%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : MGT058+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 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 : Tue Sep 29 12:02:16 PM UTC 2026
% Result : Theorem 1.61s 1.13s
% Output : Refutation 2.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 8
% Syntax : Number of formulae : 74 ( 11 unt; 0 def)
% Number of atoms : 204 ( 41 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 219 ( 89 ~; 78 |; 32 &)
% ( 5 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 73 ( 66 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( smaller_or_equal(X0,X1)
<=> ( smaller(X0,X1)
| X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_smaller_or_equal) ).
fof(f2,axiom,
! [X0,X1] :
( greater_or_equal(X0,X1)
<=> ( greater(X0,X1)
| X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_greater_or_equal) ).
fof(f3,axiom,
! [X0,X1] :
( smaller(X0,X1)
<=> greater(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_smaller) ).
fof(f4,axiom,
! [X0,X1] :
~ ( greater(X0,X1)
& greater(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meaning_postulate_greater_strict) ).
fof(f6,axiom,
! [X0,X1] :
( smaller(X0,X1)
| X0 = X1
| greater(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meaning_postulate_greater_comparable) ).
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/sandbox2/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/sandbox2/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/sandbox2/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] :
( 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(f17,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,[],[f16]) ).
fof(f18,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(f19,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(f20,plain,
! [X0,X1] :
( greater(X0,X1)
| X0 = X1
| ~ greater_or_equal(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f21,plain,
! [X0,X1] :
( greater(X0,X1)
| X0 = X1
| ~ greater_or_equal(X0,X1) ),
inference(flattening,[],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( smaller_or_equal(X0,X1)
| ( ~ smaller(X0,X1)
& X0 != X1 ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f25,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| ~ greater(X1,X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f26,plain,
( fragile_position(sK0)
& robust_position(sK0)
& zero = age(sK0,sK1)
& greater_or_equal(sigma,zero)
& greater_or_equal(tau,zero) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f17]) ).
fof(f27,plain,
! [X0,X1] :
( ( smaller(X0,X1)
| ~ greater(X1,X0) )
& ( greater(X1,X0)
| ~ smaller(X0,X1) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f28,plain,
greater_or_equal(tau,zero),
inference(cnf_transformation,[],[f26]) ).
fof(f29,plain,
greater_or_equal(sigma,zero),
inference(cnf_transformation,[],[f26]) ).
fof(f30,plain,
zero = age(sK0,sK1),
inference(cnf_transformation,[],[f26]) ).
fof(f31,plain,
robust_position(sK0),
inference(cnf_transformation,[],[f26]) ).
fof(f32,plain,
fragile_position(sK0),
inference(cnf_transformation,[],[f26]) ).
fof(f34,plain,
! [X0,X1] :
( ~ smaller_or_equal(age(X0,X1),sigma)
| positional_advantage(X0,X1)
| ~ fragile_position(X0) ),
inference(cnf_transformation,[],[f18]) ).
fof(f36,plain,
! [X0,X1] :
( ~ smaller_or_equal(age(X0,X1),tau)
| ~ positional_advantage(X0,X1)
| ~ robust_position(X0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f37,plain,
! [X0,X1] :
( greater(X0,X1)
| X0 = X1
| ~ greater_or_equal(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f38,plain,
! [X0,X1] :
( smaller_or_equal(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f22]) ).
fof(f39,plain,
! [X0,X1] :
( smaller_or_equal(X0,X1)
| ~ smaller(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f41,plain,
! [X0,X1] :
( ~ greater(X1,X0)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f42,plain,
! [X0,X1] :
( greater(X0,X1)
| X0 = X1
| smaller(X0,X1) ),
inference(cnf_transformation,[],[f6]) ).
fof(f44,plain,
! [X0,X1] :
( smaller(X0,X1)
| ~ greater(X1,X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f45,plain,
! [X1] : smaller_or_equal(X1,X1),
inference(equality_resolution,[],[f38]) ).
fof(f52,plain,
! [X0,X1] :
( ~ greater(X1,X0)
| ~ greater_or_equal(X0,X1)
| X0 = X1 ),
inference(resolution,[],[f37,f41]) ).
fof(f62,plain,
! [X0,X1] :
( ~ greater_or_equal(X0,X1)
| X0 = X1
| X0 = X1
| smaller(X1,X0) ),
inference(resolution,[],[f52,f42]) ).
fof(f67,plain,
! [X0,X1] :
( smaller(X1,X0)
| X0 = X1
| ~ greater_or_equal(X0,X1) ),
inference(duplicate_literal_removal,[],[f62]) ).
fof(f82,plain,
! [X0,X1] :
( ~ smaller(age(X0,X1),sigma)
| ~ fragile_position(X0)
| positional_advantage(X0,X1) ),
inference(resolution,[],[f34,f39]) ).
fof(f83,plain,
( ~ smaller_or_equal(zero,sigma)
| positional_advantage(sK0,sK1)
| ~ fragile_position(sK0) ),
inference(superposition,[],[f34,f30]) ).
fof(f84,plain,
( positional_advantage(sK0,sK1)
| ~ smaller_or_equal(zero,sigma) ),
inference(forward_subsumption_resolution,[],[f83,f32]) ).
fof(f97,plain,
! [X0,X1] :
( ~ smaller(age(X0,X1),tau)
| ~ robust_position(X0)
| ~ positional_advantage(X0,X1) ),
inference(resolution,[],[f36,f39]) ).
fof(f98,plain,
( ~ smaller_or_equal(zero,tau)
| ~ positional_advantage(sK0,sK1)
| ~ robust_position(sK0) ),
inference(superposition,[],[f36,f30]) ).
fof(f99,plain,
( ~ positional_advantage(sK0,sK1)
| ~ smaller_or_equal(zero,tau) ),
inference(forward_subsumption_resolution,[],[f98,f31]) ).
fof(f101,plain,
( ~ smaller_or_equal(zero,tau)
| ~ smaller_or_equal(zero,sigma) ),
inference(resolution,[],[f99,f84]) ).
fof(f114,plain,
( ~ smaller(zero,sigma)
| ~ fragile_position(sK0)
| positional_advantage(sK0,sK1) ),
inference(superposition,[],[f82,f30]) ).
fof(f115,plain,
( positional_advantage(sK0,sK1)
| ~ smaller(zero,sigma) ),
inference(forward_subsumption_resolution,[],[f114,f32]) ).
fof(f116,plain,
( ~ smaller(zero,tau)
| ~ smaller_or_equal(zero,sigma) ),
inference(resolution,[],[f101,f39]) ).
fof(f123,plain,
( ~ smaller(zero,sigma)
| ~ smaller_or_equal(zero,tau) ),
inference(resolution,[],[f115,f99]) ).
fof(f126,plain,
( ~ smaller(zero,tau)
| ~ robust_position(sK0)
| ~ positional_advantage(sK0,sK1) ),
inference(superposition,[],[f97,f30]) ).
fof(f127,plain,
( ~ positional_advantage(sK0,sK1)
| ~ smaller(zero,tau) ),
inference(forward_subsumption_resolution,[],[f126,f31]) ).
fof(f138,plain,
( ~ smaller(zero,tau)
| ~ smaller(zero,sigma) ),
inference(resolution,[],[f127,f115]) ).
fof(f158,plain,
( ~ greater(tau,zero)
| ~ smaller_or_equal(zero,sigma) ),
inference(resolution,[],[f116,f44]) ).
fof(f193,plain,
( ~ smaller_or_equal(zero,sigma)
| tau = zero
| ~ greater_or_equal(tau,zero) ),
inference(resolution,[],[f158,f37]) ).
fof(f195,plain,
( ~ smaller_or_equal(zero,sigma)
| tau = zero ),
inference(forward_subsumption_resolution,[],[f193,f28]) ).
fof(f254,plain,
( tau = zero
| ~ greater_or_equal(tau,zero)
| ~ smaller(zero,sigma) ),
inference(resolution,[],[f67,f138]) ).
fof(f256,plain,
( sigma = zero
| ~ greater_or_equal(sigma,zero)
| ~ smaller_or_equal(zero,tau) ),
inference(resolution,[],[f67,f123]) ).
fof(f259,plain,
( ~ smaller_or_equal(zero,tau)
| sigma = zero ),
inference(forward_subsumption_resolution,[],[f256,f29]) ).
fof(f260,plain,
( ~ smaller(zero,sigma)
| tau = zero ),
inference(forward_subsumption_resolution,[],[f254,f28]) ).
fof(f275,plain,
( tau = zero
| sigma = zero
| ~ greater_or_equal(sigma,zero) ),
inference(resolution,[],[f260,f67]) ).
fof(f277,plain,
( tau = zero
| sigma = zero ),
inference(forward_subsumption_resolution,[],[f275,f29]) ).
fof(f391,plain,
( ~ smaller_or_equal(tau,tau)
| sigma = tau
| sigma = zero ),
inference(superposition,[],[f259,f277]) ).
fof(f395,plain,
( sigma != tau
| sigma = zero ),
inference(equality_factoring,[],[f277]) ).
fof(f396,plain,
( sigma = tau
| sigma = zero ),
inference(forward_subsumption_resolution,[],[f391,f45]) ).
fof(f461,plain,
sigma = zero,
inference(forward_subsumption_resolution,[],[f396,f395]) ).
fof(f482,plain,
( ~ smaller_or_equal(sigma,sigma)
| sigma = tau ),
inference(superposition,[],[f195,f461]) ).
fof(f492,plain,
sigma = tau,
inference(forward_subsumption_resolution,[],[f482,f45]) ).
fof(f511,plain,
( ~ smaller_or_equal(zero,sigma)
| ~ smaller_or_equal(zero,sigma) ),
inference(superposition,[],[f101,f492]) ).
fof(f537,plain,
~ smaller_or_equal(zero,sigma),
inference(duplicate_literal_removal,[],[f511]) ).
fof(f546,plain,
~ smaller_or_equal(sigma,sigma),
inference(forward_demodulation,[],[f537,f461]) ).
fof(f551,plain,
$false,
inference(forward_subsumption_resolution,[],[f546,f45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT058+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.39 % Computer : n005.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Sun Sep 27 17:29:47 UTC 2026
% 0.14/0.39 % CPUTime :
% 0.14/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.42 Running first-order theorem proving
% 0.14/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.61/1.13 % (44172)Detected formulas, will run a generic FOF schedule.
% 1.61/1.13 % (44181)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3432797184:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.61/1.13 % (44181)First to succeed.
% 1.61/1.13 % (44181)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-44172"
% 1.61/1.13 % (44180)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1689021191:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.61/1.13 % (44178)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=909171717:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.61/1.13 % (44183)dis-21_1_sil=8000:lcm=predicate:random_seed=4169605446:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 1.61/1.13 % (44182)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=77473149:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.61/1.13 % (44177)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=571250960:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.61/1.13 % (44179)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2899901442:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.61/1.13 % (44180)Refutation not found, incomplete strategy
% 1.61/1.13 % (44180)------------------------------
% 1.61/1.13 % (44180)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.61/1.13 % (44180)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.61/1.13 % (44180)CaDiCaL version: 2.1.3
% 1.61/1.13 % (44180)Termination reason: Refutation not found, incomplete strategy
% 1.61/1.13 % (44180)Time elapsed: 0.002 s
% 1.61/1.13 % (44180)Peak memory usage: 88 MB
% 1.61/1.13 % (44180)Instructions burned: 1 (million)
% 1.61/1.13 % (44182)Also succeeded, but the first one will report.
% 1.61/1.13 % (44183)Instruction limit reached!
% 1.61/1.13 % (44183)------------------------------
% 1.61/1.13 % (44183)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.61/1.13 % (44183)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.61/1.13 % (44183)CaDiCaL version: 2.1.3
% 1.61/1.13 % (44183)Termination reason: Instruction limit
% 1.61/1.13 % (44183)Termination phase: Saturation
% 1.61/1.13 % (44183)Time elapsed: 0.052 s
% 1.61/1.13 % (44183)Peak memory usage: 88 MB
% 1.61/1.13 % (44183)Instructions burned: 129 (million)
% 1.61/1.13 % (44181)Refutation found. Thanks to Tanya!
% 1.61/1.13 % SZS status Theorem for theBenchmark
% 1.61/1.13 % SZS output start Proof for theBenchmark
% See solution above
% 2.55/1.31 % (44181)------------------------------
% 2.55/1.31 % (44181)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.55/1.31 % (44181)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/1.31 % (44181)CaDiCaL version: 2.1.3
% 2.55/1.31 % (44181)Termination reason: Refutation
% 2.55/1.31 % (44181)Time elapsed: 0.006 s
% 2.55/1.31 % (44181)Peak memory usage: 88 MB
% 2.55/1.31 % (44181)Instructions burned: 17 (million)
% 2.55/1.31 % (44181)------------------------------
% 2.55/1.31 % (44181)------------------------------
% 2.55/1.31 % (44172)Success in time 0.272 s
% 2.55/1.31 % Vampire exiting
%------------------------------------------------------------------------------