%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYO038-1.003.003 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 09:50:02 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.38s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 6
% Syntax : Number of formulae : 53 ( 51 unt; 0 def)
% Number of atoms : 55 ( 6 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 40 ( 38 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 16 ( 4 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 10 ( 1 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax1,axiom,
! [VAR_0] : f(VAR_0,one) = s(one),
file('theBenchmark.p',ax1) ).
cnf(c_1,plain,
f(A,one) = s(one),
inference(clausify,[status(thm)],[ax1]) ).
fof(ax2,axiom,
! [VAR_0] : f(one,s(VAR_0)) = s(s(f(one,VAR_0))),
file('theBenchmark.p',ax2) ).
cnf(c_2,plain,
f(one,s(A)) = s(s(f(one,A))),
inference(clausify,[status(thm)],[ax2]) ).
fof(ax3,axiom,
! [VAR_0,VAR_1] : f(s(VAR_0),s(VAR_1)) = f(VAR_0,f(s(VAR_0),VAR_1)),
file('theBenchmark.p',ax3) ).
cnf(c_3,plain,
f(s(A),s(B)) = f(A,f(s(A),B)),
inference(clausify,[status(thm)],[ax3]) ).
fof(ax4,axiom,
d(one),
file('theBenchmark.p',ax4) ).
cnf(c_4,plain,
d(one),
inference(clausify,[status(thm)],[ax4]) ).
fof(ax5,axiom,
! [VAR_0] :
( d(s(VAR_0))
| ~ d(VAR_0) ),
file('theBenchmark.p',ax5) ).
cnf(c_5,plain,
( d(s(A))
| ~ d(A) ),
inference(clausify,[status(thm)],[ax5]) ).
fof(conj,axiom,
~ d(f(s(s(one)),s(s(one)))),
file('theBenchmark.p',conj) ).
cnf(c_6,plain,
~ d(f(s(s(one)),s(s(one)))),
inference(clausify,[status(thm)],[conj]) ).
cnf(c_24,plain,
~ d(f(s(one),f(s(s(one)),s(one)))),
inference(paramod,[status(thm)],[c_3,c_6]) ).
cnf(c_25,plain,
~ d(f(s(one),f(s(one),f(s(s(one)),one)))),
inference(paramod,[status(thm)],[c_3,c_24]) ).
cnf(c_26,plain,
~ d(f(s(one),f(s(one),s(one)))),
inference(paramod,[status(thm)],[c_1,c_25]) ).
cnf(c_27,plain,
~ d(f(s(one),f(one,f(s(one),one)))),
inference(paramod,[status(thm)],[c_3,c_26]) ).
cnf(c_28,plain,
~ d(f(s(one),f(one,s(one)))),
inference(paramod,[status(thm)],[c_1,c_27]) ).
cnf(c_29,plain,
~ d(f(s(one),s(s(f(one,one))))),
inference(paramod,[status(thm)],[c_2,c_28]) ).
cnf(c_30,plain,
~ d(f(s(one),s(s(s(one))))),
inference(paramod,[status(thm)],[c_1,c_29]) ).
cnf(c_31,plain,
~ d(f(one,f(s(one),s(s(one))))),
inference(paramod,[status(thm)],[c_3,c_30]) ).
cnf(c_32,plain,
~ d(f(one,f(one,f(s(one),s(one))))),
inference(paramod,[status(thm)],[c_3,c_31]) ).
cnf(c_33,plain,
~ d(f(one,f(one,f(one,f(s(one),one))))),
inference(paramod,[status(thm)],[c_3,c_32]) ).
cnf(c_34,plain,
~ d(f(one,f(one,f(one,s(one))))),
inference(paramod,[status(thm)],[c_1,c_33]) ).
cnf(c_35,plain,
~ d(f(one,f(one,s(s(f(one,one)))))),
inference(paramod,[status(thm)],[c_2,c_34]) ).
cnf(c_36,plain,
~ d(f(one,f(one,s(s(s(one)))))),
inference(paramod,[status(thm)],[c_1,c_35]) ).
cnf(c_37,plain,
~ d(f(one,s(s(f(one,s(s(one))))))),
inference(paramod,[status(thm)],[c_2,c_36]) ).
cnf(c_38,plain,
~ d(f(one,s(s(s(s(f(one,s(one)))))))),
inference(paramod,[status(thm)],[c_2,c_37]) ).
cnf(c_39,plain,
~ d(f(one,s(s(s(s(s(s(f(one,one))))))))),
inference(paramod,[status(thm)],[c_2,c_38]) ).
cnf(c_40,plain,
~ d(f(one,s(s(s(s(s(s(s(one))))))))),
inference(paramod,[status(thm)],[c_1,c_39]) ).
cnf(c_41,plain,
~ d(s(s(f(one,s(s(s(s(s(s(one)))))))))),
inference(paramod,[status(thm)],[c_2,c_40]) ).
cnf(c_42,plain,
~ d(s(s(s(s(f(one,s(s(s(s(s(one))))))))))),
inference(paramod,[status(thm)],[c_2,c_41]) ).
cnf(c_43,plain,
~ d(s(s(s(s(s(s(f(one,s(s(s(s(one)))))))))))),
inference(paramod,[status(thm)],[c_2,c_42]) ).
cnf(c_44,plain,
~ d(s(s(s(s(s(s(s(s(f(one,s(s(s(one))))))))))))),
inference(paramod,[status(thm)],[c_2,c_43]) ).
cnf(c_45,plain,
~ d(s(s(s(s(s(s(s(s(s(s(f(one,s(s(one)))))))))))))),
inference(paramod,[status(thm)],[c_2,c_44]) ).
cnf(c_46,plain,
~ d(s(s(s(s(s(s(s(s(s(s(s(s(f(one,s(one))))))))))))))),
inference(paramod,[status(thm)],[c_2,c_45]) ).
cnf(c_47,plain,
~ d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(f(one,one)))))))))))))))),
inference(paramod,[status(thm)],[c_2,c_46]) ).
cnf(c_7,plain,
~ d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one)))))))))))))))),
inference(paramod,[status(thm)],[c_1,c_47]) ).
cnf(c_8,plain,
d(s(one)),
inference(resolve,[status(thm)],[c_5,c_4]) ).
cnf(c_9,plain,
~ d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one))))))))))))))),
inference(resolve,[status(thm)],[c_5,c_7]) ).
cnf(c_10,plain,
d(s(s(one))),
inference(resolve,[status(thm)],[c_5,c_8]) ).
cnf(c_11,plain,
~ d(s(s(s(s(s(s(s(s(s(s(s(s(s(one)))))))))))))),
inference(resolve,[status(thm)],[c_5,c_9]) ).
cnf(c_12,plain,
~ d(s(s(s(s(s(s(s(s(s(s(s(s(one))))))))))))),
inference(resolve,[status(thm)],[c_5,c_11]) ).
cnf(c_13,plain,
~ d(s(s(s(s(s(s(s(s(s(s(s(one)))))))))))),
inference(resolve,[status(thm)],[c_5,c_12]) ).
cnf(c_14,plain,
~ d(s(s(s(s(s(s(s(s(s(s(one))))))))))),
inference(resolve,[status(thm)],[c_5,c_13]) ).
cnf(c_15,plain,
d(s(s(s(one)))),
inference(resolve,[status(thm)],[c_5,c_10]) ).
cnf(c_16,plain,
d(s(s(s(s(one))))),
inference(resolve,[status(thm)],[c_5,c_15]) ).
cnf(c_17,plain,
d(s(s(s(s(s(one)))))),
inference(resolve,[status(thm)],[c_5,c_16]) ).
cnf(c_18,plain,
d(s(s(s(s(s(s(one))))))),
inference(resolve,[status(thm)],[c_5,c_17]) ).
cnf(c_19,plain,
~ d(s(s(s(s(s(s(s(s(s(one)))))))))),
inference(resolve,[status(thm)],[c_5,c_14]) ).
cnf(c_20,plain,
~ d(s(s(s(s(s(s(s(s(one))))))))),
inference(resolve,[status(thm)],[c_5,c_19]) ).
cnf(c_21,plain,
~ d(s(s(s(s(s(s(s(one)))))))),
inference(resolve,[status(thm)],[c_5,c_20]) ).
cnf(c_22,plain,
~ d(s(s(s(s(s(s(one))))))),
inference(resolve,[status(thm)],[c_5,c_21]) ).
cnf(c_23,plain,
$false,
inference(resolve,[status(thm)],[c_22,c_18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO038-1.003.003 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n013.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
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 18:55:21 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 3400751 was started by sandbox2 on n013,
% 0.10/0.37 % Sat Sep 26 18:55:21 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.10/0.38
% 0.10/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.38
% 0.10/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/0.38 % Length of proof is 23.
% 0.10/0.38 % Level of proof is 11.
% 0.10/0.38 % Maximum clause weight is 17.000.
% 0.10/0.38 % Given clauses 19.
% 0.10/0.38
% 0.10/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------