%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD061-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% 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 07:11:40 AM UTC 2026
% Result : Unsatisfiable 29.89s 4.26s
% Output : CNFRefutation 29.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of formulae : 49 ( 27 unt; 0 def)
% Number of atoms : 84 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 77 ( 42 ~; 35 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 41 ( 0 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_addition,axiom,
! [VAR_0,VAR_1] :
( ~ defined(VAR_1)
| ~ defined(VAR_0)
| equalish(add(VAR_0,VAR_1),add(VAR_1,VAR_0)) ),
file('theBenchmark.p',commutativity_addition) ).
cnf(c_4,plain,
( ~ defined(B)
| ~ defined(A)
| equalish(add(A,B),add(B,A)) ),
inference(clausify,[status(thm)],[commutativity_addition]) ).
fof(transitivity_of_order_relation,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ less_or_equal(VAR_2,VAR_1)
| ~ less_or_equal(VAR_0,VAR_2)
| less_or_equal(VAR_0,VAR_1) ),
file('theBenchmark.p',transitivity_of_order_relation) ).
cnf(c_17,plain,
( ~ less_or_equal(C,B)
| ~ less_or_equal(A,C)
| less_or_equal(A,B) ),
inference(clausify,[status(thm)],[transitivity_of_order_relation]) ).
fof(totality_of_order_relation,axiom,
! [VAR_0,VAR_1] :
( ~ defined(VAR_1)
| ~ defined(VAR_0)
| less_or_equal(VAR_1,VAR_0)
| less_or_equal(VAR_0,VAR_1) ),
file('theBenchmark.p',totality_of_order_relation) ).
cnf(c_18,plain,
( ~ defined(B)
| ~ defined(A)
| less_or_equal(B,A)
| less_or_equal(A,B) ),
inference(clausify,[status(thm)],[totality_of_order_relation]) ).
fof(compatibility_of_order_relation_and_addition,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ less_or_equal(VAR_0,VAR_2)
| ~ defined(VAR_1)
| less_or_equal(add(VAR_0,VAR_1),add(VAR_2,VAR_1)) ),
file('theBenchmark.p',compatibility_of_order_relation_and_addition) ).
cnf(c_19,plain,
( ~ less_or_equal(A,C)
| ~ defined(B)
| less_or_equal(add(A,B),add(C,B)) ),
inference(clausify,[status(thm)],[compatibility_of_order_relation_and_addition]) ).
fof(symmetry_of_equality,axiom,
! [VAR_0,VAR_1] :
( ~ equalish(VAR_1,VAR_0)
| equalish(VAR_0,VAR_1) ),
file('theBenchmark.p',symmetry_of_equality) ).
cnf(c_22,plain,
( ~ equalish(B,A)
| equalish(A,B) ),
inference(clausify,[status(thm)],[symmetry_of_equality]) ).
fof(compatibility_of_equality_and_order_relation,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ equalish(VAR_2,VAR_0)
| ~ less_or_equal(VAR_2,VAR_1)
| less_or_equal(VAR_0,VAR_1) ),
file('theBenchmark.p',compatibility_of_equality_and_order_relation) ).
cnf(c_26,plain,
( ~ equalish(C,A)
| ~ less_or_equal(C,B)
| less_or_equal(A,B) ),
inference(clausify,[status(thm)],[compatibility_of_equality_and_order_relation]) ).
fof(b_is_defined,axiom,
defined(b),
file('theBenchmark.p',b_is_defined) ).
cnf(c_29,plain,
defined(b),
inference(clausify,[status(thm)],[b_is_defined]) ).
fof(c_is_defined,axiom,
defined(c),
file('theBenchmark.p',c_is_defined) ).
cnf(c_30,plain,
defined(c),
inference(clausify,[status(thm)],[c_is_defined]) ).
fof(v_is_defined,axiom,
defined(v),
file('theBenchmark.p',v_is_defined) ).
cnf(c_33,plain,
defined(v),
inference(clausify,[status(thm)],[v_is_defined]) ).
fof(add_equals_u_7,axiom,
equalish(add(a,c),u),
file('theBenchmark.p',add_equals_u_7) ).
cnf(c_34,plain,
equalish(add(a,c),u),
inference(clausify,[status(thm)],[add_equals_u_7]) ).
fof(add_equals_v_8,axiom,
equalish(add(d,b),v),
file('theBenchmark.p',add_equals_v_8) ).
cnf(c_35,plain,
equalish(add(d,b),v),
inference(clausify,[status(thm)],[add_equals_v_8]) ).
fof(less_or_equal_9,axiom,
less_or_equal(a,b),
file('theBenchmark.p',less_or_equal_9) ).
cnf(c_36,plain,
less_or_equal(a,b),
inference(clausify,[status(thm)],[less_or_equal_9]) ).
fof(less_or_equal_10,axiom,
less_or_equal(c,d),
file('theBenchmark.p',less_or_equal_10) ).
cnf(c_37,plain,
less_or_equal(c,d),
inference(clausify,[status(thm)],[less_or_equal_10]) ).
fof(not_less_or_equal_11,axiom,
~ less_or_equal(u,v),
file('theBenchmark.p',not_less_or_equal_11) ).
cnf(c_38,plain,
~ less_or_equal(u,v),
inference(clausify,[status(thm)],[not_less_or_equal_11]) ).
cnf(c_178,plain,
( ~ less_or_equal(A,B)
| less_or_equal(add(A,b),add(B,b)) ),
inference(resolve,[status(thm)],[c_29,c_19]) ).
cnf(c_196,plain,
( ~ defined(A)
| equalish(add(A,b),add(b,A)) ),
inference(resolve,[status(thm)],[c_29,c_4]) ).
cnf(c_216,plain,
( ~ less_or_equal(A,B)
| less_or_equal(add(A,c),add(B,c)) ),
inference(resolve,[status(thm)],[c_30,c_19]) ).
cnf(c_331,plain,
( ~ defined(A)
| less_or_equal(v,A)
| less_or_equal(A,v) ),
inference(resolve,[status(thm)],[c_33,c_18]) ).
cnf(c_24356,plain,
( ~ defined(v)
| less_or_equal(v,v) ),
inference(factor,[status(thm)],[c_331]) ).
cnf(c_355,plain,
less_or_equal(v,v),
inference(resolve,[status(thm)],[c_33,c_24356]) ).
cnf(c_376,plain,
equalish(v,add(d,b)),
inference(resolve,[status(thm)],[c_35,c_22]) ).
cnf(c_24357,plain,
( ~ equalish(A,u)
| ~ less_or_equal(A,v) ),
inference(resolve,[status(thm)],[c_26,c_38]) ).
cnf(c_389,plain,
~ less_or_equal(add(a,c),v),
inference(resolve,[status(thm)],[c_24357,c_34]) ).
cnf(c_579,plain,
( ~ equalish(v,A)
| less_or_equal(A,v) ),
inference(resolve,[status(thm)],[c_355,c_26]) ).
cnf(c_14119,plain,
less_or_equal(add(d,b),v),
inference(resolve,[status(thm)],[c_376,c_579]) ).
cnf(c_21087,plain,
less_or_equal(add(c,b),add(d,b)),
inference(resolve,[status(thm)],[c_178,c_37]) ).
cnf(c_21364,plain,
equalish(add(c,b),add(b,c)),
inference(resolve,[status(thm)],[c_196,c_30]) ).
cnf(c_22078,plain,
less_or_equal(add(a,c),add(b,c)),
inference(resolve,[status(thm)],[c_216,c_36]) ).
cnf(c_24358,plain,
( ~ less_or_equal(A,v)
| ~ less_or_equal(add(a,c),A) ),
inference(resolve,[status(thm)],[c_17,c_389]) ).
cnf(c_24340,plain,
~ less_or_equal(add(b,c),v),
inference(resolve,[status(thm)],[c_24358,c_22078]) ).
cnf(c_24359,plain,
( ~ equalish(A,add(b,c))
| ~ less_or_equal(A,v) ),
inference(resolve,[status(thm)],[c_26,c_24340]) ).
cnf(c_24343,plain,
~ less_or_equal(add(c,b),v),
inference(resolve,[status(thm)],[c_24359,c_21364]) ).
cnf(c_24360,plain,
( ~ less_or_equal(A,v)
| ~ less_or_equal(add(c,b),A) ),
inference(resolve,[status(thm)],[c_17,c_24343]) ).
cnf(c_24361,plain,
~ less_or_equal(add(c,b),add(d,b)),
inference(resolve,[status(thm)],[c_24360,c_14119]) ).
cnf(c_24355,plain,
$false,
inference(resolve,[status(thm)],[c_21087,c_24361]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD061-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.38 % Computer : n010.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 02:33:16 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 548747 was started by sandbox2 on n010,
% 0.10/0.38 % Sun Sep 27 02:33:16 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.39
% 0.10/0.39 % From the command line: assign(max_seconds, 300).
% 29.89/4.26
% 29.89/4.26 % given #500 (A,wt=20): 126 less_or_equal(add(A,multiplicative_identity),add(B,multiplicative_identity)) | -less_or_equal(A,B). [resolve(19,b,14,a)].
% 29.89/4.26
% 29.89/4.26 % given #1000 (F,wt=17): 21402 -equalish(add(u,additive_identity),multiply(v,multiplicative_identity)). [ur(23,a,21295,a,c,5403,a)].
% 29.89/4.26
% 29.89/4.26 % given #1500 (T,wt=17): 11385 less_or_equal(a,d) | less_or_equal(c,u) | less_or_equal(u,A) | -less_or_equal(a,A). [resolve(5035,b,17,b)].
% 29.89/4.26
% 29.89/4.26 % SZS status Unsatisfiable for theBenchmark
% 29.89/4.26
% 29.89/4.26 % Proof 1 at 2.60 (+ 1.22) seconds.
% 29.89/4.26 % Length of proof is 29.
% 29.89/4.26 % Level of proof is 5.
% 29.89/4.26 % Maximum clause weight is 22.000.
% 29.89/4.26 % Given clauses 1881.
% 29.89/4.26
% 29.89/4.26 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------