%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM021-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n016.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 : Fri Sep 25 02:18:32 PM UTC 2026
% Result : Unsatisfiable 27.93s 4.61s
% Output : Proof 27.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 46 ( 18 unt; 0 def)
% Number of atoms : 87 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 79 ( 38 ~; 41 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 62 ( 2 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f8,axiom,
( equalish(add(successor(predecessor_of_1st_minus_2nd(B,A)),A),B)
| ~ less(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_lemma) ).
fof(f8_nnf,plain,
! [A,B] :
( equalish(add(successor(predecessor_of_1st_minus_2nd(B,A)),A),B)
| ~ less(A,B) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A,B] :
( equalish(add(successor(predecessor_of_1st_minus_2nd(B,A)),A),B)
| ~ less(A,B) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( equalish(add(successor(predecessor_of_1st_minus_2nd(X1,X0)),X0),X1)
| ~ less(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(f15,hypothesis,
less(b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_less_than_c) ).
fof(f15_nnf,plain,
less(b,c),
inference(nnf_transformation,[status(thm)],[f15]) ).
cnf(c15,plain,
less(b,c),
inference(cnf_transformation,[status(esa)],[f15_nnf]) ).
cnf(p54,plain,
equalish(add(successor(predecessor_of_1st_minus_2nd(c,b)),b),c),
inference(resolution,[status(thm)],[c8,c15]) ).
cnf(f13,axiom,
( equalish(Y,X)
| ~ equalish(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry) ).
fof(f13_nnf,plain,
! [X,Y] :
( equalish(Y,X)
| ~ equalish(X,Y) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X,Y] :
( equalish(Y,X)
| ~ equalish(X,Y) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( equalish(X1,X0)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(p203,plain,
equalish(c,add(successor(predecessor_of_1st_minus_2nd(c,b)),b)),
inference(resolution,[status(thm)],[p54,c13]) ).
cnf(f9,axiom,
( equalish(A,B)
| less(A,B)
| ~ divides(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divides_only_less_or_equal) ).
fof(f9_nnf,plain,
! [A,B] :
( equalish(A,B)
| less(A,B)
| ~ divides(A,B) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [A,B] :
( equalish(A,B)
| less(A,B)
| ~ divides(A,B) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( equalish(X0,X1)
| less(X0,X1)
| ~ divides(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(f17,negated_conjecture,
divides(c,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',impossible_c_divides_a) ).
fof(f17_nnf,plain,
divides(c,a),
inference(nnf_transformation,[status(thm)],[f17]) ).
cnf(c17,plain,
divides(c,a),
inference(cnf_transformation,[status(esa)],[f17_nnf]) ).
cnf(p60,plain,
( equalish(c,a)
| less(c,a) ),
inference(resolution,[status(thm)],[c9,c17]) ).
cnf(f6,axiom,
( less(C,B)
| ~ less(C,A)
| ~ less(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_less) ).
fof(f6_nnf,plain,
! [A,B,C] :
( less(C,B)
| ~ less(C,A)
| ~ less(A,B) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A,B,C] :
( less(C,B)
| ~ less(C,A)
| ~ less(A,B) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( less(X2,X1)
| ~ less(X2,X0)
| ~ less(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p61,plain,
( less(X0,a)
| ~ less(X0,c)
| equalish(c,a) ),
inference(resolution,[status(thm)],[p60,c6]) ).
cnf(p63,plain,
( less(b,a)
| equalish(c,a) ),
inference(resolution,[status(thm)],[p61,c15]) ).
cnf(f16,hypothesis,
~ less(b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_greater_equal_a) ).
fof(f16_nnf,plain,
~ less(b,a),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
~ less(b,a),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
~ less(b,a),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(p64,plain,
equalish(c,a),
inference(resolution,[status(thm)],[p63,c16]) ).
cnf(p65,plain,
equalish(a,c),
inference(resolution,[status(thm)],[p64,c13]) ).
cnf(f14,axiom,
( equalish(X,Z)
| ~ equalish(Y,Z)
| ~ equalish(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).
fof(f14_nnf,plain,
! [X,Y,Z] :
( equalish(X,Z)
| ~ equalish(Y,Z)
| ~ equalish(X,Y) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [X,Y,Z] :
( equalish(X,Z)
| ~ equalish(Y,Z)
| ~ equalish(X,Y) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( equalish(X0,X2)
| ~ equalish(X1,X2)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(p80,plain,
( equalish(a,X0)
| ~ equalish(c,X0) ),
inference(resolution,[status(thm)],[p65,c14]) ).
cnf(p1084,plain,
equalish(a,add(successor(predecessor_of_1st_minus_2nd(c,b)),b)),
inference(resolution,[status(thm)],[p203,p80]) ).
cnf(p1090,plain,
equalish(add(successor(predecessor_of_1st_minus_2nd(c,b)),b),a),
inference(resolution,[status(thm)],[p1084,c13]) ).
cnf(f7,axiom,
( less(B,C)
| ~ equalish(add(successor(A),B),C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',smaller_number) ).
fof(f7_nnf,plain,
! [A,B,C] :
( less(B,C)
| ~ equalish(add(successor(A),B),C) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A,B,C] :
( less(B,C)
| ~ equalish(add(successor(A),B),C) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( less(X1,X2)
| ~ equalish(add(successor(X0),X1),X2) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p1095,plain,
less(b,a),
inference(resolution,[status(thm)],[p1090,c7]) ).
cnf(p1098,plain,
$false,
inference(resolution,[status(thm)],[p1095,c16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM021-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/0.37 % Computer : n016.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Thu Sep 24 02:45:41 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 27.93/4.61 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 27.93/4.61 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------