%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM022-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n001.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 02:18:33 PM UTC 2026
% Result : Unsatisfiable 4.60s 6.10s
% Output : Proof 4.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 39 ( 13 unt; 0 def)
% Number of atoms : 79 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 75 ( 35 ~; 40 |; 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 : 54 ( 2 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f6,axiom,
( equalish(C,B)
| ~ equalish(C,A)
| ~ equalish(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).
fof(f6_nnf,plain,
! [A,B,C] :
( equalish(C,B)
| ~ equalish(C,A)
| ~ equalish(A,B) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A,B,C] :
( equalish(C,B)
| ~ equalish(C,A)
| ~ equalish(A,B) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( equalish(X2,X1)
| ~ equalish(X2,X0)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(f3,axiom,
( equalish(A,B)
| less(A,B)
| ~ divides(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divides_only_less_or_equal) ).
fof(f3_nnf,plain,
! [A,B] :
( equalish(A,B)
| less(A,B)
| ~ divides(A,B) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B] :
( equalish(A,B)
| less(A,B)
| ~ divides(A,B) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( equalish(X0,X1)
| less(X0,X1)
| ~ divides(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(f8,hypothesis,
divides(b,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_divides_d) ).
fof(f8_nnf,plain,
divides(b,d),
inference(nnf_transformation,[status(thm)],[f8]) ).
cnf(c8,plain,
divides(b,d),
inference(cnf_transformation,[status(esa)],[f8_nnf]) ).
cnf(p14,plain,
( equalish(b,d)
| less(b,d) ),
inference(resolution,[status(thm)],[c3,c8]) ).
cnf(p16,plain,
( less(b,d)
| equalish(X0,d)
| ~ equalish(X0,b) ),
inference(resolution,[status(thm)],[c6,p14]) ).
cnf(f2,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(f2_nnf,plain,
! [A,B] :
( equalish(add(successor(predecessor_of_1st_minus_2nd(B,A)),A),B)
| ~ less(A,B) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B] :
( equalish(add(successor(predecessor_of_1st_minus_2nd(B,A)),A),B)
| ~ less(A,B) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( equalish(add(successor(predecessor_of_1st_minus_2nd(X1,X0)),X0),X1)
| ~ less(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(f7,hypothesis,
less(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_less_than_b) ).
fof(f7_nnf,plain,
less(a,b),
inference(nnf_transformation,[status(thm)],[f7]) ).
cnf(c7,plain,
less(a,b),
inference(cnf_transformation,[status(esa)],[f7_nnf]) ).
cnf(p12,plain,
equalish(add(successor(predecessor_of_1st_minus_2nd(b,a)),a),b),
inference(resolution,[status(thm)],[c2,c7]) ).
cnf(p17,plain,
( less(b,d)
| equalish(add(successor(predecessor_of_1st_minus_2nd(b,a)),a),d) ),
inference(resolution,[status(thm)],[p16,p12]) ).
cnf(f1,axiom,
( less(B,C)
| ~ equalish(add(successor(A),B),C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',smaller_number) ).
fof(f1_nnf,plain,
! [A,B,C] :
( less(B,C)
| ~ equalish(add(successor(A),B),C) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B,C] :
( less(B,C)
| ~ equalish(add(successor(A),B),C) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( less(X1,X2)
| ~ equalish(add(successor(X0),X1),X2) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p19,plain,
( less(a,d)
| less(b,d) ),
inference(resolution,[status(thm)],[p17,c1]) ).
cnf(f0,axiom,
( less(C,B)
| ~ less(C,A)
| ~ less(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_less) ).
fof(f0_nnf,plain,
! [A,B,C] :
( less(C,B)
| ~ less(C,A)
| ~ less(A,B) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B,C] :
( less(C,B)
| ~ less(C,A)
| ~ less(A,B) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( less(X2,X1)
| ~ less(X2,X0)
| ~ less(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p21,plain,
( less(X0,d)
| ~ less(X0,b)
| less(a,d) ),
inference(resolution,[status(thm)],[p19,c0]) ).
cnf(p23,plain,
( ~ less(a,b)
| less(a,d) ),
inference(factoring,[status(thm)],[p21]) ).
cnf(p25,plain,
less(a,d),
inference(resolution,[status(thm)],[p23,c7]) ).
cnf(f9,negated_conjecture,
~ less(a,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_less_than_d) ).
fof(f9_nnf,plain,
~ less(a,d),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
~ less(a,d),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
~ less(a,d),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p26,plain,
$false,
inference(resolution,[status(thm)],[p25,c9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM022-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/5.38 % Computer : n001.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Thu Sep 24 02:46:27 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.60/6.10 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.60/6.10 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------