%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW579_2 : TPTP v9.3.1. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 01:30:51 PM UTC 2026
% Result : Theorem 1.08s 0.95s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 32 ( 19 unt; 0 typ; 9 def)
% Number of atoms : 117 ( 18 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 135 ( 50 ~; 4 |; 52 &)
% ( 5 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number arithmetic : 369 ( 88 atm; 149 fun; 102 num; 30 var)
% Number of types : 7 ( 4 usr; 2 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 6 usr; 6 prp; 0-2 aty)
% Number of functors : 30 ( 24 usr; 23 con; 0-4 aty)
% Number of variables : 30 ( 18 !; 12 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
uni: $tType ).
tff(type_def_6,type,
ty: $tType ).
tff(type_def_7,type,
bool: $tType ).
tff(type_def_8,type,
tuple0: $tType ).
tff(func_def_0,type,
witness: ty > uni ).
tff(func_def_1,type,
int: ty ).
tff(func_def_2,type,
real: ty ).
tff(func_def_3,type,
bool1: ty ).
tff(func_def_4,type,
true: bool ).
tff(func_def_5,type,
false: bool ).
tff(func_def_6,type,
match_bool: ( ty * bool * uni * uni ) > uni ).
tff(func_def_7,type,
tuple01: ty ).
tff(func_def_8,type,
tuple02: tuple0 ).
tff(func_def_9,type,
qtmark: ty ).
tff(func_def_18,type,
min: ( $real * $real ) > $real ).
tff(func_def_19,type,
max: ( $real * $real ) > $real ).
tff(func_def_25,type,
sK0: $real ).
tff(func_def_26,type,
sK1: $real ).
tff(func_def_27,type,
sK2: $real ).
tff(func_def_28,type,
sK3: $int ).
tff(func_def_29,type,
sF4: $real ).
tff(func_def_30,type,
sF5: $real ).
tff(func_def_31,type,
sF6: $real ).
tff(func_def_32,type,
sF7: $real ).
tff(func_def_33,type,
sF8: $real ).
tff(func_def_34,type,
sF9: $real ).
tff(func_def_35,type,
sF10: $real ).
tff(func_def_36,type,
sF11: $real ).
tff(pred_def_1,type,
sort: ( ty * uni ) > $o ).
tff(f20,conjecture,
! [X1: $real,X2: $int,X3: $real,X0: $real] :
( ( $lesseq(0/1,X0)
& $lesseq(1,X2)
& ( X1 = $product($to_real(X2),X3) )
& $less(0/1,X3) )
=> ( ~ ( $less(1/1,X1)
& $less(X0,X1) )
=> ( $lesseq($product($to_real(X2),X3),max(X0,1/1))
=> ( $less(0/1,$quotient(1/1,X3))
=> ( $lesseq($product($product($to_real(X2),X3),$quotient(1/1,X3)),$product(max(X0,1/1),$quotient(1/1,X3)))
=> ( $lesseq($quotient($product($to_real(X2),X3),X3),$quotient(max(X0,1/1),X3))
=> $lesseq($to_real(X2),$quotient(max(X0,1/1),X3)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wP_parameter_sqrt) ).
tff(f21,negated_conjecture,
~ ! [X1: $real,X2: $int,X3: $real,X0: $real] :
( ( $lesseq(0/1,X0)
& $lesseq(1,X2)
& ( X1 = $product($to_real(X2),X3) )
& $less(0/1,X3) )
=> ( ~ ( $less(1/1,X1)
& $less(X0,X1) )
=> ( $lesseq($product($to_real(X2),X3),max(X0,1/1))
=> ( $less(0/1,$quotient(1/1,X3))
=> ( $lesseq($product($product($to_real(X2),X3),$quotient(1/1,X3)),$product(max(X0,1/1),$quotient(1/1,X3)))
=> ( $lesseq($quotient($product($to_real(X2),X3),X3),$quotient(max(X0,1/1),X3))
=> $lesseq($to_real(X2),$quotient(max(X0,1/1),X3)) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
tff(f24,plain,
~ ! [X1: $real,X2: $int,X3: $real,X0: $real] :
( ( ~ $less(X0,0/1)
& ~ $less(X2,1)
& ( X1 = $product($to_real(X2),X3) )
& $less(0/1,X3) )
=> ( ~ ( $less(1/1,X1)
& $less(X0,X1) )
=> ( ~ $less(max(X0,1/1),$product($to_real(X2),X3))
=> ( $less(0/1,$quotient(1/1,X3))
=> ( ~ $less($product(max(X0,1/1),$quotient(1/1,X3)),$product($product($to_real(X2),X3),$quotient(1/1,X3)))
=> ( ~ $less($quotient(max(X0,1/1),X3),$quotient($product($to_real(X2),X3),X3))
=> ~ $less($quotient(max(X0,1/1),X3),$to_real(X2)) ) ) ) ) ) ),
inference(theory_normalization,[],[f21]) ).
tff(f57,plain,
! [X0: $real,X1: $real] : ( $product(X0,X1) = $product(X1,X0) ),
introduced(definition,[],[tha_commutativity]) ).
tff(f69,plain,
~ ! [X0: $real,X1: $int,X2: $real,X3: $real] :
( ( $less(0/1,X2)
& ~ $less(X3,0/1)
& ( $product($to_real(X1),X2) = X0 )
& ~ $less(X1,1) )
=> ( ~ ( $less(1/1,X0)
& $less(X3,X0) )
=> ( ~ $less(max(X3,1/1),$product($to_real(X1),X2))
=> ( $less(0/1,$quotient(1/1,X2))
=> ( ~ $less($product(max(X3,1/1),$quotient(1/1,X2)),$product($product($to_real(X1),X2),$quotient(1/1,X2)))
=> ( ~ $less($quotient(max(X3,1/1),X2),$quotient($product($to_real(X1),X2),X2))
=> ~ $less($quotient(max(X3,1/1),X2),$to_real(X1)) ) ) ) ) ) ),
inference(rectify,[],[f24]) ).
tff(f79,plain,
? [X0: $real,X1: $int,X2: $real,X3: $real] :
( $less($quotient(max(X3,1/1),X2),$to_real(X1))
& ~ $less($quotient(max(X3,1/1),X2),$quotient($product($to_real(X1),X2),X2))
& ~ $less($product(max(X3,1/1),$quotient(1/1,X2)),$product($product($to_real(X1),X2),$quotient(1/1,X2)))
& $less(0/1,$quotient(1/1,X2))
& ~ $less(max(X3,1/1),$product($to_real(X1),X2))
& ( ~ $less(X3,X0)
| ~ $less(1/1,X0) )
& $less(0/1,X2)
& ~ $less(X3,0/1)
& ( $product($to_real(X1),X2) = X0 )
& ~ $less(X1,1) ),
inference(ennf_transformation,[],[f69]) ).
tff(f80,plain,
? [X3: $real,X2: $real,X0: $real,X1: $int] :
( ( $product($to_real(X1),X2) = X0 )
& ~ $less($product(max(X3,1/1),$quotient(1/1,X2)),$product($product($to_real(X1),X2),$quotient(1/1,X2)))
& ~ $less($quotient(max(X3,1/1),X2),$quotient($product($to_real(X1),X2),X2))
& $less($quotient(max(X3,1/1),X2),$to_real(X1))
& ( ~ $less(X3,X0)
| ~ $less(1/1,X0) )
& $less(0/1,X2)
& ~ $less(X1,1)
& ~ $less(X3,0/1)
& $less(0/1,$quotient(1/1,X2))
& ~ $less(max(X3,1/1),$product($to_real(X1),X2)) ),
inference(flattening,[],[f79]) ).
tff(f93,plain,
? [X0: $real,X1: $real,X2: $real,X3: $int] :
( ( $product($to_real(X3),X1) = X2 )
& ~ $less($product(max(X0,1/1),$quotient(1/1,X1)),$product($product($to_real(X3),X1),$quotient(1/1,X1)))
& ~ $less($quotient(max(X0,1/1),X1),$quotient($product($to_real(X3),X1),X1))
& $less($quotient(max(X0,1/1),X1),$to_real(X3))
& ( ~ $less(X0,X2)
| ~ $less(1/1,X2) )
& $less(0/1,X1)
& ~ $less(X3,1)
& ~ $less(X0,0/1)
& $less(0/1,$quotient(1/1,X1))
& ~ $less(max(X0,1/1),$product($to_real(X3),X1)) ),
inference(rectify,[],[f80]) ).
tff(f94,plain,
( ( $product($to_real(sK3),sK1) = sK2 )
& ~ $less($product(max(sK0,1/1),$quotient(1/1,sK1)),$product($product($to_real(sK3),sK1),$quotient(1/1,sK1)))
& ~ $less($quotient(max(sK0,1/1),sK1),$quotient($product($to_real(sK3),sK1),sK1))
& $less($quotient(max(sK0,1/1),sK1),$to_real(sK3))
& ( ~ $less(sK0,sK2)
| ~ $less(1/1,sK2) )
& $less(0/1,sK1)
& ~ $less(sK3,1)
& ~ $less(sK0,0/1)
& $less(0/1,$quotient(1/1,sK1))
& ~ $less(max(sK0,1/1),$product($to_real(sK3),sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f93]) ).
tff(f102,plain,
~ $less(max(sK0,1/1),$product($to_real(sK3),sK1)),
inference(cnf_transformation,[],[f94]) ).
tff(f106,plain,
$less(0/1,sK1),
inference(cnf_transformation,[],[f94]) ).
tff(f108,plain,
$less($quotient(max(sK0,1/1),sK1),$to_real(sK3)),
inference(cnf_transformation,[],[f94]) ).
tff(f135,definition,
sF4 = $to_real(sK3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
tff(f136,plain,
$to_real(sK3) = sF4,
inference(reorient_equations,[],[f135]) ).
tff(f137,definition,
sF5 = $product(sF4,sK1),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
tff(f139,definition,
sF6 = max(sK0,1/1),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
tff(f140,plain,
max(sK0,1/1) = sF6,
inference(reorient_equations,[],[f139]) ).
tff(f147,definition,
sF10 = $quotient(sF6,sK1),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
tff(f150,plain,
$less(sF10,sF4),
inference(definition_folding,[],[f108,f136,f147,f140]) ).
tff(f152,plain,
~ $less(sF6,sF5),
inference(definition_folding,[],[f102,f137,f136,f140]) ).
tff(f154,definition,
( spl12_1
<=> $less(sF10,sF4) ),
introduced(definition,[new_symbols(definition,[spl12_1])],[avatar_definition]) ).
tff(f157,plain,
spl12_1,
inference(avatar_split_clause,[],[f150,f154]) ).
tff(f187,plain,
sF5 = $product(sK1,sF4),
inference(forward_demodulation,[],[f137,f57]) ).
tff(f199,definition,
( spl12_10
<=> $less(sF6,sF5) ),
introduced(definition,[new_symbols(definition,[spl12_10])],[avatar_definition]) ).
tff(f202,plain,
~ spl12_10,
inference(avatar_split_clause,[],[f152,f199]) ).
tff(f209,definition,
( spl12_12
<=> $less(0/1,sK1) ),
introduced(definition,[new_symbols(definition,[spl12_12])],[avatar_definition]) ).
tff(f212,plain,
spl12_12,
inference(avatar_split_clause,[],[f106,f209]) ).
tff(f214,definition,
( spl12_13
<=> ( sF10 = $quotient(sF6,sK1) ) ),
introduced(definition,[new_symbols(definition,[spl12_13])],[avatar_definition]) ).
tff(f217,plain,
spl12_13,
inference(avatar_split_clause,[],[f147,f214]) ).
tff(f245,definition,
( spl12_19
<=> ( sF5 = $product(sK1,sF4) ) ),
introduced(definition,[new_symbols(definition,[spl12_19])],[avatar_definition]) ).
tff(f248,plain,
spl12_19,
inference(avatar_split_clause,[],[f187,f245]) ).
tff(f254,plain,
$false,
inference(avatar_smt_refutation,[],[f248,f217,f212,f202,f157]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW579_2 : TPTP v9.3.1. Released v6.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.17 % Computer : n019.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Mon Sep 28 14:20:03 UTC 2026
% 0.06/0.17 % CPUTime :
% 0.06/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.21 Running first-order theorem proving
% 0.06/0.21 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.08/0.95 % (4027518)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 1.08/0.95 % (4027529)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=2253614220:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 1.08/0.95 % (4027529)First to succeed.
% 1.08/0.95 % (4027529)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4027518"
% 1.08/0.95 % (4027524)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=1325650494:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 1.08/0.95 % (4027523)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=2722887441:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 1.08/0.95 % (4027526)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=1527990178:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 1.08/0.95 % (4027528)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=3890144876:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 1.08/0.95 % (4027527)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=2631978390:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 1.08/0.95 % (4027525)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=859919818:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 1.08/0.95 % (4027527)Instruction limit reached!
% 1.08/0.95 % (4027527)------------------------------
% 1.08/0.95 % (4027527)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.08/0.95 % (4027527)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.08/0.95 % (4027527)CaDiCaL version: 2.1.3
% 1.08/0.95 % (4027527)Termination reason: Instruction limit
% 1.08/0.95 % (4027527)Termination phase: Saturation
% 1.08/0.95 % (4027527)Time elapsed: 0.003 s
% 1.08/0.95 % (4027527)Peak memory usage: 89 MB
% 1.08/0.95 % (4027527)Instructions burned: 4 (million)
% 1.08/0.95 % (4027526)Instruction limit reached!
% 1.08/0.95 % (4027526)------------------------------
% 1.08/0.95 % (4027526)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.08/0.95 % (4027526)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.08/0.95 % (4027526)CaDiCaL version: 2.1.3
% 1.08/0.95 % (4027526)Termination reason: Instruction limit
% 1.08/0.95 % (4027526)Termination phase: Saturation
% 1.08/0.95 % (4027526)Time elapsed: 0.005 s
% 1.08/0.95 % (4027526)Peak memory usage: 89 MB
% 1.08/0.95 % (4027526)Instructions burned: 8 (million)
% 1.08/0.95 % (4027523)Instruction limit reached!
% 1.08/0.95 % (4027523)------------------------------
% 1.08/0.95 % (4027523)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.08/0.95 % (4027523)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.08/0.95 % (4027523)CaDiCaL version: 2.1.3
% 1.08/0.95 % (4027523)Termination reason: Instruction limit
% 1.08/0.95 % (4027523)Termination phase: Saturation
% 1.08/0.95 % (4027523)Time elapsed: 0.031 s
% 1.08/0.95 % (4027523)Peak memory usage: 117 MB
% 1.08/0.95 % (4027523)Instructions burned: 13 (million)
% 1.08/0.95 % (4027524)Also succeeded, but the first one will report.
% 1.08/0.95 % (4027528)Also succeeded, but the first one will report.
% 1.08/0.95 % (4027525)Instruction limit reached!
% 1.08/0.95 % (4027525)------------------------------
% 1.08/0.95 % (4027525)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.08/0.95 % (4027525)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.08/0.95 % (4027525)CaDiCaL version: 2.1.3
% 1.08/0.95 % (4027525)Termination reason: Instruction limit
% 1.08/0.95 % (4027525)Termination phase: Saturation
% 1.08/0.95 % (4027525)Time elapsed: 0.124 s
% 1.08/0.95 % (4027525)Peak memory usage: 117 MB
% 1.08/0.95 % (4027525)Instructions burned: 202 (million)
% 1.08/0.95 % (4027529)Refutation found. Thanks to Tanya!
% 1.08/0.95 % SZS status Theorem for theBenchmark
% 1.08/0.95 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.14 % (4027529)------------------------------
% 0.17/1.14 % (4027529)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.14 % (4027529)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.14 % (4027529)CaDiCaL version: 2.1.3
% 0.17/1.14 % (4027529)Termination reason: Refutation
% 0.17/1.14 % (4027529)Time elapsed: 0.028 s
% 0.17/1.14 % (4027529)Peak memory usage: 119 MB
% 0.17/1.14 % (4027529)Instructions burned: 28 (million)
% 0.17/1.14 % (4027529)------------------------------
% 0.17/1.14 % (4027529)------------------------------
% 0.17/1.14 % (4027518)Success in time 0.296 s
% 0.17/1.14 % Vampire exiting
%------------------------------------------------------------------------------