%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP001_2 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 11:27:38 AM UTC 2026
% Result : Theorem 3.35s 1.34s
% Output : Refutation 3.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 1
% Syntax : Number of formulae : 4 ( 4 unt; 0 def)
% Number of atoms : 4 ( 0 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 1 ( 1 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 0 ( 0 avg)
% Number of predicates : 3 ( 1 usr; 2 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
del: $tType ).
tff(type_def_6,type,
tp__o: $tType ).
tff(func_def_0,type,
bool: del ).
tff(func_def_1,type,
ind: del ).
tff(func_def_2,type,
arr: ( del * del ) > del ).
tff(func_def_4,type,
k: ( del * $i ) > $i ).
tff(func_def_5,type,
i: del > $i ).
tff(func_def_6,type,
inj__o: tp__o > $i ).
tff(func_def_7,type,
surj__o: $i > tp__o ).
tff(func_def_9,type,
fo__c_2Ebool_2ET: tp__o ).
tff(func_def_10,type,
c_2Emin_2E_3D: del > $i ).
tff(pred_def_1,type,
mem: ( $i * del ) > $o ).
fof(f15,conjecture,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ebool_2ETRUTH) ).
fof(f16,negated_conjecture,
~ $true,
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f17,plain,
$false,
inference(true_and_false_elimination,[],[f16]) ).
fof(f18,plain,
$false,
inference(cnf_transformation,[],[f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP001_2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n014.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 11:47:17 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 3.35/1.34 % (664979)Detected formulas, will run a generic FOF schedule.
% 3.35/1.34 % (665030)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=60805160:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.35/1.34 % (665035)dis-21_1_sil=8000:lcm=predicate:random_seed=3391938142: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)
% 3.35/1.34 % (665032)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2160473285:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.35/1.34 % (665034)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=734831288:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.35/1.34 % (665029)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=1527867808:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.35/1.34 % (665033)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1156107022:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.35/1.34 % (665031)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=2937528982:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.35/1.34 % (665032)Also succeeded, but the first one will report.
% 3.35/1.34 % (665033)First to succeed.
% 3.35/1.34 % (665035)Also succeeded, but the first one will report.
% 3.35/1.34 % (665034)Also succeeded, but the first one will report.
% 3.35/1.34 % (665033)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-664979"
% 3.35/1.34 [W927 11:47:18.597240015 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 3.35/1.34 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 3.35/1.34 [W927 11:47:18.597264079 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 3.35/1.34 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 3.35/1.34 [W927 11:47:18.597284494 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 3.35/1.34 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 3.35/1.34 [W927 11:47:18.597290354 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 3.35/1.34 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 3.35/1.34 [W927 11:47:18.597303834 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 3.35/1.34 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 3.35/1.34 [W927 11:47:18.597310408 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 3.35/1.34 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 3.35/1.34 [W927 11:47:18.597323401 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 3.35/1.34 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 3.35/1.34 [W927 11:47:18.597329566 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 3.35/1.34 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 3.35/1.34 [W927 11:47:18.597342044 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 3.35/1.34 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 3.35/1.34 [W927 11:47:18.597349441 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 3.35/1.34 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 3.35/1.34 [W927 11:47:18.597361854 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 3.35/1.34 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 3.35/1.34 [W927 11:47:18.597367358 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 3.35/1.34 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 3.35/1.34 % (665033)Refutation found. Thanks to Tanya!
% 3.35/1.34 % SZS status Theorem for theBenchmark
% 3.35/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 3.35/1.34 % (665033)------------------------------
% 3.35/1.34 % (665033)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.35/1.34 % (665033)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/1.34 % (665033)CaDiCaL version: 2.1.3
% 3.35/1.34 % (665033)Termination reason: Refutation
% 3.35/1.34 % (665033)Time elapsed: 0.001 s
% 3.35/1.34 % (665033)Peak memory usage: 87 MB
% 3.35/1.34 % (665033)------------------------------
% 3.35/1.34 % (665033)------------------------------
% 3.35/1.34 % (664979)Success in time 0.398 s
% 3.35/1.34 % Vampire exiting
%------------------------------------------------------------------------------