%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : MGT058+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n006.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 : Tue Sep 29 12:02:45 PM UTC 2026
% Result : Theorem 0.10s 0.46s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 12
% Syntax : Number of formulae : 89 ( 14 unt; 6 def)
% Number of atoms : 220 ( 22 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 225 ( 94 ~; 79 |; 26 &)
% ( 11 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 7 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 56 ( 0 sgn 49 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( smaller_or_equal(X0,X1)
<=> ( smaller(X0,X1)
| X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/MGT001+0.ax',definition_smaller_or_equal) ).
fof(f2,axiom,
! [X0,X1] :
( greater_or_equal(X0,X1)
<=> ( greater(X0,X1)
| X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/MGT001+0.ax',definition_greater_or_equal) ).
fof(f3,axiom,
! [X0,X1] :
( smaller(X0,X1)
<=> greater(X1,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/MGT001+0.ax',definition_smaller) ).
fof(f7,axiom,
! [X0] :
( fragile_position(X0)
<=> ! [X1] :
( ( smaller_or_equal(age(X0,X1),sigma)
=> positional_advantage(X0,X1) )
& ( greater(age(X0,X1),sigma)
=> ~ positional_advantage(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_3) ).
fof(f8,axiom,
! [X0] :
( robust_position(X0)
<=> ! [X1] :
( ( smaller_or_equal(age(X0,X1),tau)
=> ~ positional_advantage(X0,X1) )
& ( greater(age(X0,X1),tau)
=> positional_advantage(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_4) ).
fof(f9,conjecture,
! [X0] :
( ( organization(X0)
& ? [X1] : age(X0,X1) = zero
& greater_or_equal(sigma,zero)
& greater_or_equal(tau,zero) )
=> ~ ( fragile_position(X0)
& robust_position(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_10) ).
fof(f10,negated_conjecture,
~ ! [X0] :
( ( organization(X0)
& ? [X1] : age(X0,X1) = zero
& greater_or_equal(sigma,zero)
& greater_or_equal(tau,zero) )
=> ~ ( fragile_position(X0)
& robust_position(X0) ) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,plain,
! [X0] :
( robust_position(X0)
=> ! [X1] :
( ( smaller_or_equal(age(X0,X1),tau)
=> ~ positional_advantage(X0,X1) )
& ( greater(age(X0,X1),tau)
=> positional_advantage(X0,X1) ) ) ),
inference(unused_predicate_definition_removal,[],[f8]) ).
fof(f12,plain,
! [X0] :
( fragile_position(X0)
=> ! [X1] :
( ( smaller_or_equal(age(X0,X1),sigma)
=> positional_advantage(X0,X1) )
& ( greater(age(X0,X1),sigma)
=> ~ positional_advantage(X0,X1) ) ) ),
inference(unused_predicate_definition_removal,[],[f7]) ).
fof(f13,plain,
! [X0,X1] :
( ( smaller(X0,X1)
| X0 = X1 )
=> smaller_or_equal(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f14,plain,
! [X0,X1] :
( greater_or_equal(X0,X1)
=> ( greater(X0,X1)
| X0 = X1 ) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f15,plain,
~ ! [X0] :
( ( ? [X1] : age(X0,X1) = zero
& greater_or_equal(sigma,zero)
& greater_or_equal(tau,zero) )
=> ~ ( fragile_position(X0)
& robust_position(X0) ) ),
inference(pure_predicate_removal,[],[f10]) ).
fof(f16,plain,
! [X0,X1] :
( smaller_or_equal(X0,X1)
| ( ~ smaller(X0,X1)
& X0 != X1 ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f17,plain,
! [X0,X1] :
( greater(X0,X1)
| X0 = X1
| ~ greater_or_equal(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f18,plain,
! [X0,X1] :
( greater(X0,X1)
| X0 = X1
| ~ greater_or_equal(X0,X1) ),
inference(flattening,[],[f17]) ).
fof(f22,plain,
! [X0] :
( ! [X1] :
( ( positional_advantage(X0,X1)
| ~ smaller_or_equal(age(X0,X1),sigma) )
& ( ~ positional_advantage(X0,X1)
| ~ greater(age(X0,X1),sigma) ) )
| ~ fragile_position(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f23,plain,
! [X0] :
( ! [X1] :
( ( ~ positional_advantage(X0,X1)
| ~ smaller_or_equal(age(X0,X1),tau) )
& ( positional_advantage(X0,X1)
| ~ greater(age(X0,X1),tau) ) )
| ~ robust_position(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f24,plain,
? [X0] :
( fragile_position(X0)
& robust_position(X0)
& ? [X1] : age(X0,X1) = zero
& greater_or_equal(sigma,zero)
& greater_or_equal(tau,zero) ),
inference(ennf_transformation,[],[f15]) ).
fof(f25,plain,
? [X0] :
( fragile_position(X0)
& robust_position(X0)
& ? [X1] : age(X0,X1) = zero
& greater_or_equal(sigma,zero)
& greater_or_equal(tau,zero) ),
inference(flattening,[],[f24]) ).
fof(f26,plain,
! [X0,X1] :
( X0 != X1
| smaller_or_equal(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f27,plain,
! [X0,X1] :
( ~ smaller(X0,X1)
| smaller_or_equal(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f28,plain,
! [X0,X1] :
( ~ greater_or_equal(X0,X1)
| X0 = X1
| greater(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f29,plain,
! [X0,X1] :
( smaller(X0,X1)
| ~ greater(X1,X0) ),
inference(cnf_transformation,[],[f3]) ).
fof(f34,plain,
! [X0,X1] :
( ~ fragile_position(X0)
| ~ smaller_or_equal(age(X0,X1),sigma)
| positional_advantage(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f36,plain,
! [X0,X1] :
( ~ robust_position(X0)
| ~ smaller_or_equal(age(X0,X1),tau)
| ~ positional_advantage(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f38,plain,
greater_or_equal(tau,zero),
inference(cnf_transformation,[],[f25]) ).
fof(f39,plain,
greater_or_equal(sigma,zero),
inference(cnf_transformation,[],[f25]) ).
fof(f40,plain,
zero = age(sK0,sK1),
inference(cnf_transformation,[],[f25]) ).
fof(f41,plain,
robust_position(sK0),
inference(cnf_transformation,[],[f25]) ).
fof(f42,plain,
fragile_position(sK0),
inference(cnf_transformation,[],[f25]) ).
fof(f43,plain,
! [X1] : smaller_or_equal(X1,X1),
inference(equality_resolution,[],[f26]) ).
fof(f44,plain,
! [X0,X1] :
( smaller_or_equal(X1,X0)
| ~ greater(X0,X1) ),
inference(resolution,[],[f29,f27]) ).
fof(f46,plain,
( tau = zero
| greater(tau,zero) ),
inference(resolution,[],[f28,f38]) ).
fof(f47,plain,
( sigma = zero
| greater(sigma,zero) ),
inference(resolution,[],[f28,f39]) ).
fof(f49,definition,
( spl2_1
<=> greater(sigma,zero) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f51,plain,
( greater(sigma,zero)
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f53,definition,
( spl2_2
<=> sigma = zero ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f55,plain,
( sigma = zero
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f56,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f47,f53,f49]) ).
fof(f58,definition,
( spl2_3
<=> greater(tau,zero) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f60,plain,
( greater(tau,zero)
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f62,definition,
( spl2_4
<=> tau = zero ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
fof(f64,plain,
( tau = zero
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f65,plain,
( spl2_3
| spl2_4 ),
inference(avatar_split_clause,[],[f46,f62,f58]) ).
fof(f66,plain,
( greater(tau,sigma)
| ~ spl2_2
| ~ spl2_3 ),
inference(forward_demodulation,[],[f60,f55]) ).
fof(f82,plain,
! [X0] :
( positional_advantage(sK0,X0)
| ~ smaller_or_equal(age(sK0,X0),sigma) ),
inference(resolution,[],[f34,f42]) ).
fof(f86,plain,
! [X0] :
( ~ positional_advantage(sK0,X0)
| ~ smaller_or_equal(age(sK0,X0),tau) ),
inference(resolution,[],[f36,f41]) ).
fof(f99,plain,
! [X0] :
( ~ smaller_or_equal(age(sK0,X0),tau)
| ~ smaller_or_equal(age(sK0,X0),sigma) ),
inference(resolution,[],[f86,f82]) ).
fof(f271,plain,
( ~ smaller_or_equal(zero,tau)
| ~ smaller_or_equal(zero,sigma) ),
inference(superposition,[],[f99,f40]) ).
fof(f272,plain,
( ~ smaller_or_equal(sigma,tau)
| ~ smaller_or_equal(zero,sigma)
| ~ spl2_2 ),
inference(forward_demodulation,[],[f271,f55]) ).
fof(f274,plain,
( ~ smaller_or_equal(sigma,sigma)
| ~ smaller_or_equal(sigma,tau)
| ~ spl2_2 ),
inference(forward_demodulation,[],[f272,f55]) ).
fof(f275,plain,
( ~ smaller_or_equal(sigma,tau)
| ~ spl2_2 ),
inference(forward_subsumption_resolution,[],[f274,f43]) ).
fof(f277,plain,
( ~ greater(tau,sigma)
| ~ spl2_2 ),
inference(resolution,[],[f275,f44]) ).
fof(f278,plain,
( $false
| ~ spl2_2
| ~ spl2_3 ),
inference(forward_subsumption_resolution,[],[f277,f66]) ).
fof(f279,plain,
( ~ spl2_2
| ~ spl2_3 ),
inference(avatar_contradiction_clause,[],[f278]) ).
fof(f286,definition,
( spl2_6
<=> smaller_or_equal(zero,sigma) ),
introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition]) ).
fof(f288,plain,
( ~ smaller_or_equal(zero,sigma)
| spl2_6 ),
inference(avatar_component_clause,[],[f286]) ).
fof(f291,definition,
( spl2_7
<=> smaller_or_equal(zero,tau) ),
introduced(definition,[new_symbols(definition,[spl2_7])],[avatar_definition]) ).
fof(f293,plain,
( ~ smaller_or_equal(zero,tau)
| spl2_7 ),
inference(avatar_component_clause,[],[f291]) ).
fof(f294,plain,
( ~ spl2_6
| ~ spl2_7 ),
inference(avatar_split_clause,[],[f271,f291,f286]) ).
fof(f300,plain,
( ~ greater(sigma,zero)
| spl2_6 ),
inference(resolution,[],[f288,f44]) ).
fof(f301,plain,
( $false
| ~ spl2_1
| spl2_6 ),
inference(forward_subsumption_resolution,[],[f300,f51]) ).
fof(f302,plain,
( ~ spl2_1
| spl2_6 ),
inference(avatar_contradiction_clause,[],[f301]) ).
fof(f348,plain,
( ~ greater(tau,zero)
| spl2_7 ),
inference(resolution,[],[f293,f44]) ).
fof(f349,plain,
( $false
| ~ spl2_3
| spl2_7 ),
inference(forward_subsumption_resolution,[],[f348,f60]) ).
fof(f350,plain,
( ~ spl2_3
| spl2_7 ),
inference(avatar_contradiction_clause,[],[f349]) ).
fof(f369,plain,
( ~ smaller_or_equal(tau,tau)
| ~ spl2_4
| spl2_7 ),
inference(superposition,[],[f293,f64]) ).
fof(f372,plain,
( $false
| ~ spl2_4
| spl2_7 ),
inference(forward_subsumption_resolution,[],[f369,f43]) ).
fof(f373,plain,
( ~ spl2_4
| spl2_7 ),
inference(avatar_contradiction_clause,[],[f372]) ).
fof(f384,plain,
( sigma = tau
| ~ spl2_2
| ~ spl2_4 ),
inference(superposition,[],[f64,f55]) ).
fof(f423,plain,
( ~ smaller_or_equal(sigma,sigma)
| ~ spl2_2
| ~ spl2_4 ),
inference(superposition,[],[f275,f384]) ).
fof(f424,plain,
( $false
| ~ spl2_2
| ~ spl2_4 ),
inference(forward_subsumption_resolution,[],[f423,f43]) ).
fof(f425,plain,
( ~ spl2_2
| ~ spl2_4 ),
inference(avatar_contradiction_clause,[],[f424]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f56]) ).
cnf(s2,plain,
( spl2_3
| spl2_4 ),
inference(sat_conversion,[],[f65]) ).
cnf(s3,plain,
( ~ spl2_2
| ~ spl2_3 ),
inference(sat_conversion,[],[f279]) ).
cnf(s5,plain,
( ~ spl2_6
| ~ spl2_7 ),
inference(sat_conversion,[],[f294]) ).
cnf(s6,plain,
( ~ spl2_1
| spl2_6 ),
inference(sat_conversion,[],[f302]) ).
cnf(s8,plain,
( ~ spl2_3
| spl2_7 ),
inference(sat_conversion,[],[f350]) ).
cnf(s10,plain,
( ~ spl2_4
| spl2_7 ),
inference(sat_conversion,[],[f373]) ).
cnf(s11,plain,
( ~ spl2_2
| ~ spl2_4 ),
inference(sat_conversion,[],[f425]) ).
cnf(s12,plain,
~ spl2_2,
inference(rat,[],[s2,s3,s11]) ).
cnf(s13,plain,
spl2_1,
inference(rat,[],[s1,s12]) ).
cnf(s14,plain,
spl2_6,
inference(rat,[],[s6,s13]) ).
cnf(s15,plain,
~ spl2_7,
inference(rat,[],[s5,s14]) ).
cnf(s17,plain,
~ spl2_4,
inference(rat,[],[s10,s15]) ).
cnf(s18,plain,
~ spl2_3,
inference(rat,[],[s8,s15]) ).
cnf(s19,plain,
$false,
inference(rat,[],[s2,s17,s18]) ).
fof(f426,plain,
$false,
inference(avatar_sat_refutation,[],[s19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT058+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n006.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 17:29:41 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.46 % (3197072)Will run a generic schedule for satisfiability detection.
% 0.10/0.46 % (3197081)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1099875168:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.46 % (3197078)% WARNING: option uhcvi not known.
% 0.10/0.46 % (3197081) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3197072-3197081"...
% 0.10/0.46 % (3197077)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=862242751_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.46 % (3197078)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=754378697:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.10/0.46 % (3197080)dis+10_1_sil=32000:sp=arity:random_seed=3456305889:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.46 % (3197079)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3912419007:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.46 % (3197082)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2373237102:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.46 % (3197083)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=765011988:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.46 % (3197081)...printing done.
% 0.10/0.46 % TRYING [1]
% 0.10/0.46 % (3197081)Refutation found. Thanks to Tanya!
% 0.10/0.46 % SZS status Theorem for theBenchmark
% 0.10/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.46 % (3197081)------------------------------
% 0.10/0.46 % (3197081)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.46 % (3197081)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.46 % (3197081)CaDiCaL version: 2.1.3
% 0.10/0.46 % (3197081)Termination reason: Refutation
% 0.10/0.46 % (3197081)Time elapsed: 0.007 s
% 0.10/0.46 % (3197081)Peak memory usage: 12 MB
% 0.10/0.46 % (3197081)Instructions burned: 19 (million)
% 0.10/0.46 % (3197072)Success in time 0.035 s
% 0.10/0.46 % Vampire exiting
%------------------------------------------------------------------------------