%------------------------------------------------------------------------------
% 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 : n002.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 : Unsatisfiable 2.94s 1.39s
% Output : Refutation 2.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 18
% Syntax : Number of formulae : 63 ( 13 unt; 7 def)
% Number of atoms : 125 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 113 ( 51 ~; 55 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 8 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 15 ( 0 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( ~ smaller(X0,X1)
| smaller_or_equal(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_smaller_or_equal_2) ).
fof(f3,axiom,
! [X0,X1] :
( X0 != X1
| smaller_or_equal(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_smaller_or_equal_3) ).
fof(f4,axiom,
! [X0,X1] :
( greater(X0,X1)
| ~ greater_or_equal(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_greater_or_equal_4) ).
fof(f8,axiom,
! [X0,X1] :
( ~ greater(X0,X1)
| smaller(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_smaller_8) ).
fof(f12,axiom,
! [X0,X1] :
( ~ smaller_or_equal(age(X0,X1),sigma)
| ~ fragile_position(X0)
| positional_advantage(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_3_30) ).
fof(f18,axiom,
! [X0,X1] :
( ~ smaller_or_equal(age(X0,X1),tau)
| ~ robust_position(X0)
| ~ positional_advantage(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_4_36) ).
fof(f25,negated_conjecture,
age(sk3,sk4) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_10_43) ).
fof(f26,negated_conjecture,
greater_or_equal(sigma,zero),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_10_44) ).
fof(f27,negated_conjecture,
greater_or_equal(tau,zero),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_10_45) ).
fof(f28,negated_conjecture,
fragile_position(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_10_46) ).
fof(f29,negated_conjecture,
robust_position(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_10_47) ).
fof(f31,plain,
! [X1] : smaller_or_equal(X1,X1),
inference(equality_resolution,[],[f3]) ).
fof(f40,plain,
! [X0,X1] :
( ~ greater_or_equal(X0,X1)
| X0 = X1
| smaller(X1,X0) ),
inference(resolution,[],[f4,f8]) ).
fof(f57,plain,
( ~ smaller_or_equal(zero,sigma)
| ~ fragile_position(sk3)
| positional_advantage(sk3,sk4) ),
inference(superposition,[],[f12,f25]) ).
fof(f58,plain,
( ~ smaller_or_equal(zero,sigma)
| positional_advantage(sk3,sk4) ),
inference(forward_subsumption_resolution,[],[f57,f28]) ).
fof(f60,definition,
( spl0_1
<=> positional_advantage(sk3,sk4) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f63,definition,
( spl0_2
<=> smaller_or_equal(zero,sigma) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f64,plain,
( ~ smaller_or_equal(zero,sigma)
| spl0_2 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f65,plain,
( spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f58,f63,f60]) ).
fof(f77,plain,
( ~ smaller_or_equal(zero,tau)
| ~ robust_position(sk3)
| ~ positional_advantage(sk3,sk4) ),
inference(superposition,[],[f18,f25]) ).
fof(f96,definition,
( spl0_4
<=> tau = zero ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f97,plain,
( tau = zero
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f96]) ).
fof(f103,definition,
( spl0_6
<=> smaller(zero,tau) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f104,plain,
( smaller(zero,tau)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f103]) ).
fof(f160,plain,
( sigma = zero
| smaller(zero,sigma) ),
inference(resolution,[],[f40,f26]) ).
fof(f161,plain,
( tau = zero
| smaller(zero,tau) ),
inference(resolution,[],[f40,f27]) ).
fof(f163,definition,
( spl0_8
<=> smaller(zero,sigma) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f164,plain,
( smaller(zero,sigma)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f163]) ).
fof(f166,definition,
( spl0_9
<=> sigma = zero ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f167,plain,
( sigma = zero
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f166]) ).
fof(f168,plain,
( spl0_8
| spl0_9 ),
inference(avatar_split_clause,[],[f160,f166,f163]) ).
fof(f176,plain,
( spl0_6
| spl0_4 ),
inference(avatar_split_clause,[],[f161,f96,f103]) ).
fof(f191,plain,
( smaller_or_equal(zero,tau)
| ~ spl0_6 ),
inference(resolution,[],[f104,f2]) ).
fof(f202,plain,
( smaller_or_equal(zero,sigma)
| ~ spl0_8 ),
inference(resolution,[],[f164,f2]) ).
fof(f203,plain,
( $false
| spl0_2
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f202,f64]) ).
fof(f204,plain,
( spl0_2
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f203]) ).
fof(f216,plain,
( ~ smaller_or_equal(sigma,sigma)
| spl0_2
| ~ spl0_9 ),
inference(superposition,[],[f64,f167]) ).
fof(f222,plain,
( $false
| spl0_2
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f216,f31]) ).
fof(f223,plain,
( spl0_2
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f222]) ).
fof(f224,plain,
( ~ smaller_or_equal(zero,tau)
| ~ positional_advantage(sk3,sk4) ),
inference(forward_subsumption_resolution,[],[f77,f29]) ).
fof(f230,definition,
( spl0_13
<=> smaller_or_equal(zero,tau) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f231,plain,
( ~ smaller_or_equal(zero,tau)
| spl0_13 ),
inference(avatar_component_clause,[],[f230]) ).
fof(f232,plain,
( ~ spl0_1
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f224,f230,f60]) ).
fof(f258,plain,
( $false
| ~ spl0_6
| spl0_13 ),
inference(forward_subsumption_resolution,[],[f191,f231]) ).
fof(f259,plain,
( ~ spl0_6
| spl0_13 ),
inference(avatar_contradiction_clause,[],[f258]) ).
fof(f274,plain,
( ~ smaller_or_equal(tau,tau)
| ~ spl0_4
| spl0_13 ),
inference(superposition,[],[f231,f97]) ).
fof(f276,plain,
( $false
| ~ spl0_4
| spl0_13 ),
inference(forward_subsumption_resolution,[],[f274,f31]) ).
fof(f277,plain,
( ~ spl0_4
| spl0_13 ),
inference(avatar_contradiction_clause,[],[f276]) ).
cnf(s1,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f65]) ).
cnf(s6,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f168]) ).
cnf(s8,plain,
( spl0_4
| spl0_6 ),
inference(sat_conversion,[],[f176]) ).
cnf(s9,plain,
( spl0_2
| ~ spl0_8 ),
inference(sat_conversion,[],[f204]) ).
cnf(s10,plain,
( spl0_2
| ~ spl0_9 ),
inference(sat_conversion,[],[f223]) ).
cnf(s12,plain,
( ~ spl0_1
| ~ spl0_13 ),
inference(sat_conversion,[],[f232]) ).
cnf(s13,plain,
( ~ spl0_6
| spl0_13 ),
inference(sat_conversion,[],[f259]) ).
cnf(s16,plain,
( ~ spl0_4
| spl0_13 ),
inference(sat_conversion,[],[f277]) ).
cnf(s21,plain,
spl0_2,
inference(rat,[],[s6,s9,s10]) ).
cnf(s22,plain,
spl0_1,
inference(rat,[],[s1,s21]) ).
cnf(s23,plain,
~ spl0_13,
inference(rat,[],[s12,s22]) ).
cnf(s25,plain,
~ spl0_4,
inference(rat,[],[s16,s23]) ).
cnf(s26,plain,
~ spl0_6,
inference(rat,[],[s13,s23]) ).
cnf(s27,plain,
$false,
inference(rat,[],[s8,s26,s25]) ).
fof(f283,plain,
$false,
inference(avatar_sat_refutation,[],[s27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % 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
% 0.08/0.37 % Computer : n002.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.38 % CPULimit : 300
% 0.08/0.38 % WCLimit : 300
% 0.08/0.38 % DateTime : Sun Sep 27 17:32:36 UTC 2026
% 0.08/0.38 % CPUTime :
% 0.08/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.41 Running first-order theorem proving
% 0.08/0.41 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
% 2.94/1.39 % (3762807)Input is clausal, will run a generic CNF schedule.
% 2.94/1.39 % (3762818)dis-21_1_sil=8000:lcm=predicate:random_seed=3119807643:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 2.94/1.39 % (3762818)Instruction limit reached!
% 2.94/1.39 % (3762818)------------------------------
% 2.94/1.39 % (3762818)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.94/1.39 % (3762818)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.94/1.39 % (3762818)CaDiCaL version: 2.1.3
% 2.94/1.39 % (3762818)Termination reason: Instruction limit
% 2.94/1.39 % (3762818)Termination phase: Saturation
% 2.94/1.39 % (3762818)Time elapsed: 0.026 s
% 2.94/1.39 % (3762818)Peak memory usage: 88 MB
% 2.94/1.39 % (3762818)Instructions burned: 121 (million)
% 2.94/1.39 % (3762816)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2309802839:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.94/1.39 % (3762813)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=856821367:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.94/1.39 % (3762815)lrs+10_1_sil=8000:sp=occurrence:random_seed=2344586204:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.94/1.39 % (3762817)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=494811401:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.94/1.39 % (3762814)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2999180587:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.94/1.39 % (3762812)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=2364405413:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.94/1.39 % (3762816)First to succeed.
% 2.94/1.39 % (3762816)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3762807"
% 2.94/1.39 % (3762815)Also succeeded, but the first one will report.
% 2.94/1.39 % (3762817)Also succeeded, but the first one will report.
% 2.94/1.39 % (3762820)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=1898715617:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 2.94/1.39 % (3762820)Also succeeded, but the first one will report.
% 2.94/1.39 % (3762816)Refutation found. Thanks to Tanya!
% 2.94/1.39 % SZS status Unsatisfiable for theBenchmark
% 2.94/1.39 % SZS output start Proof for theBenchmark
% See solution above
% 2.94/1.39 % (3762816)------------------------------
% 2.94/1.39 % (3762816)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.94/1.39 % (3762816)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.94/1.39 % (3762816)CaDiCaL version: 2.1.3
% 2.94/1.39 % (3762816)Termination reason: Refutation
% 2.94/1.39 % (3762816)Time elapsed: 0.004 s
% 2.94/1.39 % (3762816)Peak memory usage: 89 MB
% 2.94/1.39 % (3762816)Instructions burned: 8 (million)
% 2.94/1.39 % (3762816)------------------------------
% 2.94/1.39 % (3762816)------------------------------
% 2.94/1.39 % (3762807)Success in time 0.342 s
% 2.94/1.39 % Vampire exiting
%------------------------------------------------------------------------------