%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWV005-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n005.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 03:10:59 PM UTC 2026
% Result : Unsatisfiable 10.38s 2.04s
% Output : Proof 10.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 59 ( 47 unt; 0 def)
% Number of atoms : 83 ( 24 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 70 ( 46 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-4 aty)
% Number of variables : 32 ( 2 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f19,negated_conjecture,
( ~ less_than(a(X),a(predecessor(l)))
| ~ less_than(one,l)
| less_than(n,X)
| less_than(X,l) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_8) ).
fof(f19_nnf,plain,
! [X] :
( ~ less_than(a(X),a(predecessor(l)))
| ~ less_than(one,l)
| less_than(n,X)
| less_than(X,l) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [X] :
( ~ less_than(a(X),a(predecessor(l)))
| ~ less_than(one,l)
| less_than(n,X)
| less_than(X,l) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
( ~ less_than(a(X0),a(predecessor(l)))
| ~ less_than(one,l)
| less_than(n,X0)
| less_than(X0,l) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(t36,plain,
ifeq(less_than(one,l),true,ifeq(less_than(a(X1),a(predecessor(l))),true,or(less_than(X1,l),less_than(n,X1)),true),true) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(f16,negated_conjecture,
less_than(one,l),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_5) ).
fof(f16_nnf,plain,
less_than(one,l),
inference(nnf_transformation,[status(thm)],[f16]) ).
cnf(c16,plain,
less_than(one,l),
inference(cnf_transformation,[status(esa)],[f16_nnf]) ).
cnf(t8,plain,
less_than(one,l) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t54,plain,
less_than(one,l) = true,
inference(orient,[status(thm)],[t8]) ).
cnf(t232,plain,
ifeq(true,true,ifeq(less_than(a(X1),a(predecessor(l))),true,or(less_than(X1,l),less_than(n,X1)),true),true) = true,
inference(step,[status(thm)],[t36,t54]) ).
cnf(t17,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t37,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t17]) ).
cnf(t233,plain,
ifeq(less_than(a(X1),a(predecessor(l))),true,or(less_than(X1,l),less_than(n,X1)),true) = true,
inference(step,[status(thm)],[t232,t37]) ).
cnf(t125,plain,
ifeq(less_than(a(X1),a(predecessor(l))),true,or(less_than(X1,l),less_than(n,X1)),true) = true,
inference(orient,[status(thm)],[t233]) ).
cnf(f12,negated_conjecture,
~ less_than(n,k),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1) ).
fof(f12_nnf,plain,
~ less_than(n,k),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
~ less_than(n,k),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
~ less_than(n,k),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(t7,plain,
less_than(n,k) = false,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t199,plain,
less_than(n,k) = false,
inference(orient,[status(thm)],[t7]) ).
cnf(t211,plain,
true = ifeq(less_than(a(k),a(predecessor(l))),true,or(less_than(k,l),false),true),
inference(cp,[status(thm)],[t125,t199]) ).
cnf(f17,negated_conjecture,
less_than(a(k),a(predecessor(l))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6) ).
fof(f17_nnf,plain,
less_than(a(k),a(predecessor(l))),
inference(nnf_transformation,[status(thm)],[f17]) ).
cnf(c17,plain,
less_than(a(k),a(predecessor(l))),
inference(cnf_transformation,[status(esa)],[f17_nnf]) ).
cnf(t19,plain,
less_than(a(k),a(predecessor(l))) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t52,plain,
less_than(a(k),a(predecessor(l))) = true,
inference(orient,[status(thm)],[t19]) ).
cnf(t238,plain,
true = ifeq(true,true,or(less_than(k,l),false),true),
inference(step,[status(thm)],[t211,t52]) ).
cnf(t239,plain,
true = or(less_than(k,l),false),
inference(step,[status(thm)],[t238,t37]) ).
cnf(t9,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t41,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t9]) ).
cnf(t240,plain,
true = less_than(k,l),
inference(step,[status(thm)],[t239,t41]) ).
cnf(f13,negated_conjecture,
~ less_than(k,l),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2) ).
fof(f13_nnf,plain,
~ less_than(k,l),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
~ less_than(k,l),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
~ less_than(k,l),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t5,plain,
less_than(k,l) = false,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t170,plain,
less_than(k,l) = false,
inference(orient,[status(thm)],[t5]) ).
cnf(t241,plain,
true = false,
inference(step,[status(thm)],[t240,t170]) ).
cnf(t216,plain,
false = true,
inference(orient,[status(thm)],[t241]) ).
cnf(f8,axiom,
~ less_than(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_not_less_than_x) ).
fof(f8_nnf,plain,
! [X] : ~ less_than(X,X),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X] : ~ less_than(X,X),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
~ less_than(X0,X0),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(f9,axiom,
( ~ less_than(Y,X)
| ~ less_than(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',anti_symmetry_of_less_than) ).
fof(f9_nnf,plain,
! [X,Y] :
( ~ less_than(Y,X)
| ~ less_than(X,Y) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X,Y] :
( ~ less_than(Y,X)
| ~ less_than(X,Y) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( ~ less_than(X1,X0)
| ~ less_than(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(f14,negated_conjecture,
~ less_than(k,i),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3) ).
fof(f14_nnf,plain,
~ less_than(k,i),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
~ less_than(k,i),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
~ less_than(k,i),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(f20,negated_conjecture,
( ~ less_than(a(X),a(predecessor(X)))
| ~ less_than(X,l)
| ~ less_than(one,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_9) ).
fof(f20_nnf,plain,
! [X] :
( ~ less_than(a(X),a(predecessor(X)))
| ~ less_than(X,l)
| ~ less_than(one,X) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [X] :
( ~ less_than(a(X),a(predecessor(X)))
| ~ less_than(X,l)
| ~ less_than(one,X) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
( ~ less_than(a(X0),a(predecessor(X0)))
| ~ less_than(X0,l)
| ~ less_than(one,X0) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c8,c9,c12,c13,c14,c20]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t216]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV005-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.34 % Computer : n005.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 18:17:18 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 10.38/2.04 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.38/2.04 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------