%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : MGT058-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n011.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 02:11:52 PM UTC 2026
% Result : Unsatisfiable 27.29s 29.01s
% Output : Proof 27.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 11
% Syntax : Number of formulae : 67 ( 22 unt; 0 def)
% Number of atoms : 124 ( 31 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 108 ( 51 ~; 57 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f24,negated_conjecture,
age(sk3,sk4) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_10_43) ).
fof(f24_nnf,plain,
age(sk3,sk4) = zero,
inference(nnf_transformation,[status(thm)],[f24]) ).
cnf(c24,plain,
age(sk3,sk4) = zero,
inference(cnf_transformation,[status(esa)],[f24_nnf]) ).
cnf(f17,axiom,
( ~ positional_advantage(A,B)
| ~ smaller_or_equal(age(A,B),tau)
| ~ robust_position(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_4_36) ).
fof(f17_nnf,plain,
! [A,B] :
( ~ positional_advantage(A,B)
| ~ smaller_or_equal(age(A,B),tau)
| ~ robust_position(A) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [A,B] :
( ~ positional_advantage(A,B)
| ~ smaller_or_equal(age(A,B),tau)
| ~ robust_position(A) ),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c17,plain,
( ~ positional_advantage(X0,X1)
| ~ smaller_or_equal(age(X0,X1),tau)
| ~ robust_position(X0) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(f28,negated_conjecture,
robust_position(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_10_47) ).
fof(f28_nnf,plain,
robust_position(sk3),
inference(nnf_transformation,[status(thm)],[f28]) ).
cnf(c28,plain,
robust_position(sk3),
inference(cnf_transformation,[status(esa)],[f28_nnf]) ).
cnf(p96,plain,
( ~ positional_advantage(sk3,X0)
| ~ smaller_or_equal(age(sk3,X0),tau) ),
inference(resolution,[status(thm)],[c17,c28]) ).
cnf(p97,plain,
( ~ positional_advantage(sk3,sk4)
| ~ smaller_or_equal(zero,tau) ),
inference(superposition,[status(thm)],[c24,p96]) ).
cnf(f7,axiom,
( smaller(B,A)
| ~ greater(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_smaller_8) ).
fof(f7_nnf,plain,
! [A,B] :
( smaller(B,A)
| ~ greater(A,B) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A,B] :
( smaller(B,A)
| ~ greater(A,B) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( smaller(X1,X0)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(f3,axiom,
( A = B
| greater(A,B)
| ~ greater_or_equal(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_greater_or_equal_4) ).
fof(f3_nnf,plain,
! [A,B] :
( A = B
| greater(A,B)
| ~ greater_or_equal(A,B) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B] :
( A = B
| greater(A,B)
| ~ greater_or_equal(A,B) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( X0 = X1
| greater(X0,X1)
| ~ greater_or_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(f26,negated_conjecture,
greater_or_equal(tau,zero),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_10_45) ).
fof(f26_nnf,plain,
greater_or_equal(tau,zero),
inference(nnf_transformation,[status(thm)],[f26]) ).
cnf(c26,plain,
greater_or_equal(tau,zero),
inference(cnf_transformation,[status(esa)],[f26_nnf]) ).
cnf(p31,plain,
( tau = zero
| greater(tau,zero) ),
inference(resolution,[status(thm)],[c3,c26]) ).
cnf(p34,plain,
( tau = zero
| smaller(zero,tau) ),
inference(resolution,[status(thm)],[c7,p31]) ).
cnf(f1,axiom,
( smaller_or_equal(A,B)
| ~ smaller(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_smaller_or_equal_2) ).
fof(f1_nnf,plain,
! [A,B] :
( smaller_or_equal(A,B)
| ~ smaller(A,B) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B] :
( smaller_or_equal(A,B)
| ~ smaller(A,B) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( smaller_or_equal(X0,X1)
| ~ smaller(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p39,plain,
( smaller_or_equal(zero,tau)
| tau = zero ),
inference(resolution,[status(thm)],[p34,c1]) ).
cnf(p99,plain,
( tau = zero
| ~ positional_advantage(sk3,sk4) ),
inference(resolution,[status(thm)],[p97,p39]) ).
cnf(f11,axiom,
( positional_advantage(A,B)
| ~ smaller_or_equal(age(A,B),sigma)
| ~ fragile_position(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_3_30) ).
fof(f11_nnf,plain,
! [A,B] :
( positional_advantage(A,B)
| ~ smaller_or_equal(age(A,B),sigma)
| ~ fragile_position(A) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [A,B] :
( positional_advantage(A,B)
| ~ smaller_or_equal(age(A,B),sigma)
| ~ fragile_position(A) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( positional_advantage(X0,X1)
| ~ smaller_or_equal(age(X0,X1),sigma)
| ~ fragile_position(X0) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(f27,negated_conjecture,
fragile_position(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_10_46) ).
fof(f27_nnf,plain,
fragile_position(sk3),
inference(nnf_transformation,[status(thm)],[f27]) ).
cnf(c27,plain,
fragile_position(sk3),
inference(cnf_transformation,[status(esa)],[f27_nnf]) ).
cnf(p58,plain,
( positional_advantage(sk3,X0)
| ~ smaller_or_equal(age(sk3,X0),sigma) ),
inference(resolution,[status(thm)],[c11,c27]) ).
cnf(p59,plain,
( positional_advantage(sk3,sk4)
| ~ smaller_or_equal(zero,sigma) ),
inference(superposition,[status(thm)],[c24,p58]) ).
cnf(f25,negated_conjecture,
greater_or_equal(sigma,zero),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_10_44) ).
fof(f25_nnf,plain,
greater_or_equal(sigma,zero),
inference(nnf_transformation,[status(thm)],[f25]) ).
cnf(c25,plain,
greater_or_equal(sigma,zero),
inference(cnf_transformation,[status(esa)],[f25_nnf]) ).
cnf(p30,plain,
( sigma = zero
| greater(sigma,zero) ),
inference(resolution,[status(thm)],[c3,c25]) ).
cnf(p33,plain,
( sigma = zero
| smaller(zero,sigma) ),
inference(resolution,[status(thm)],[c7,p30]) ).
cnf(p35,plain,
( smaller_or_equal(zero,sigma)
| sigma = zero ),
inference(resolution,[status(thm)],[p33,c1]) ).
cnf(p60,plain,
( sigma = zero
| positional_advantage(sk3,sk4) ),
inference(resolution,[status(thm)],[p59,p35]) ).
cnf(p101,plain,
( sigma = zero
| tau = zero ),
inference(resolution,[status(thm)],[p99,p60]) ).
cnf(p103,plain,
( zero = tau
| sigma = zero ),
inference(superposition,[status(thm)],[p101,c24]) ).
cnf(f2,axiom,
( smaller_or_equal(A,B)
| A != B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_smaller_or_equal_3) ).
fof(f2_nnf,plain,
! [A,B] :
( smaller_or_equal(A,B)
| A != B ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B] :
( smaller_or_equal(A,B)
| A != B ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( smaller_or_equal(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p121,plain,
( smaller_or_equal(zero,tau)
| sigma = zero ),
inference(resolution,[status(thm)],[p103,c2]) ).
cnf(p123,plain,
( ~ positional_advantage(sk3,sk4)
| sigma = zero ),
inference(resolution,[status(thm)],[p121,p97]) ).
cnf(p128,plain,
( sigma = zero
| sigma = zero ),
inference(resolution,[status(thm)],[p123,p60]) ).
cnf(p129,plain,
sigma = zero,
inference(factoring,[status(thm)],[p128]) ).
cnf(p131,plain,
zero = sigma,
inference(superposition,[status(thm)],[p129,c24]) ).
cnf(p158,plain,
( tau = sigma
| ~ positional_advantage(sk3,sk4) ),
inference(demodulation,[status(thm)],[p131,p99]) ).
cnf(p143,plain,
( positional_advantage(sk3,sk4)
| ~ smaller_or_equal(sigma,sigma) ),
inference(demodulation,[status(thm)],[p131,p59]) ).
cnf(p29,plain,
smaller_or_equal(X0,X0),
inference(equality_resolution,[status(thm)],[c2]) ).
cnf(p163,plain,
positional_advantage(sk3,sk4),
inference(resolution,[status(thm)],[p143,p29]) ).
cnf(p164,plain,
tau = sigma,
inference(resolution,[status(thm)],[p158,p163]) ).
cnf(p156,plain,
( ~ positional_advantage(sk3,sk4)
| ~ smaller_or_equal(sigma,tau) ),
inference(demodulation,[status(thm)],[p131,p97]) ).
cnf(p176,plain,
( ~ positional_advantage(sk3,sk4)
| ~ smaller_or_equal(sigma,sigma) ),
inference(demodulation,[status(thm)],[p164,p156]) ).
cnf(p181,plain,
~ positional_advantage(sk3,sk4),
inference(resolution,[status(thm)],[p176,p29]) ).
cnf(p182,plain,
$false,
inference(resolution,[status(thm)],[p181,p163]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT058-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.34 % Computer : n011.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
% 0.09/25.44 % CPULimit : 300
% 0.09/25.44 % WCLimit : 300
% 0.09/25.44 % DateTime : Thu Sep 24 01:16:26 UTC 2026
% 0.09/25.44 % CPUTime :
% 0.09/25.44 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 27.29/29.01 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 27.29/29.01 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------