| ~ le(s(C),D)
| ~ le(s(B),C)
| ~ le(s(A),B)
| ~ le(s(V11),A)
| ~ le(s(V10),V11)
| ~ le(s(V9),V10)
| ~ le(s(V8),V9)
| ~ le(s(V7),V8)
| ~ eq(f(V6),a0)
| ~ eq(f(F),a0)
| ~ eq(f(E),a0)
| ~ eq(f(D),a0)
| ~ eq(f(C),a0)
| ~ eq(f(B),a0)
| ~ eq(f(A),a0) ),
inference(resolve,[status(thm)],[c_4,c_13]) ).
cnf(c_15,plain,
( ~ le(s(E),F)
| ~ le(s(D),E)
| ~ le(s(C),D)
| ~ le(s(B),C)
| ~ le(s(A),B)
| ~ le(s(V11),A)
| ~ le(s(V10),V11)
| ~ le(s(V9),V10)
| ~ le(s(V8),V9)
| ~ le(s(V7),V8)
| ~ le(s(V6),V7)
| ~ eq(f(F),a0)
| ~ eq(f(E),a0)
| ~ eq(f(D),a0)
| ~ eq(f(C),a0)
| ~ eq(f(B),a0)
| ~ eq(f(A),a0) ),
inference(resolve,[status(thm)],[c_4,c_14]) ).
cnf(c_16,plain,
( ~ le(s(D),E)
| ~ le(s(C),D)
| ~ le(s(B),C)
| ~ le(s(A),B)
| ~ le(s(V11),A)
| ~ le(s(V10),V11)
| ~ le(s(V9),V10)
| ~ le(s(V8),V9)
| ~ le(s(V7),V8)
| ~ le(s(V6),V7)
| ~ le(s(F),V6)
| ~ eq(f(E),a0)
| ~ eq(f(D),a0)
| ~ eq(f(C),a0)
| ~ eq(f(B),a0)
| ~ eq(f(A),a0) ),
inference(resolve,[status(thm)],[c_4,c_15]) ).
cnf(c_17,plain,
( ~ le(s(C),D)
| ~ le(s(B),C)
| ~ le(s(A),B)
| ~ le(s(V11),A)
| ~ le(s(V10),V11)
| ~ le(s(V9),V10)
| ~ le(s(V8),V9)
| ~ le(s(V7),V8)
| ~ le(s(V6),V7)
| ~ le(s(F),V6)
| ~ le(s(E),F)
| ~ eq(f(D),a0)
| ~ eq(f(C),a0)
| ~ eq(f(B),a0)
| ~ eq(f(A),a0) ),
inference(resolve,[status(thm)],[c_4,c_16]) ).
cnf(c_18,plain,
( ~ le(s(B),C)
| ~ le(s(A),B)
| ~ le(s(V11),A)
| ~ le(s(V10),V11)
| ~ le(s(V9),V10)
| ~ le(s(V8),V9)
| ~ le(s(V7),V8)
| ~ le(s(V6),V7)
| ~ le(s(F),V6)
| ~ le(s(E),F)
| ~ le(s(D),E)
| ~ eq(f(C),a0)
| ~ eq(f(B),a0)
| ~ eq(f(A),a0) ),
inference(resolve,[status(thm)],[c_4,c_17]) ).
cnf(c_19,plain,
( ~ le(s(A),B)
| ~ le(s(V11),A)
| ~ le(s(V10),V11)
| ~ le(s(V9),V10)
| ~ le(s(V8),V9)
| ~ le(s(V7),V8)
| ~ le(s(V6),V7)
| ~ le(s(F),V6)
| ~ le(s(E),F)
| ~ le(s(D),E)
| ~ le(s(C),D)
| ~ eq(f(B),a0)
| ~ eq(f(A),a0) ),
inference(resolve,[status(thm)],[c_4,c_18]) ).
cnf(c_20,plain,
( ~ le(s(V11),A)
| ~ le(s(V10),V11)
| ~ le(s(V9),V10)
| ~ le(s(V8),V9)
| ~ le(s(V7),V8)
| ~ le(s(V6),V7)
| ~ le(s(F),V6)
| ~ le(s(E),F)
| ~ le(s(D),E)
| ~ le(s(C),D)
| ~ le(s(B),C)
| ~ eq(f(A),a0) ),
inference(resolve,[status(thm)],[c_4,c_19]) ).
cnf(c_6,plain,
( ~ le(s(V10),V11)
| ~ le(s(V9),V10)
| ~ le(s(V8),V9)
| ~ le(s(V7),V8)
| ~ le(s(V6),V7)
| ~ le(s(F),V6)
| ~ le(s(E),F)
| ~ le(s(D),E)
| ~ le(s(C),D)
| ~ le(s(B),C)
| ~ le(s(A),B) ),
inference(resolve,[status(thm)],[c_4,c_20]) ).
cnf(c_21,plain,
( ~ le(s(V9),V10)
| ~ le(s(V8),V9)
| ~ le(s(V7),V8)
| ~ le(s(V6),V7)
| ~ le(s(F),V6)
| ~ le(s(E),F)
| ~ le(s(D),E)
| ~ le(s(C),D)
| ~ le(s(B),C)
| ~ le(s(s(A)),B) ),
inference(resolve,[status(thm)],[c_6,c_1]) ).
cnf(c_22,plain,
( ~ le(s(V8),V9)
| ~ le(s(V7),V8)
| ~ le(s(V6),V7)
| ~ le(s(F),V6)
| ~ le(s(E),F)
| ~ le(s(D),E)
| ~ le(s(C),D)
| ~ le(s(B),C)
| ~ le(s(s(s(A))),B) ),
inference(resolve,[status(thm)],[c_21,c_1]) ).
cnf(c_23,plain,
( ~ le(s(V7),V8)
| ~ le(s(V6),V7)
| ~ le(s(F),V6)
| ~ le(s(E),F)
| ~ le(s(D),E)
| ~ le(s(C),D)
| ~ le(s(B),C)
| ~ le(s(s(s(s(A)))),B) ),
inference(resolve,[status(thm)],[c_22,c_1]) ).
cnf(c_24,plain,
( ~ le(s(V6),V7)
| ~ le(s(F),V6)
| ~ le(s(E),F)
| ~ le(s(D),E)
| ~ le(s(C),D)
| ~ le(s(B),C)
| ~ le(s(s(s(s(s(A))))),B) ),
inference(resolve,[status(thm)],[c_23,c_1]) ).
cnf(c_25,plain,
( ~ le(s(F),V6)
| ~ le(s(E),F)
| ~ le(s(D),E)
| ~ le(s(C),D)
| ~ le(s(B),C)
| ~ le(s(s(s(s(s(s(A)))))),B) ),
inference(resolve,[status(thm)],[c_24,c_1]) ).
cnf(c_26,plain,
( ~ le(s(E),F)
| ~ le(s(D),E)
| ~ le(s(C),D)
| ~ le(s(B),C)
| ~ le(s(s(s(s(s(s(s(A))))))),B) ),
inference(resolve,[status(thm)],[c_25,c_1]) ).
cnf(c_27,plain,
( ~ le(s(D),E)
| ~ le(s(C),D)
| ~ le(s(B),C)
| ~ le(s(s(s(s(s(s(s(s(A)))))))),B) ),
inference(resolve,[status(thm)],[c_26,c_1]) ).
cnf(c_28,plain,
( ~ le(s(C),D)
| ~ le(s(B),C)
| ~ le(s(s(s(s(s(s(s(s(s(A))))))))),B) ),
inference(resolve,[status(thm)],[c_27,c_1]) ).
cnf(c_29,plain,
( ~ le(s(B),C)
| ~ le(s(s(s(s(s(s(s(s(s(s(A)))))))))),B) ),
inference(resolve,[status(thm)],[c_28,c_1]) ).
cnf(c_30,plain,
~ le(s(s(s(s(s(s(s(s(s(s(s(A))))))))))),B),
inference(resolve,[status(thm)],[c_29,c_1]) ).
cnf(c_9,plain,
$false,
inference(resolve,[status(thm)],[c_30,c_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO613-1 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n001.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 19:44:13 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 2534659 was started by sandbox on n001,
% 0.10/0.37 % Sat Sep 26 19:44:13 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.10/0.39
% 0.10/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.39
% 0.10/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/0.39 % Length of proof is 5.
% 0.10/0.39 % Level of proof is 2.
% 0.10/0.39 % Maximum clause weight is 44.000.
% 0.10/0.39 % Given clauses 5.
% 0.10/0.39
% 0.10/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------