%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM025-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n004.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 3.90s 0.93s
% Output : Proof 3.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 24 unt; 0 def)
% Number of atoms : 36 ( 9 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 26 ( 18 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-4 aty)
% Number of variables : 24 ( 2 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f6,axiom,
( less(C,B)
| ~ less(C,A)
| ~ less(A,B) ),
file('/export/starexec/sandbox2/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(hi6,axiom,
ifeq(less(X0,X1),true,ifeq(less(X2,X0),true,less(X2,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(f14,hypothesis,
less(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_less_than_b) ).
fof(f14_nnf,plain,
less(a,b),
inference(nnf_transformation,[status(thm)],[f14]) ).
cnf(c14,plain,
less(a,b),
inference(cnf_transformation,[status(esa)],[f14_nnf]) ).
cnf(hi12,axiom,
less(a,b) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(f15,negated_conjecture,
less(b,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_b_not_less_than_a) ).
fof(f15_nnf,plain,
less(b,a),
inference(nnf_transformation,[status(thm)],[f15]) ).
cnf(c15,plain,
less(b,a),
inference(cnf_transformation,[status(esa)],[f15_nnf]) ).
cnf(hi13,negated_conjecture,
less(b,a) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(h3,plain,
less(b,b) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi12,hi13]) ).
cnf(f13,axiom,
~ less(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',no_number_less_than_itself) ).
fof(f13_nnf,plain,
! [A] : ~ less(A,A),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [A] : ~ less(A,A),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
~ less(X0,X0),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(hi15,axiom,
ifeq(less(X0,X0),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi15,h3]) ).
cnf(t122,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
cnf(f12,axiom,
~ equalish(successor(A),n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zero_is_the_first_number) ).
fof(f12_nnf,plain,
! [A] : ~ equalish(successor(A),n0),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [A] : ~ equalish(successor(A),n0),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
~ equalish(successor(X0),n0),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c12,c13]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t122]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM025-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n004.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 02:42:20 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.90/0.93 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.90/0.93 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------