%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWV003-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n007.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 7.54s 1.55s
% Output : Proof 7.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 40 ( 28 unt; 0 def)
% Number of atoms : 60 ( 9 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 62 ( 42 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-4 aty)
% Number of variables : 31 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f6,axiom,
( ~ less_than(Y,Z)
| ~ less_than(X,Y)
| less_than(X,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_less_than) ).
fof(f6_nnf,plain,
! [X,Z,Y] :
( ~ less_than(Y,Z)
| ~ less_than(X,Y)
| less_than(X,Z) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X,Z,Y] :
( ~ less_than(Y,Z)
| ~ less_than(X,Y)
| less_than(X,Z) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( ~ less_than(X2,X1)
| ~ less_than(X0,X2)
| less_than(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi6,axiom,
ifeq(less_than(X0,X1),true,ifeq(less_than(X1,X2),true,less_than(X0,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(f13,negated_conjecture,
less_than(k,j),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2) ).
fof(f13_nnf,plain,
less_than(k,j),
inference(nnf_transformation,[status(thm)],[f13]) ).
cnf(c13,plain,
less_than(k,j),
inference(cnf_transformation,[status(esa)],[f13_nnf]) ).
cnf(hi10,negated_conjecture,
less_than(k,j) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(f20,negated_conjecture,
less_than(j,i),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_9) ).
fof(f20_nnf,plain,
less_than(j,i),
inference(nnf_transformation,[status(thm)],[f20]) ).
cnf(c20,plain,
less_than(j,i),
inference(cnf_transformation,[status(esa)],[f20_nnf]) ).
cnf(hi15,negated_conjecture,
less_than(j,i) = true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(h12,plain,
less_than(k,i) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi10,hi15]) ).
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(hi19,negated_conjecture,
ifeq(less_than(k,i),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi19,h12]) ).
cnf(t84,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
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(f12,negated_conjecture,
~ less_than(n,j),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1) ).
fof(f12_nnf,plain,
~ less_than(n,j),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
~ less_than(n,j),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
~ less_than(n,j),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(f19,negated_conjecture,
( ~ less_than(a(X),a(predecessor(X)))
| ~ less_than(X,i)
| ~ less_than(one,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_8) ).
fof(f19_nnf,plain,
! [X] :
( ~ less_than(a(X),a(predecessor(X)))
| ~ less_than(X,i)
| ~ less_than(one,X) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [X] :
( ~ less_than(a(X),a(predecessor(X)))
| ~ less_than(X,i)
| ~ less_than(one,X) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
( ~ less_than(a(X0),a(predecessor(X0)))
| ~ less_than(X0,i)
| ~ less_than(one,X0) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c8,c9,c12,c14,c19]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t84]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV003-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n007.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 18:14:22 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.54/1.55 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.54/1.55 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------