%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM023-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n019.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 4.54s 6.36s
% Output : Proof 4.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 25 unt; 0 def)
% Number of atoms : 33 ( 12 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 18 ( 14 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-4 aty)
% Number of variables : 32 ( 9 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f14,negated_conjecture,
~ less(n0,successor(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_zero_is_less_than_all_successors) ).
fof(f14_nnf,plain,
~ less(n0,successor(a)),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
~ less(n0,successor(a)),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
~ less(n0,successor(a)),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t22,plain,
ifeq(less(n0,successor(a)),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(f7,axiom,
( less(B,C)
| ~ equalish(add(successor(A),B),C) ),
file('/export/starexec/sandbox2/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(hi7,axiom,
ifeq(equalish(add(successor(X0),X1),X2),true,less(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(f0,axiom,
equalish(add(A,n0),A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',adding_zero) ).
fof(f0_nnf,plain,
! [A] : equalish(add(A,n0),A),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A] : equalish(add(A,n0),A),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
equalish(add(X0,n0),X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
equalish(add(X0,n0),X0) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t3,plain,
less(n0,successor(X1)) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi0]) ).
cnf(t72,plain,
less(n0,successor(X1)) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(t241,plain,
ifeq(true,true,false,true) = true,
inference(step,[status(thm)],[t22,t72]) ).
cnf(t9,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t43,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t9]) ).
cnf(t242,plain,
false = true,
inference(step,[status(thm)],[t241,t43]) ).
cnf(t239,plain,
false = true,
inference(orient,[status(thm)],[t242]) ).
cnf(f12,axiom,
~ equalish(successor(A),n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zero_is_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,c14]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t239]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM023-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/5.58 % Computer : n019.cluster.edu
% 0.11/5.58 % Model : x86_64 x86_64
% 0.11/5.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.58 % Memory : 8046.5625MB
% 0.11/5.58 % OS : Linux 6.8.0-71-generic
% 0.11/5.58 % CPULimit : 300
% 0.11/5.58 % WCLimit : 300
% 0.11/5.58 % DateTime : Thu Sep 24 02:40:43 UTC 2026
% 0.11/5.59 % CPUTime :
% 0.11/5.59 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.54/6.36 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.54/6.36 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------