%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG011-1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 06:49:06 AM UTC 2026
% Result : Unsatisfiable 0.14s 10.44s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 34 ( 20 unt; 0 def)
% Number of atoms : 53 ( 3 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 41 ( 22 ~; 19 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f_is_associative,axiom,
! [VAR_0,VAR_1,VAR_2] : f(VAR_0,f(VAR_1,VAR_2)) = f(f(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',f_is_associative) ).
cnf(c_1,plain,
f(A,f(B,C)) = f(f(A,B),C),
inference(clausify,[status(thm)],[f_is_associative]) ).
cnf(c_2,plain,
f(f(A,B),C) = f(A,f(B,C)),
inference(copy,[status(thm)],[c_1]) ).
fof(partitions_union,axiom,
! [VAR_0] :
( d(VAR_0)
| c(VAR_0) ),
file('theBenchmark.p',partitions_union) ).
cnf(c_3,plain,
( d(A)
| c(A) ),
inference(clausify,[status(thm)],[partitions_union]) ).
fof(partitions_exclusive,axiom,
! [VAR_0] :
( ~ d(VAR_0)
| ~ c(VAR_0) ),
file('theBenchmark.p',partitions_exclusive) ).
cnf(c_4,plain,
( ~ d(A)
| ~ c(A) ),
inference(clausify,[status(thm)],[partitions_exclusive]) ).
fof(partition_c_not_empty,axiom,
c(a1),
file('theBenchmark.p',partition_c_not_empty) ).
cnf(c_5,plain,
c(a1),
inference(clausify,[status(thm)],[partition_c_not_empty]) ).
fof(partition_d_not_empty,axiom,
d(a2),
file('theBenchmark.p',partition_d_not_empty) ).
cnf(c_6,plain,
d(a2),
inference(clausify,[status(thm)],[partition_d_not_empty]) ).
fof(conjecture_1,axiom,
! [VAR_0,VAR_1] :
( ~ c(VAR_1)
| ~ c(VAR_0)
| d(f(VAR_0,VAR_1)) ),
file('theBenchmark.p',conjecture_1) ).
cnf(c_7,plain,
( ~ c(B)
| ~ c(A)
| d(f(A,B)) ),
inference(clausify,[status(thm)],[conjecture_1]) ).
fof(conjecture_2,axiom,
! [VAR_0,VAR_1] :
( ~ d(VAR_1)
| ~ d(VAR_0)
| c(f(VAR_0,VAR_1)) ),
file('theBenchmark.p',conjecture_2) ).
cnf(c_8,plain,
( ~ d(B)
| ~ d(A)
| c(f(A,B)) ),
inference(clausify,[status(thm)],[conjecture_2]) ).
cnf(c_9,plain,
( ~ c(A)
| d(f(A,A)) ),
inference(factor,[status(thm)],[c_7]) ).
cnf(c_10,plain,
( ~ d(A)
| c(f(A,A)) ),
inference(factor,[status(thm)],[c_8]) ).
cnf(c_12,plain,
~ c(a2),
inference(resolve,[status(thm)],[c_6,c_4]) ).
cnf(c_14,plain,
( ~ c(A)
| d(f(A,a1)) ),
inference(resolve,[status(thm)],[c_7,c_5]) ).
cnf(c_15,plain,
( ~ d(A)
| c(f(a2,A)) ),
inference(resolve,[status(thm)],[c_8,c_6]) ).
cnf(c_16,plain,
( c(A)
| ~ d(B)
| c(f(A,B)) ),
inference(resolve,[status(thm)],[c_8,c_3]) ).
cnf(c_19,plain,
d(f(a1,a1)),
inference(resolve,[status(thm)],[c_9,c_5]) ).
cnf(c_20,plain,
c(f(a2,a2)),
inference(resolve,[status(thm)],[c_10,c_6]) ).
cnf(c_71,plain,
d(f(f(a2,a2),a1)),
inference(resolve,[status(thm)],[c_14,c_20]) ).
cnf(c_31,plain,
d(f(a2,f(a2,a1))),
inference(paramod,[status(thm)],[c_2,c_71]) ).
cnf(c_32,plain,
c(f(a2,f(a1,a1))),
inference(resolve,[status(thm)],[c_15,c_19]) ).
cnf(c_53,plain,
~ c(f(a2,f(a2,a1))),
inference(resolve,[status(thm)],[c_31,c_4]) ).
cnf(c_72,plain,
( c(a2)
| ~ d(f(a2,a1)) ),
inference(resolve,[status(thm)],[c_16,c_53]) ).
cnf(c_58,plain,
~ d(f(a2,a1)),
inference(resolve,[status(thm)],[c_72,c_12]) ).
cnf(c_59,plain,
c(f(a2,a1)),
inference(resolve,[status(thm)],[c_58,c_3]) ).
cnf(c_73,plain,
d(f(f(a2,a1),a1)),
inference(resolve,[status(thm)],[c_59,c_14]) ).
cnf(c_60,plain,
d(f(a2,f(a1,a1))),
inference(paramod,[status(thm)],[c_2,c_73]) ).
cnf(c_74,plain,
~ d(f(a2,f(a1,a1))),
inference(resolve,[status(thm)],[c_4,c_32]) ).
cnf(c_70,plain,
$false,
inference(resolve,[status(thm)],[c_60,c_74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ALG011-1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/10.42 % Computer : n006.cluster.edu
% 0.14/10.42 % Model : x86_64 x86_64
% 0.14/10.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/10.42 % Memory : 8046.5625MB
% 0.14/10.42 % OS : Linux 6.8.0-71-generic
% 0.14/10.42 % CPULimit : 300
% 0.14/10.42 % WCLimit : 300
% 0.14/10.42 % DateTime : Sat Sep 26 20:58:07 UTC 2026
% 0.14/10.42 % CPUTime :
% 0.14/10.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/10.42 % Process 2109674 was started by sandbox2 on n006,
% 0.14/10.42 % Sat Sep 26 20:58:07 2026
% 0.14/10.42 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/10.43
% 0.14/10.43 % From the command line: assign(max_seconds, 300).
% 0.14/10.44
% 0.14/10.44 % SZS status Unsatisfiable for theBenchmark
% 0.14/10.44
% 0.14/10.44 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.14/10.44 % Length of proof is 23.
% 0.14/10.44 % Level of proof is 8.
% 0.14/10.44 % Maximum clause weight is 11.000.
% 0.14/10.44 % Given clauses 28.
% 0.14/10.44
% 0.14/10.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------