%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG014+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 09:07:32 AM UTC 2026
% Result : Theorem 2.94s 1.08s
% Output : Refutation 3.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 4
% Syntax : Number of formulae : 60 ( 9 unt; 3 def)
% Number of atoms : 294 ( 226 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 369 ( 135 ~; 145 |; 89 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,conjecture,
( ( op(e0,e0) = e0
& op(e1,e1) = e0
& op(e2,e2) = e0
& op(e3,e3) = e0 )
| ( op(e0,e0) = e1
& op(e1,e1) = e1
& op(e2,e2) = e1
& op(e3,e3) = e1 )
| ( op(e0,e0) = e2
& op(e1,e1) = e2
& op(e2,e2) = e2
& op(e3,e3) = e2 )
| ( op(e0,e0) = e3
& op(e1,e1) = e3
& op(e2,e2) = e3
& op(e3,e3) = e3 )
| ~ ( ( op(e0,e0) = e0
& op(e1,e1) = e0
& op(e2,e2) = e0
& op(e3,e3) = e0 )
| ( op(e0,e0) = e1
& op(e1,e1) = e1
& op(e2,e2) = e1
& op(e3,e3) = e1 )
| ( op(e0,e0) = e2
& op(e1,e1) = e2
& op(e2,e2) = e2
& op(e3,e3) = e2 )
| ( op(e0,e0) = e3
& op(e1,e1) = e3
& op(e2,e2) = e3
& op(e3,e3) = e3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f13,negated_conjecture,
~ ( ( op(e0,e0) = e0
& op(e1,e1) = e0
& op(e2,e2) = e0
& op(e3,e3) = e0 )
| ( op(e0,e0) = e1
& op(e1,e1) = e1
& op(e2,e2) = e1
& op(e3,e3) = e1 )
| ( op(e0,e0) = e2
& op(e1,e1) = e2
& op(e2,e2) = e2
& op(e3,e3) = e2 )
| ( op(e0,e0) = e3
& op(e1,e1) = e3
& op(e2,e2) = e3
& op(e3,e3) = e3 )
| ~ ( ( op(e0,e0) = e0
& op(e1,e1) = e0
& op(e2,e2) = e0
& op(e3,e3) = e0 )
| ( op(e0,e0) = e1
& op(e1,e1) = e1
& op(e2,e2) = e1
& op(e3,e3) = e1 )
| ( op(e0,e0) = e2
& op(e1,e1) = e2
& op(e2,e2) = e2
& op(e3,e3) = e2 )
| ( op(e0,e0) = e3
& op(e1,e1) = e3
& op(e2,e2) = e3
& op(e3,e3) = e3 ) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
( ( e0 != op(e0,e0)
| e0 != op(e1,e1)
| e0 != op(e2,e2)
| e0 != op(e3,e3) )
& ( op(e0,e0) != e1
| e1 != op(e1,e1)
| e1 != op(e2,e2)
| e1 != op(e3,e3) )
& ( op(e0,e0) != e2
| e2 != op(e1,e1)
| e2 != op(e2,e2)
| e2 != op(e3,e3) )
& ( op(e0,e0) != e3
| e3 != op(e1,e1)
| e3 != op(e2,e2)
| e3 != op(e3,e3) )
& ( ( op(e0,e0) = e0
& op(e1,e1) = e0
& op(e2,e2) = e0
& op(e3,e3) = e0 )
| ( op(e0,e0) = e1
& op(e1,e1) = e1
& op(e2,e2) = e1
& op(e3,e3) = e1 )
| ( op(e0,e0) = e2
& op(e1,e1) = e2
& op(e2,e2) = e2
& op(e3,e3) = e2 )
| ( op(e0,e0) = e3
& op(e1,e1) = e3
& op(e2,e2) = e3
& op(e3,e3) = e3 ) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f15,definition,
( ( op(e0,e0) = e3
& op(e1,e1) = e3
& op(e2,e2) = e3
& op(e3,e3) = e3 )
| ~ sP0 ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f16,definition,
( ( op(e0,e0) = e2
& op(e1,e1) = e2
& op(e2,e2) = e2
& op(e3,e3) = e2 )
| ~ sP1 ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f17,definition,
( ( op(e0,e0) = e1
& op(e1,e1) = e1
& op(e2,e2) = e1
& op(e3,e3) = e1 )
| ~ sP2 ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f18,plain,
( ( e0 != op(e0,e0)
| e0 != op(e1,e1)
| e0 != op(e2,e2)
| e0 != op(e3,e3) )
& ( op(e0,e0) != e1
| e1 != op(e1,e1)
| e1 != op(e2,e2)
| e1 != op(e3,e3) )
& ( op(e0,e0) != e2
| e2 != op(e1,e1)
| e2 != op(e2,e2)
| e2 != op(e3,e3) )
& ( op(e0,e0) != e3
| e3 != op(e1,e1)
| e3 != op(e2,e2)
| e3 != op(e3,e3) )
& ( ( op(e0,e0) = e0
& op(e1,e1) = e0
& op(e2,e2) = e0
& op(e3,e3) = e0 )
| sP2
| sP1
| sP0 ) ),
inference(definition_folding,[],[f14,f17,f16,f15]) ).
fof(f19,plain,
( ( op(e0,e0) = e1
& op(e1,e1) = e1
& op(e2,e2) = e1
& op(e3,e3) = e1 )
| ~ sP2 ),
inference(nnf_transformation,[],[f17]) ).
fof(f20,plain,
( ( op(e0,e0) = e2
& op(e1,e1) = e2
& op(e2,e2) = e2
& op(e3,e3) = e2 )
| ~ sP1 ),
inference(nnf_transformation,[],[f16]) ).
fof(f21,plain,
( ( op(e0,e0) = e3
& op(e1,e1) = e3
& op(e2,e2) = e3
& op(e3,e3) = e3 )
| ~ sP0 ),
inference(nnf_transformation,[],[f15]) ).
fof(f22,plain,
( e1 = op(e3,e3)
| ~ sP2 ),
inference(cnf_transformation,[],[f19]) ).
fof(f23,plain,
( e1 = op(e2,e2)
| ~ sP2 ),
inference(cnf_transformation,[],[f19]) ).
fof(f24,plain,
( e1 = op(e1,e1)
| ~ sP2 ),
inference(cnf_transformation,[],[f19]) ).
fof(f25,plain,
( op(e0,e0) = e1
| ~ sP2 ),
inference(cnf_transformation,[],[f19]) ).
fof(f26,plain,
( e2 = op(e3,e3)
| ~ sP1 ),
inference(cnf_transformation,[],[f20]) ).
fof(f27,plain,
( e2 = op(e2,e2)
| ~ sP1 ),
inference(cnf_transformation,[],[f20]) ).
fof(f28,plain,
( e2 = op(e1,e1)
| ~ sP1 ),
inference(cnf_transformation,[],[f20]) ).
fof(f29,plain,
( op(e0,e0) = e2
| ~ sP1 ),
inference(cnf_transformation,[],[f20]) ).
fof(f30,plain,
( e3 = op(e3,e3)
| ~ sP0 ),
inference(cnf_transformation,[],[f21]) ).
fof(f31,plain,
( e3 = op(e2,e2)
| ~ sP0 ),
inference(cnf_transformation,[],[f21]) ).
fof(f32,plain,
( e3 = op(e1,e1)
| ~ sP0 ),
inference(cnf_transformation,[],[f21]) ).
fof(f33,plain,
( op(e0,e0) = e3
| ~ sP0 ),
inference(cnf_transformation,[],[f21]) ).
fof(f34,plain,
( e0 = op(e3,e3)
| sP2
| sP1
| sP0 ),
inference(cnf_transformation,[],[f18]) ).
fof(f35,plain,
( e0 = op(e2,e2)
| sP2
| sP1
| sP0 ),
inference(cnf_transformation,[],[f18]) ).
fof(f36,plain,
( e0 = op(e1,e1)
| sP2
| sP1
| sP0 ),
inference(cnf_transformation,[],[f18]) ).
fof(f37,plain,
( e0 = op(e0,e0)
| sP2
| sP1
| sP0 ),
inference(cnf_transformation,[],[f18]) ).
fof(f38,plain,
( e3 != op(e3,e3)
| e3 != op(e1,e1)
| e3 != op(e2,e2)
| op(e0,e0) != e3 ),
inference(cnf_transformation,[],[f18]) ).
fof(f39,plain,
( e2 != op(e3,e3)
| e2 != op(e1,e1)
| e2 != op(e2,e2)
| op(e0,e0) != e2 ),
inference(cnf_transformation,[],[f18]) ).
fof(f40,plain,
( e1 != op(e3,e3)
| e1 != op(e1,e1)
| e1 != op(e2,e2)
| op(e0,e0) != e1 ),
inference(cnf_transformation,[],[f18]) ).
fof(f41,plain,
( e0 != op(e3,e3)
| e0 != op(e1,e1)
| e0 != op(e2,e2)
| e0 != op(e0,e0) ),
inference(cnf_transformation,[],[f18]) ).
fof(f179,plain,
( e0 != e0
| e0 != op(e1,e1)
| e0 != op(e2,e2)
| e0 != op(e0,e0)
| sP2
| sP1
| sP0 ),
inference(superposition,[],[f41,f34]) ).
fof(f180,plain,
( e0 != op(e1,e1)
| e0 != op(e2,e2)
| e0 != op(e0,e0)
| sP2
| sP1
| sP0 ),
inference(trivial_inequality_removal,[],[f179]) ).
fof(f181,plain,
( e0 != op(e2,e2)
| e0 != op(e0,e0)
| sP2
| sP1
| sP0 ),
inference(forward_subsumption_resolution,[],[f180,f36]) ).
fof(f182,plain,
( e0 != op(e0,e0)
| sP2
| sP1
| sP0 ),
inference(forward_subsumption_resolution,[],[f181,f35]) ).
fof(f183,plain,
( sP2
| sP1
| sP0 ),
inference(forward_subsumption_resolution,[],[f182,f37]) ).
fof(f186,plain,
( e1 != e1
| e1 != op(e1,e1)
| e1 != op(e2,e2)
| op(e0,e0) != e1
| ~ sP2 ),
inference(superposition,[],[f40,f22]) ).
fof(f190,plain,
( e1 != op(e2,e2)
| e1 != op(e1,e1)
| op(e0,e0) != e1
| ~ sP2 ),
inference(trivial_inequality_removal,[],[f186]) ).
fof(f193,plain,
( e1 != e1
| e1 != op(e1,e1)
| op(e0,e0) != e1
| ~ sP2
| ~ sP2 ),
inference(superposition,[],[f190,f23]) ).
fof(f195,plain,
( e1 != e1
| e1 != op(e1,e1)
| op(e0,e0) != e1
| ~ sP2 ),
inference(duplicate_literal_removal,[],[f193]) ).
fof(f196,plain,
( e1 != op(e1,e1)
| op(e0,e0) != e1
| ~ sP2 ),
inference(trivial_inequality_removal,[],[f195]) ).
fof(f199,plain,
( op(e0,e0) != e1
| ~ sP2 ),
inference(forward_subsumption_resolution,[],[f196,f24]) ).
fof(f202,plain,
~ sP2,
inference(forward_subsumption_resolution,[],[f199,f25]) ).
fof(f203,plain,
( sP1
| sP0 ),
inference(resolution,[],[f202,f183]) ).
fof(f209,plain,
( e2 != e2
| e2 != op(e1,e1)
| e2 != op(e2,e2)
| op(e0,e0) != e2
| ~ sP1 ),
inference(superposition,[],[f39,f26]) ).
fof(f212,plain,
( e2 != op(e1,e1)
| e2 != op(e2,e2)
| op(e0,e0) != e2
| ~ sP1 ),
inference(trivial_inequality_removal,[],[f209]) ).
fof(f218,plain,
( e2 != op(e1,e1)
| op(e0,e0) != e2
| ~ sP1 ),
inference(forward_subsumption_resolution,[],[f212,f27]) ).
fof(f223,plain,
( e2 != e2
| op(e0,e0) != e2
| ~ sP1
| ~ sP1 ),
inference(superposition,[],[f218,f28]) ).
fof(f226,plain,
( e2 != e2
| op(e0,e0) != e2
| ~ sP1 ),
inference(duplicate_literal_removal,[],[f223]) ).
fof(f227,plain,
( op(e0,e0) != e2
| ~ sP1 ),
inference(trivial_inequality_removal,[],[f226]) ).
fof(f230,plain,
~ sP1,
inference(forward_subsumption_resolution,[],[f29,f227]) ).
fof(f231,plain,
sP0,
inference(resolution,[],[f230,f203]) ).
fof(f232,plain,
e3 = op(e3,e3),
inference(forward_subsumption_resolution,[],[f30,f231]) ).
fof(f239,plain,
( e3 != e3
| e3 != op(e1,e1)
| e3 != op(e2,e2)
| op(e0,e0) != e3 ),
inference(superposition,[],[f38,f232]) ).
fof(f243,plain,
( e3 != op(e1,e1)
| e3 != op(e2,e2)
| op(e0,e0) != e3 ),
inference(trivial_inequality_removal,[],[f239]) ).
fof(f244,plain,
e3 = op(e2,e2),
inference(forward_subsumption_resolution,[],[f31,f231]) ).
fof(f252,plain,
( e3 != op(e1,e1)
| op(e0,e0) != e3 ),
inference(forward_subsumption_resolution,[],[f243,f244]) ).
fof(f253,plain,
e3 = op(e1,e1),
inference(forward_subsumption_resolution,[],[f32,f231]) ).
fof(f261,plain,
op(e0,e0) = e3,
inference(forward_subsumption_resolution,[],[f33,f231]) ).
fof(f267,plain,
op(e0,e0) != e3,
inference(forward_subsumption_resolution,[],[f252,f253]) ).
fof(f268,plain,
$false,
inference(forward_subsumption_resolution,[],[f267,f261]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG014+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n020.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 19:18:20 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running first-order theorem proving
% 0.08/0.23 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
% 2.94/1.08 % (445496)Detected formulas, will run a generic FOF schedule.
% 2.94/1.08 % (445501)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=3492616777:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.94/1.08 % (445502)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=1865248174:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.94/1.08 % (445506)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1601938111:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.94/1.08 % (445505)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4050111917:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.94/1.08 % (445504)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2576370140:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.94/1.08 % (445503)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=328520718:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.94/1.08 % (445505)First to succeed.
% 2.94/1.08 % (445506)Also succeeded, but the first one will report.
% 2.94/1.08 % (445505)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-445496"
% 2.94/1.08 % (445507)dis-21_1_sil=8000:lcm=predicate:random_seed=4209145077: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)
% 2.94/1.08 % (445507)Also succeeded, but the first one will report.
% 2.94/1.08 % (445504)Also succeeded, but the first one will report.
% 2.94/1.08 [W928 19:18:21.609081978 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.
% 2.94/1.08 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 2.94/1.08 [W928 19:18:21.609110941 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.
% 2.94/1.08 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 2.94/1.08 [W928 19:18:21.609131739 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.
% 2.94/1.08 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 2.94/1.08 [W928 19:18:21.609137853 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.
% 2.94/1.08 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 2.94/1.08 [W928 19:18:21.609150727 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.
% 2.94/1.08 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 2.94/1.08 [W928 19:18:21.609156250 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.
% 2.94/1.08 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 2.94/1.08 % (445505)Refutation found. Thanks to Tanya!
% 2.94/1.08 % SZS status Theorem for theBenchmark
% 2.94/1.08 % SZS output start Proof for theBenchmark
% See solution above
% 3.46/1.28 % (445505)------------------------------
% 3.46/1.28 % (445505)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.46/1.28 % (445505)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/1.28 % (445505)CaDiCaL version: 2.1.3
% 3.46/1.28 % (445505)Termination reason: Refutation
% 3.46/1.28 % (445505)Time elapsed: 0.006 s
% 3.46/1.28 % (445505)Peak memory usage: 88 MB
% 3.46/1.28 % (445505)Instructions burned: 9 (million)
% 3.46/1.28 % (445505)------------------------------
% 3.46/1.28 % (445505)------------------------------
% 3.46/1.28 % (445496)Success in time 0.409 s
% 3.46/1.28 % Vampire exiting
%------------------------------------------------------------------------------