%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG175+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 09:18:06 AM UTC 2026
% Result : Theorem 0.19s 1.30s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 10 unt; 0 def)
% Number of atoms : 173 ( 172 equ)
% Maximal formula atoms : 50 ( 11 avg)
% Number of connectives : 172 ( 14 ~; 0 |; 158 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 52 ( 12 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
( e0 != e1
& e0 != e2
& e0 != e3
& e0 != e4
& e1 != e2
& e1 != e3
& e1 != e4
& e2 != e3
& e2 != e4
& e3 != e4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).
fof(f6,axiom,
( e0 = op(op(e3,e1),e3)
& e2 = op(e3,op(op(e3,e1),e3))
& e4 = op(e3,e1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax6) ).
fof(f7,conjecture,
~ ( op(e0,op(e0,e0)) = e0
& op(e0,op(e0,e1)) = e1
& op(e0,op(e0,e2)) = e2
& op(e0,op(e0,e3)) = e3
& op(e0,op(e0,e4)) = e4
& op(e1,op(e1,e0)) = e0
& op(e1,op(e1,e1)) = e1
& op(e1,op(e1,e2)) = e2
& op(e1,op(e1,e3)) = e3
& op(e1,op(e1,e4)) = e4
& op(e2,op(e2,e0)) = e0
& op(e2,op(e2,e1)) = e1
& op(e2,op(e2,e2)) = e2
& op(e2,op(e2,e3)) = e3
& op(e2,op(e2,e4)) = e4
& op(e3,op(e3,e0)) = e0
& op(e3,op(e3,e1)) = e1
& op(e3,op(e3,e2)) = e2
& op(e3,op(e3,e3)) = e3
& op(e3,op(e3,e4)) = e4
& op(e4,op(e4,e0)) = e0
& op(e4,op(e4,e1)) = e1
& op(e4,op(e4,e2)) = e2
& op(e4,op(e4,e3)) = e3
& op(e4,op(e4,e4)) = e4
& op(op(e0,e0),e0) = e0
& op(op(e0,e1),e1) = e0
& op(op(e0,e2),e2) = e0
& op(op(e0,e3),e3) = e0
& op(op(e0,e4),e4) = e0
& op(op(e1,e0),e0) = e1
& op(op(e1,e1),e1) = e1
& op(op(e1,e2),e2) = e1
& op(op(e1,e3),e3) = e1
& op(op(e1,e4),e4) = e1
& op(op(e2,e0),e0) = e2
& op(op(e2,e1),e1) = e2
& op(op(e2,e2),e2) = e2
& op(op(e2,e3),e3) = e2
& op(op(e2,e4),e4) = e2
& op(op(e3,e0),e0) = e3
& op(op(e3,e1),e1) = e3
& op(op(e3,e2),e2) = e3
& op(op(e3,e3),e3) = e3
& op(op(e3,e4),e4) = e3
& op(op(e4,e0),e0) = e4
& op(op(e4,e1),e1) = e4
& op(op(e4,e2),e2) = e4
& op(op(e4,e3),e3) = e4
& op(op(e4,e4),e4) = e4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f8,negated_conjecture,
~ ~ ( op(e0,op(e0,e0)) = e0
& op(e0,op(e0,e1)) = e1
& op(e0,op(e0,e2)) = e2
& op(e0,op(e0,e3)) = e3
& op(e0,op(e0,e4)) = e4
& op(e1,op(e1,e0)) = e0
& op(e1,op(e1,e1)) = e1
& op(e1,op(e1,e2)) = e2
& op(e1,op(e1,e3)) = e3
& op(e1,op(e1,e4)) = e4
& op(e2,op(e2,e0)) = e0
& op(e2,op(e2,e1)) = e1
& op(e2,op(e2,e2)) = e2
& op(e2,op(e2,e3)) = e3
& op(e2,op(e2,e4)) = e4
& op(e3,op(e3,e0)) = e0
& op(e3,op(e3,e1)) = e1
& op(e3,op(e3,e2)) = e2
& op(e3,op(e3,e3)) = e3
& op(e3,op(e3,e4)) = e4
& op(e4,op(e4,e0)) = e0
& op(e4,op(e4,e1)) = e1
& op(e4,op(e4,e2)) = e2
& op(e4,op(e4,e3)) = e3
& op(e4,op(e4,e4)) = e4
& op(op(e0,e0),e0) = e0
& op(op(e0,e1),e1) = e0
& op(op(e0,e2),e2) = e0
& op(op(e0,e3),e3) = e0
& op(op(e0,e4),e4) = e0
& op(op(e1,e0),e0) = e1
& op(op(e1,e1),e1) = e1
& op(op(e1,e2),e2) = e1
& op(op(e1,e3),e3) = e1
& op(op(e1,e4),e4) = e1
& op(op(e2,e0),e0) = e2
& op(op(e2,e1),e1) = e2
& op(op(e2,e2),e2) = e2
& op(op(e2,e3),e3) = e2
& op(op(e2,e4),e4) = e2
& op(op(e3,e0),e0) = e3
& op(op(e3,e1),e1) = e3
& op(op(e3,e2),e2) = e3
& op(op(e3,e3),e3) = e3
& op(op(e3,e4),e4) = e3
& op(op(e4,e0),e0) = e4
& op(op(e4,e1),e1) = e4
& op(op(e4,e2),e2) = e4
& op(op(e4,e3),e3) = e4
& op(op(e4,e4),e4) = e4 ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,plain,
( op(e0,op(e0,e0)) = e0
& op(e0,op(e0,e1)) = e1
& op(e0,op(e0,e2)) = e2
& op(e0,op(e0,e3)) = e3
& op(e0,op(e0,e4)) = e4
& op(e1,op(e1,e0)) = e0
& op(e1,op(e1,e1)) = e1
& op(e1,op(e1,e2)) = e2
& op(e1,op(e1,e3)) = e3
& op(e1,op(e1,e4)) = e4
& op(e2,op(e2,e0)) = e0
& op(e2,op(e2,e1)) = e1
& op(e2,op(e2,e2)) = e2
& op(e2,op(e2,e3)) = e3
& op(e2,op(e2,e4)) = e4
& op(e3,op(e3,e0)) = e0
& op(e3,op(e3,e1)) = e1
& op(e3,op(e3,e2)) = e2
& op(e3,op(e3,e3)) = e3
& op(e3,op(e3,e4)) = e4
& op(e4,op(e4,e0)) = e0
& op(e4,op(e4,e1)) = e1
& op(e4,op(e4,e2)) = e2
& op(e4,op(e4,e3)) = e3
& op(e4,op(e4,e4)) = e4
& op(op(e0,e0),e0) = e0
& op(op(e0,e1),e1) = e0
& op(op(e0,e2),e2) = e0
& op(op(e0,e3),e3) = e0
& op(op(e0,e4),e4) = e0
& op(op(e1,e0),e0) = e1
& op(op(e1,e1),e1) = e1
& op(op(e1,e2),e2) = e1
& op(op(e1,e3),e3) = e1
& op(op(e1,e4),e4) = e1
& op(op(e2,e0),e0) = e2
& op(op(e2,e1),e1) = e2
& op(op(e2,e2),e2) = e2
& op(op(e2,e3),e3) = e2
& op(op(e2,e4),e4) = e2
& op(op(e3,e0),e0) = e3
& op(op(e3,e1),e1) = e3
& op(op(e3,e2),e2) = e3
& op(op(e3,e3),e3) = e3
& op(op(e3,e4),e4) = e3
& op(op(e4,e0),e0) = e4
& op(op(e4,e1),e1) = e4
& op(op(e4,e2),e2) = e4
& op(op(e4,e3),e3) = e4
& op(op(e4,e4),e4) = e4 ),
inference(flattening,[],[f8]) ).
fof(f18,plain,
e3 = op(op(e3,e1),e1),
inference(cnf_transformation,[],[f9]) ).
fof(f38,plain,
e1 = op(e4,op(e4,e1)),
inference(cnf_transformation,[],[f9]) ).
fof(f69,plain,
e0 != e1,
inference(cnf_transformation,[],[f5]) ).
fof(f70,plain,
e4 = op(e3,e1),
inference(cnf_transformation,[],[f6]) ).
fof(f72,plain,
e0 = op(op(e3,e1),e3),
inference(cnf_transformation,[],[f6]) ).
fof(f274,plain,
e3 = op(e4,e1),
inference(superposition,[],[f18,f70]) ).
fof(f275,plain,
e0 = op(e4,e3),
inference(forward_demodulation,[],[f72,f70]) ).
fof(f280,plain,
e1 = op(e4,e3),
inference(superposition,[],[f38,f274]) ).
fof(f282,plain,
e0 = e1,
inference(forward_demodulation,[],[f280,f275]) ).
fof(f283,plain,
$false,
inference(forward_subsumption_resolution,[],[f282,f69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG175+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n004.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 19:38:18 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 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
% 0.19/1.30 % (679535)Detected formulas, will run a generic FOF schedule.
% 0.19/1.30 % (679542)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=186089970:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.19/1.30 % (679545)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3657178871:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.19/1.30 % (679544)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3979571066:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.19/1.30 % (679540)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=1032742561:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.19/1.30 % (679541)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=4093292501:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.19/1.30 % (679543)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=611473732:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.19/1.30 % (679546)dis-21_1_sil=8000:lcm=predicate:random_seed=3483570637: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)
% 0.19/1.30 % (679544)First to succeed.
% 0.19/1.30 % (679544)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-679535"
% 0.19/1.30 % (679546)Refutation not found, incomplete strategy
% 0.19/1.30 % (679546)------------------------------
% 0.19/1.30 % (679546)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.30 % (679546)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.30 % (679546)CaDiCaL version: 2.1.3
% 0.19/1.30 % (679546)Termination reason: Refutation not found, incomplete strategy
% 0.19/1.30 % (679546)Time elapsed: 0.010 s
% 0.19/1.30 % (679546)Peak memory usage: 88 MB
% 0.19/1.30 % (679546)Instructions burned: 20 (million)
% 0.19/1.30 % (679543)Also succeeded, but the first one will report.
% 0.19/1.30 % (679545)Also succeeded, but the first one will report.
% 0.19/1.30 [W928 19:38:19.047448603 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.
% 0.19/1.30 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 0.19/1.30 [W928 19:38:19.047477637 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.
% 0.19/1.30 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 0.19/1.30 [W928 19:38:19.047497562 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.
% 0.19/1.30 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 0.19/1.30 [W928 19:38:19.047503622 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.
% 0.19/1.30 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 0.19/1.30 [W928 19:38:19.047516376 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.
% 0.19/1.30 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 0.19/1.30 [W928 19:38:19.047521736 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.
% 0.19/1.30 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 0.19/1.30 % (679546)------------------------------
% 0.19/1.30 % (679546)------------------------------
% 0.19/1.30 % (679544)Refutation found. Thanks to Tanya!
% 0.19/1.30 % SZS status Theorem for theBenchmark
% 0.19/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/1.30 % (679544)------------------------------
% 0.19/1.30 % (679544)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.30 % (679544)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.30 % (679544)CaDiCaL version: 2.1.3
% 0.19/1.30 % (679544)Termination reason: Refutation
% 0.19/1.30 % (679544)Time elapsed: 0.007 s
% 0.19/1.30 % (679544)Peak memory usage: 88 MB
% 0.19/1.30 % (679544)Instructions burned: 15 (million)
% 0.19/1.30 % (679544)------------------------------
% 0.19/1.30 % (679544)------------------------------
% 0.19/1.30 % (679535)Success in time 0.443 s
% 0.19/1.30 % Vampire exiting
%------------------------------------------------------------------------------