%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYO691-1.000 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 09:51:14 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 24 ( 12 unt; 0 def)
% Number of atoms : 38 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 33 ( 19 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 64 ( 0 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rewrite_top,axiom,
! [VAR_0,VAR_1] :
( step(VAR_0,VAR_1)
| ~ top(VAR_0,VAR_1) ),
file('theBenchmark.p',rewrite_top) ).
cnf(c_1,plain,
( step(A,B)
| ~ top(A,B) ),
inference(clausify,[status(thm)],[rewrite_top]) ).
fof(rule_1,axiom,
! [VAR_0,VAR_1,VAR_2] : top(f(f(VAR_0,VAR_1),f(VAR_2,a)),f(f(VAR_2,f(VAR_1,a)),VAR_0)),
file('theBenchmark.p',rule_1) ).
cnf(c_2,plain,
top(f(f(A,B),f(C,a)),f(f(C,f(B,a)),A)),
inference(clausify,[status(thm)],[rule_1]) ).
cnf(c_3,plain,
step(f(f(A,B),f(C,a)),f(f(C,f(B,a)),A)),
inference(resolve,[status(thm)],[c_1,c_2]) ).
fof(rewrite_sequence_succ,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( seq(succ(VAR_0),VAR_1,VAR_3)
| ~ step(VAR_2,VAR_3)
| ~ seq(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',rewrite_sequence_succ) ).
cnf(c_4,plain,
( seq(succ(A),B,D)
| ~ step(C,D)
| ~ seq(A,B,C) ),
inference(clausify,[status(thm)],[rewrite_sequence_succ]) ).
fof(rewrite_sequence_zero,axiom,
! [VAR_0] : seq(zero,VAR_0,VAR_0),
file('theBenchmark.p',rewrite_sequence_zero) ).
cnf(c_5,plain,
seq(zero,A,A),
inference(clausify,[status(thm)],[rewrite_sequence_zero]) ).
fof(rewrite_right,axiom,
! [VAR_0,VAR_1,VAR_2] :
( step(f(VAR_2,VAR_0),f(VAR_2,VAR_1))
| ~ step(VAR_0,VAR_1) ),
file('theBenchmark.p',rewrite_right) ).
cnf(c_6,plain,
( step(f(C,A),f(C,B))
| ~ step(A,B) ),
inference(clausify,[status(thm)],[rewrite_right]) ).
fof(rewrite_left,axiom,
! [VAR_0,VAR_1,VAR_2] :
( step(f(VAR_0,VAR_2),f(VAR_1,VAR_2))
| ~ step(VAR_0,VAR_1) ),
file('theBenchmark.p',rewrite_left) ).
cnf(c_7,plain,
( step(f(A,C),f(B,C))
| ~ step(A,B) ),
inference(clausify,[status(thm)],[rewrite_left]) ).
fof(prove,axiom,
! [VAR_0] : ~ seq(succ(succ(succ(zero))),VAR_0,VAR_0),
file('theBenchmark.p',prove) ).
cnf(c_8,plain,
~ seq(succ(succ(succ(zero))),A,A),
inference(clausify,[status(thm)],[prove]) ).
cnf(c_42,plain,
( seq(succ(zero),A,B)
| ~ step(A,B) ),
inference(resolve,[status(thm)],[c_4,c_5]) ).
cnf(c_9,plain,
seq(succ(zero),f(f(A,B),f(C,a)),f(f(C,f(B,a)),A)),
inference(resolve,[status(thm)],[c_42,c_3]) ).
cnf(c_10,plain,
step(f(A,f(f(B,C),f(D,a))),f(A,f(f(D,f(C,a)),B))),
inference(resolve,[status(thm)],[c_6,c_3]) ).
cnf(c_12,plain,
( ~ step(B,A)
| ~ seq(succ(succ(zero)),A,B) ),
inference(resolve,[status(thm)],[c_8,c_4]) ).
cnf(c_16,plain,
( ~ step(C,A)
| ~ seq(succ(succ(zero)),f(A,B),f(C,B)) ),
inference(resolve,[status(thm)],[c_12,c_7]) ).
cnf(c_30,plain,
~ seq(succ(succ(zero)),f(f(f(A,f(B,a)),C),D),f(f(f(C,B),f(A,a)),D)),
inference(resolve,[status(thm)],[c_16,c_3]) ).
cnf(c_43,plain,
( seq(succ(succ(zero)),f(f(C,B),f(A,a)),D)
| ~ step(f(f(A,f(B,a)),C),D) ),
inference(resolve,[status(thm)],[c_4,c_9]) ).
cnf(c_40,plain,
seq(succ(succ(zero)),f(f(f(f(A,B),f(C,a)),D),f(E,a)),f(f(E,f(D,a)),f(f(C,f(B,a)),A))),
inference(resolve,[status(thm)],[c_43,c_10]) ).
cnf(c_41,plain,
$false,
inference(resolve,[status(thm)],[c_40,c_30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO691-1.000 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n010.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 19:46:46 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.13/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.36 % Process 4080635 was started by sandbox2 on n010,
% 0.13/0.36 % Sat Sep 26 19:46:46 2026
% 0.13/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 0.13/0.38
% 0.13/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.38
% 0.13/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.13/0.38 % Length of proof is 15.
% 0.13/0.38 % Level of proof is 4.
% 0.13/0.38 % Maximum clause weight is 30.000.
% 0.13/0.38 % Given clauses 12.
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------