%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI638_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 : 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 09:33:33 AM UTC 2026
% Result : Theorem 4.14s 1.62s
% Output : Refutation 4.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 25 ( 22 unt; 0 typ; 3 def)
% Number of atoms : 28 ( 2 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 8 ~; 0 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number arithmetic : 83 ( 19 atm; 41 fun; 19 num; 4 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 : 7 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 9 ( 5 usr; 6 con; 0-2 aty)
% Number of variables : 4 ( 4 !; 0 ?; 4 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
a: $real ).
tff(func_def_1,type,
b: $real ).
tff(func_def_2,type,
c: $real ).
tff(func_def_3,type,
d: $real ).
tff(func_def_4,type,
f: $real > $real ).
tff(f1,axiom,
! [X0: $real,X1: $real] : ( f($sum(X0,X1)) = $product(f(X0),f(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f_feature) ).
tff(f2,axiom,
$greater(f($sum(a,b)),2/1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis) ).
tff(f3,axiom,
$greater(f($sum(c,d)),2/1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_01) ).
tff(f4,conjecture,
$greater(f($sum(a,$sum(b,$sum(c,d)))),4/1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conclusion) ).
tff(f5,negated_conjecture,
~ $greater(f($sum(a,$sum(b,$sum(c,d)))),4/1),
inference(negated_conjecture,[status(cth)],[f4]) ).
tff(f6,plain,
$less(2/1,f($sum(a,b))),
inference(theory_normalization,[],[f2]) ).
tff(f7,plain,
~ $less(4/1,f($sum(a,$sum(b,$sum(c,d))))),
inference(theory_normalization,[],[f5]) ).
tff(f8,plain,
$less(2/1,f($sum(c,d))),
inference(theory_normalization,[],[f3]) ).
tff(f9,plain,
~ $less(4/1,f($sum(a,$sum(b,$sum(c,d))))),
inference(flattening,[],[f7]) ).
tff(f10,plain,
$less(2/1,f($sum(c,d))),
inference(cnf_transformation,[],[f8]) ).
tff(f11,plain,
! [X0: $real,X1: $real] : ( f($sum(X0,X1)) = $product(f(X0),f(X1)) ),
inference(cnf_transformation,[],[f1]) ).
tff(f12,plain,
~ $less(4/1,f($sum(a,$sum(b,$sum(c,d))))),
inference(cnf_transformation,[],[f9]) ).
tff(f13,plain,
$less(2/1,f($sum(a,b))),
inference(cnf_transformation,[],[f6]) ).
tff(f14,plain,
$less(2/1,$product(f(c),f(d))),
inference(forward_demodulation,[],[f10,f11]) ).
tff(f15,plain,
~ $less(4/1,$product(f(a),f($sum(b,$sum(c,d))))),
inference(forward_demodulation,[],[f12,f11]) ).
tff(f16,plain,
$less(2/1,$product(f(a),f(b))),
inference(forward_demodulation,[],[f13,f11]) ).
tff(f18,definition,
( spl0_1
<=> $less(2/1,$product(f(c),f(d))) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
tff(f21,plain,
spl0_1,
inference(avatar_split_clause,[],[f14,f18]) ).
tff(f22,plain,
~ $less(4/1,$product(f(a),$product(f(b),f($sum(c,d))))),
inference(forward_demodulation,[],[f15,f11]) ).
tff(f24,definition,
( spl0_2
<=> $less(2/1,$product(f(a),f(b))) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
tff(f27,plain,
spl0_2,
inference(avatar_split_clause,[],[f16,f24]) ).
tff(f28,plain,
~ $less(4/1,$product(f(a),$product(f(b),$product(f(c),f(d))))),
inference(forward_demodulation,[],[f22,f11]) ).
tff(f30,definition,
( spl0_3
<=> $less(4/1,$product(f(a),$product(f(b),$product(f(c),f(d))))) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
tff(f33,plain,
~ spl0_3,
inference(avatar_split_clause,[],[f28,f30]) ).
tff(f34,plain,
$false,
inference(avatar_smt_refutation,[],[f33,f27,f21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI638_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.25 % Computer : n006.cluster.edu
% 0.09/0.25 % Model : x86_64 x86_64
% 0.09/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.25 % Memory : 8046.5625MB
% 0.09/0.25 % OS : Linux 6.8.0-71-generic
% 0.09/0.25 % CPULimit : 300
% 0.09/0.25 % WCLimit : 300
% 0.09/0.25 % DateTime : Mon Sep 28 20:54:10 UTC 2026
% 0.09/0.25 % CPUTime :
% 0.09/0.25 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.31 Running first-order theorem proving
% 0.25/0.31 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
% 4.14/1.62 % (186494)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 4.14/1.62 % (186504)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=186891208:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 4.14/1.62 % (186503)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=2342181073:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 4.14/1.62 % (186503)Instruction limit reached!
% 4.14/1.62 % (186503)------------------------------
% 4.14/1.62 % (186503)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.14/1.62 % (186503)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.14/1.62 % (186503)CaDiCaL version: 2.1.3
% 4.14/1.62 % (186503)Termination reason: Instruction limit
% 4.14/1.62 % (186503)Termination phase: Saturation
% 4.14/1.62 % (186503)Time elapsed: 0.005 s
% 4.14/1.62 % (186503)Peak memory usage: 89 MB
% 4.14/1.62 % (186503)Instructions burned: 4 (million)
% 4.14/1.62 % (186504)First to succeed.
% 4.14/1.62 % (186504)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-186494"
% 4.14/1.62 % (186501)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=2486880132:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 4.14/1.62 % (186499)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=1571169837:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 4.14/1.62 % (186500)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=990908687:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 4.14/1.62 % (186502)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=1244455291:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 4.14/1.62 % (186505)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=3393437605:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 4.14/1.62 % (186502)Instruction limit reached!
% 4.14/1.62 % (186502)------------------------------
% 4.14/1.62 % (186502)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.14/1.62 % (186502)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.14/1.62 % (186502)CaDiCaL version: 2.1.3
% 4.14/1.62 % (186502)Termination reason: Instruction limit
% 4.14/1.62 % (186502)Termination phase: Saturation
% 4.14/1.62 % (186502)Time elapsed: 0.008 s
% 4.14/1.62 % (186502)Peak memory usage: 88 MB
% 4.14/1.62 % (186502)Instructions burned: 7 (million)
% 4.14/1.62 % (186499)Instruction limit reached!
% 4.14/1.62 % (186499)------------------------------
% 4.14/1.62 % (186499)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.14/1.62 % (186499)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.14/1.62 % (186499)CaDiCaL version: 2.1.3
% 4.14/1.62 % (186499)Termination reason: Instruction limit
% 4.14/1.62 % (186499)Termination phase: Saturation
% 4.14/1.62 % (186499)Time elapsed: 0.044 s
% 4.14/1.62 % (186499)Peak memory usage: 116 MB
% 4.14/1.62 % (186499)Instructions burned: 12 (million)
% 4.14/1.62 % (186500)Refutation not found, incomplete strategy
% 4.14/1.62 % (186500)------------------------------
% 4.14/1.62 % (186500)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.14/1.62 % (186500)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.14/1.62 % (186500)CaDiCaL version: 2.1.3
% 4.14/1.62 % (186500)Termination reason: Refutation not found, incomplete strategy
% 4.14/1.62 % (186500)Time elapsed: 0.046 s
% 4.14/1.62 % (186500)Peak memory usage: 116 MB
% 4.14/1.62 % (186500)Instructions burned: 10 (million)
% 4.14/1.62 % (186505)Instruction limit reached!
% 4.14/1.62 % (186505)------------------------------
% 4.14/1.62 % (186505)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.14/1.62 % (186505)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.14/1.62 % (186505)CaDiCaL version: 2.1.3
% 4.14/1.62 % (186505)Termination reason: Instruction limit
% 4.14/1.62 % (186505)Termination phase: Saturation
% 4.14/1.62 % (186505)Time elapsed: 0.073 s
% 4.14/1.62 % (186505)Peak memory usage: 117 MB
% 4.14/1.62 % (186505)Instructions burned: 33 (million)
% 4.14/1.62 % (186504)Refutation found. Thanks to Tanya!
% 4.14/1.62 % SZS status Theorem for theBenchmark
% 4.14/1.62 % SZS output start Proof for theBenchmark
% See solution above
% 4.14/1.63 % (186504)------------------------------
% 4.14/1.63 % (186504)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.14/1.63 % (186504)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.14/1.63 % (186504)CaDiCaL version: 2.1.3
% 4.14/1.63 % (186504)Termination reason: Refutation
% 4.14/1.63 % (186504)Time elapsed: 0.034 s
% 4.14/1.63 % (186504)Peak memory usage: 117 MB
% 4.14/1.63 % (186504)Instructions burned: 19 (million)
% 4.14/1.63 % (186504)------------------------------
% 4.14/1.63 % (186504)------------------------------
% 4.14/1.63 % (186494)Success in time 0.445 s
% 4.14/1.63 % Vampire exiting
%------------------------------------------------------------------------------