%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI634_1 : TPTP v9.3.1. Released v6.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 09:33:32 AM UTC 2026
% Result : Theorem 2.86s 1.18s
% Output : Refutation 2.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 18
% Syntax : Number of formulae : 42 ( 30 unt; 0 typ; 14 def)
% Number of atoms : 54 ( 14 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 24 ( 12 ~; 3 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number arithmetic : 62 ( 18 atm; 26 fun; 15 num; 3 var)
% Number of types : 1 ( 0 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 9 usr; 10 prp; 0-2 aty)
% Number of functors : 15 ( 10 usr; 12 con; 0-2 aty)
% Number of variables : 3 ( 3 !; 0 ?; 3 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
u: $real ).
tff(func_def_1,type,
v: $real ).
tff(func_def_2,type,
w: $real ).
tff(func_def_3,type,
x: $real ).
tff(func_def_4,type,
f: $real > $real ).
tff(func_def_10,type,
sF0: $real ).
tff(func_def_11,type,
sF1: $real ).
tff(func_def_12,type,
sF2: $real ).
tff(func_def_13,type,
sF3: $real ).
tff(func_def_14,type,
sF4: $real ).
tff(f1,axiom,
! [X0: $real] : $lesseq(f(X0),2/1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f_less_equal_2) ).
tff(f2,axiom,
$less(u,v),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis) ).
tff(f3,axiom,
$greater(w,0/1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_01) ).
tff(f4,conjecture,
$less($sum(u,$product(w,$sum(-1/1,f(x)))),$sum(v,w)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conclusion) ).
tff(f5,negated_conjecture,
~ $less($sum(u,$product(w,$sum(-1/1,f(x)))),$sum(v,w)),
inference(negated_conjecture,[status(cth)],[f4]) ).
tff(f6,plain,
! [X0: $real] : ~ $less(2/1,f(X0)),
inference(theory_normalization,[],[f1]) ).
tff(f7,plain,
$less(0/1,w),
inference(theory_normalization,[],[f3]) ).
tff(f8,plain,
~ $less($sum(u,$product(w,$sum(-1/1,f(x)))),$sum(v,w)),
inference(flattening,[],[f5]) ).
tff(f9,plain,
$less(0/1,w),
inference(cnf_transformation,[],[f7]) ).
tff(f10,plain,
~ $less($sum(u,$product(w,$sum(-1/1,f(x)))),$sum(v,w)),
inference(cnf_transformation,[],[f8]) ).
tff(f11,plain,
$less(u,v),
inference(cnf_transformation,[],[f2]) ).
tff(f12,plain,
! [X0: $real] : ~ $less(2/1,f(X0)),
inference(cnf_transformation,[],[f6]) ).
tff(f13,definition,
sF0 = f(x),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
tff(f14,plain,
f(x) = sF0,
inference(reorient_equations,[],[f13]) ).
tff(f15,definition,
sF1 = $sum(-1/1,sF0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
tff(f16,definition,
sF2 = $product(w,sF1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
tff(f17,definition,
sF3 = $sum(u,sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
tff(f18,plain,
$sum(u,sF2) = sF3,
inference(reorient_equations,[],[f17]) ).
tff(f19,definition,
sF4 = $sum(v,w),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
tff(f20,plain,
$sum(v,w) = sF4,
inference(reorient_equations,[],[f19]) ).
tff(f21,plain,
~ $less(sF3,sF4),
inference(definition_folding,[],[f10,f20,f18,f16,f15,f14]) ).
tff(f23,definition,
( spl5_1
<=> $less(0/1,w) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
tff(f26,plain,
spl5_1,
inference(avatar_split_clause,[],[f9,f23]) ).
tff(f28,definition,
( spl5_2
<=> ( sF2 = $product(w,sF1) ) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
tff(f31,plain,
spl5_2,
inference(avatar_split_clause,[],[f16,f28]) ).
tff(f33,definition,
( spl5_3
<=> ( sF1 = $sum(-1/1,sF0) ) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
tff(f36,plain,
spl5_3,
inference(avatar_split_clause,[],[f15,f33]) ).
tff(f38,definition,
( spl5_4
<=> $less(u,v) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
tff(f41,plain,
spl5_4,
inference(avatar_split_clause,[],[f11,f38]) ).
tff(f43,definition,
( spl5_5
<=> $less(sF3,sF4) ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
tff(f46,plain,
~ spl5_5,
inference(avatar_split_clause,[],[f21,f43]) ).
tff(f48,definition,
( spl5_6
<=> ( $sum(u,sF2) = sF3 ) ),
introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition]) ).
tff(f51,plain,
spl5_6,
inference(avatar_split_clause,[],[f18,f48]) ).
tff(f53,definition,
( spl5_7
<=> ( f(x) = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl5_7])],[avatar_definition]) ).
tff(f55,plain,
( ( f(x) = sF0 )
| ~ spl5_7 ),
inference(avatar_component_clause,[],[f53]) ).
tff(f56,plain,
spl5_7,
inference(avatar_split_clause,[],[f14,f53]) ).
tff(f58,definition,
( spl5_8
<=> ( $sum(v,w) = sF4 ) ),
introduced(definition,[new_symbols(definition,[spl5_8])],[avatar_definition]) ).
tff(f61,plain,
spl5_8,
inference(avatar_split_clause,[],[f20,f58]) ).
tff(f62,plain,
( ~ $less(2/1,sF0)
| ~ spl5_7 ),
inference(superposition,[],[f12,f55]) ).
tff(f64,definition,
( spl5_9
<=> $less(2/1,sF0) ),
introduced(definition,[new_symbols(definition,[spl5_9])],[avatar_definition]) ).
tff(f67,plain,
( ~ spl5_9
| ~ spl5_7 ),
inference(avatar_split_clause,[],[f62,f53,f64]) ).
tff(f68,plain,
$false,
inference(avatar_smt_refutation,[],[f67,f61,f56,f51,f46,f41,f36,f31,f26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ARI634_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n010.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 20:54:32 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running first-order theorem proving
% 0.08/0.23 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
% 2.86/1.18 % (2320877)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 2.86/1.18 % (2320883)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=3700506028:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 2.86/1.18 % (2320883)First to succeed.
% 2.86/1.18 % (2320883)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2320877"
% 2.86/1.18 % (2320882)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=357504094:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 2.86/1.18 % (2320886)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=3106536211:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 2.86/1.18 % (2320887)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=1522895568:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 2.86/1.18 % (2320885)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=2614308546:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 2.86/1.18 % (2320884)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=4262385041:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 2.86/1.18 % (2320888)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=1410393358:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 2.86/1.18 % (2320886)Instruction limit reached!
% 2.86/1.18 % (2320886)------------------------------
% 2.86/1.18 % (2320886)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.86/1.18 % (2320886)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.86/1.18 % (2320886)CaDiCaL version: 2.1.3
% 2.86/1.18 % (2320886)Termination reason: Instruction limit
% 2.86/1.18 % (2320886)Termination phase: Saturation
% 2.86/1.18 % (2320886)Time elapsed: 0.003 s
% 2.86/1.18 % (2320886)Peak memory usage: 88 MB
% 2.86/1.18 % (2320886)Instructions burned: 4 (million)
% 2.86/1.18 % (2320885)Instruction limit reached!
% 2.86/1.18 % (2320885)------------------------------
% 2.86/1.18 % (2320885)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.86/1.18 % (2320885)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.86/1.18 % (2320885)CaDiCaL version: 2.1.3
% 2.86/1.18 % (2320885)Termination reason: Instruction limit
% 2.86/1.18 % (2320885)Termination phase: Saturation
% 2.86/1.18 % (2320885)Time elapsed: 0.005 s
% 2.86/1.18 % (2320885)Peak memory usage: 88 MB
% 2.86/1.18 % (2320885)Instructions burned: 8 (million)
% 2.86/1.18 % (2320887)Refutation not found, incomplete strategy
% 2.86/1.18 % (2320887)------------------------------
% 2.86/1.18 % (2320887)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.86/1.18 % (2320887)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.86/1.18 % (2320887)CaDiCaL version: 2.1.3
% 2.86/1.18 % (2320887)Termination reason: Refutation not found, incomplete strategy
% 2.86/1.18 % (2320887)Time elapsed: 0.030 s
% 2.86/1.18 % (2320887)Peak memory usage: 116 MB
% 2.86/1.18 % (2320887)Instructions burned: 7 (million)
% 2.86/1.18 % (2320882)Instruction limit reached!
% 2.86/1.18 % (2320882)------------------------------
% 2.86/1.18 % (2320882)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.86/1.18 % (2320882)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.86/1.18 % (2320882)CaDiCaL version: 2.1.3
% 2.86/1.18 % (2320882)Termination reason: Instruction limit
% 2.86/1.18 % (2320882)Termination phase: Saturation
% 2.86/1.18 % (2320882)Time elapsed: 0.032 s
% 2.86/1.18 % (2320882)Peak memory usage: 117 MB
% 2.86/1.18 % (2320882)Instructions burned: 12 (million)
% 2.86/1.18 % (2320888)Also succeeded, but the first one will report.
% 2.86/1.18 % (2320883)Refutation found. Thanks to Tanya!
% 2.86/1.18 % SZS status Theorem for theBenchmark
% 2.86/1.18 % SZS output start Proof for theBenchmark
% See solution above
% 2.86/1.18 % (2320883)------------------------------
% 2.86/1.18 % (2320883)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.86/1.18 % (2320883)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.86/1.18 % (2320883)CaDiCaL version: 2.1.3
% 2.86/1.18 % (2320883)Termination reason: Refutation
% 2.86/1.18 % (2320883)Time elapsed: 0.023 s
% 2.86/1.18 % (2320883)Peak memory usage: 117 MB
% 2.86/1.18 % (2320883)Instructions burned: 13 (million)
% 2.86/1.18 % (2320883)------------------------------
% 2.86/1.18 % (2320883)------------------------------
% 2.86/1.18 % (2320877)Success in time 0.315 s
% 2.86/1.18 % Vampire exiting
%------------------------------------------------------------------------------