%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : MGT058-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 : Thu Sep 24 01:25:29 PM UTC 2026
% Result : Unsatisfiable 0.18s 0.50s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 24
% Syntax : Number of formulae : 81 ( 16 unt; 12 def)
% Number of atoms : 175 ( 15 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 172 ( 78 ~; 82 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 13 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 37 ( 37 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] :
( smaller_or_equal(A,B)
| ~ smaller(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] :
( smaller_or_equal(A,B)
| A != B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] :
( A = B
| greater(A,B)
| ~ greater_or_equal(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B] :
( smaller(B,A)
| ~ greater(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B] :
( positional_advantage(A,B)
| ~ smaller_or_equal(age(A,B),sigma)
| ~ fragile_position(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A,B] :
( ~ positional_advantage(A,B)
| ~ greater(age(A,B),sigma)
| ~ fragile_position(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [A,B] :
( ~ positional_advantage(A,B)
| ~ smaller_or_equal(age(A,B),tau)
| ~ robust_position(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
age(sk3,sk4) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
greater_or_equal(sigma,zero),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
greater_or_equal(tau,zero),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
fragile_position(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
robust_position(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,plain,
! [X0,X1] :
( smaller_or_equal(X0,X1)
| ~ smaller(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f32,plain,
! [X0,X1] :
( smaller_or_equal(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f33,plain,
! [X0,X1] :
( X0 = X1
| greater(X0,X1)
| ~ greater_or_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f37,plain,
! [X0,X1] :
( smaller(X1,X0)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f42,plain,
! [X0,X1] :
( positional_advantage(X0,X1)
| ~ smaller_or_equal(age(X0,X1),sigma)
| ~ fragile_position(X0) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f43,plain,
! [X0,X1] :
( ~ positional_advantage(X0,X1)
| ~ greater(age(X0,X1),sigma)
| ~ fragile_position(X0) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f48,plain,
! [X0,X1] :
( ~ positional_advantage(X0,X1)
| ~ smaller_or_equal(age(X0,X1),tau)
| ~ robust_position(X0) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f55,plain,
age(sk3,sk4) = zero,
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f56,plain,
greater_or_equal(sigma,zero),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f57,plain,
greater_or_equal(tau,zero),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f58,plain,
fragile_position(sk3),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f59,plain,
robust_position(sk3),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f60,plain,
! [X0] : smaller_or_equal(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f32]) ).
fof(f62,plain,
! [X0] :
( ~ positional_advantage(sk3,X0)
| ~ greater(age(sk3,X0),sigma) ),
inference(resolution,[status(thm)],[f43,f58]) ).
fof(f63,plain,
! [X0] :
( ~ smaller_or_equal(age(sk3,X0),sigma)
| ~ fragile_position(sk3)
| ~ greater(age(sk3,X0),sigma) ),
inference(resolution,[status(thm)],[f62,f42]) ).
fof(f64,definition,
! [X0] :
( sQ0_spl
<=> ( ~ smaller_or_equal(age(sk3,X0),sigma)
| ~ greater(age(sk3,X0),sigma) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f65,plain,
! [X0] :
( ~ sQ0_spl
| ~ smaller_or_equal(age(sk3,X0),sigma)
| ~ greater(age(sk3,X0),sigma) ),
inference(component_clause,[status(thm)],[f64]) ).
fof(f67,definition,
( sQ1_spl
<=> fragile_position(sk3) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f69,plain,
( sQ1_spl
| ~ fragile_position(sk3) ),
inference(component_clause,[status(thm)],[f67]) ).
fof(f70,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f63,f64,f67]) ).
fof(f71,plain,
( ~ positional_advantage(sk3,sk4)
| ~ smaller_or_equal(zero,tau)
| ~ robust_position(sk3) ),
inference(paramodulation,[status(thm)],[f55,f48]) ).
fof(f72,definition,
( sQ2_spl
<=> robust_position(sk3) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f74,plain,
( sQ2_spl
| ~ robust_position(sk3) ),
inference(component_clause,[status(thm)],[f72]) ).
fof(f75,definition,
( sQ3_spl
<=> smaller_or_equal(zero,tau) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f77,plain,
( sQ3_spl
| ~ smaller_or_equal(zero,tau) ),
inference(component_clause,[status(thm)],[f75]) ).
fof(f78,definition,
( sQ4_spl
<=> positional_advantage(sk3,sk4) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f80,plain,
( sQ4_spl
| ~ positional_advantage(sk3,sk4) ),
inference(component_clause,[status(thm)],[f78]) ).
fof(f81,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f71,f72,f75,f78]) ).
fof(f82,plain,
( sQ4_spl
| ~ smaller_or_equal(age(sk3,sk4),sigma)
| ~ fragile_position(sk3) ),
inference(resolution,[status(thm)],[f80,f42]) ).
fof(f83,definition,
( sQ5_spl
<=> smaller_or_equal(age(sk3,sk4),sigma) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f85,plain,
( sQ5_spl
| ~ smaller_or_equal(age(sk3,sk4),sigma) ),
inference(component_clause,[status(thm)],[f83]) ).
fof(f86,plain,
( sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f82,f67,f83,f78]) ).
fof(f87,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f69,f58]) ).
fof(f88,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f87]) ).
fof(f89,plain,
( sQ5_spl
| ~ smaller_or_equal(zero,sigma) ),
inference(forward_demodulation,[status(thm)],[f55,f85]) ).
fof(f90,plain,
! [X0,X1] :
( X1 = X0
| ~ greater_or_equal(X1,X0)
| smaller(X0,X1) ),
inference(resolution,[status(thm)],[f37,f33]) ).
fof(f97,plain,
! [X0,X1] :
( smaller_or_equal(X1,X0)
| X0 = X1
| ~ greater_or_equal(X0,X1) ),
inference(resolution,[status(thm)],[f90,f31]) ).
fof(f105,plain,
( ~ sQ0_spl
| ~ smaller_or_equal(age(sk3,sk4),sigma)
| ~ greater(zero,sigma) ),
inference(paramodulation,[status(thm)],[f55,f65]) ).
fof(f106,definition,
( sQ6_spl
<=> greater(zero,sigma) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f108,plain,
( sQ6_spl
| ~ greater(zero,sigma) ),
inference(component_clause,[status(thm)],[f106]) ).
fof(f109,plain,
( ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f105,f106,f83,f64]) ).
fof(f110,plain,
( sQ6_spl
| zero = sigma
| ~ greater_or_equal(zero,sigma) ),
inference(resolution,[status(thm)],[f108,f33]) ).
fof(f111,definition,
( sQ7_spl
<=> greater_or_equal(zero,sigma) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f114,definition,
( sQ8_spl
<=> zero = sigma ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f115,plain,
( ~ sQ8_spl
| zero = sigma ),
inference(component_clause,[status(thm)],[f114]) ).
fof(f117,plain,
( sQ6_spl
| sQ8_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f110,f111,f114,f106]) ).
fof(f120,plain,
( sQ5_spl
| ~ sQ8_spl
| ~ smaller_or_equal(zero,zero) ),
inference(backward_demodulation,[status(thm)],[f115,f89]) ).
fof(f128,plain,
( sQ5_spl
| ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f120,f60]) ).
fof(f129,plain,
( sQ5_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f128]) ).
fof(f133,plain,
( sQ5_spl
| sigma = zero
| ~ greater_or_equal(sigma,zero) ),
inference(resolution,[status(thm)],[f97,f89]) ).
fof(f134,plain,
( sQ3_spl
| tau = zero
| ~ greater_or_equal(tau,zero) ),
inference(resolution,[status(thm)],[f97,f77]) ).
fof(f136,definition,
( sQ9_spl
<=> greater_or_equal(sigma,zero) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f138,plain,
( sQ9_spl
| ~ greater_or_equal(sigma,zero) ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f139,plain,
( sQ5_spl
| sQ8_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f133,f136,f114,f83]) ).
fof(f140,definition,
( sQ10_spl
<=> greater_or_equal(tau,zero) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f142,plain,
( sQ10_spl
| ~ greater_or_equal(tau,zero) ),
inference(component_clause,[status(thm)],[f140]) ).
fof(f143,definition,
( sQ11_spl
<=> tau = zero ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f144,plain,
( ~ sQ11_spl
| tau = zero ),
inference(component_clause,[status(thm)],[f143]) ).
fof(f146,plain,
( sQ3_spl
| sQ11_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f134,f140,f143,f75]) ).
fof(f147,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f138,f56]) ).
fof(f148,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f147]) ).
fof(f149,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f74,f59]) ).
fof(f150,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f149]) ).
fof(f152,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f142,f57]) ).
fof(f153,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f152]) ).
fof(f161,plain,
( sQ3_spl
| ~ sQ11_spl
| ~ smaller_or_equal(zero,zero) ),
inference(forward_demodulation,[status(thm)],[f144,f77]) ).
fof(f162,plain,
( sQ3_spl
| ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f161,f60]) ).
fof(f163,plain,
( sQ3_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f162]) ).
fof(f164,plain,
$false,
inference(sat_refutation,[status(thm)],[f70,f81,f86,f88,f109,f117,f129,f139,f146,f148,f150,f153,f163]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : MGT058-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n016.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Mon Sep 21 01:28:38 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.47 % Drodi V4.1.1
% 0.18/0.50 % Refutation found
% 0.18/0.50 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.18/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.25/0.58 % Elapsed time: 0.117721 seconds
% 0.25/0.58 % CPU time: 0.118445 seconds
% 0.25/0.58 % Total memory used: 9.748 MB
% 0.25/0.58 % Net memory used: 9.736 MB
%------------------------------------------------------------------------------