%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : TOP049-1 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 02:34:07 PM UTC 2026
% Result : Unsatisfiable 3.04s 1.07s
% Output : Refutation 3.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 14
% Syntax : Number of formulae : 94 ( 94 unt; 0 def)
% Number of atoms : 94 ( 93 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 11 ( 11 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-9 aty)
% Number of variables : 12 ( 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : product(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutory_quandle) ).
fof(f2,axiom,
! [X0,X1] : product(product(X0,X1),X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutory_quandle_01) ).
fof(f3,axiom,
! [X2,X0,X1] : product(product(X0,X1),X2) = product(product(X0,X2),product(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutory_quandle_02) ).
fof(f4,axiom,
a1 = product(a9,a7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot) ).
fof(f5,axiom,
a3 = product(a1,a2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_03) ).
fof(f6,axiom,
a2 = product(a3,a4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_04) ).
fof(f7,axiom,
a5 = product(a2,a10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_05) ).
fof(f8,axiom,
a6 = product(a5,a4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_06) ).
fof(f9,axiom,
a7 = product(a6,a1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_07) ).
fof(f10,axiom,
a8 = product(a7,a4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_08) ).
fof(f11,axiom,
a10 = product(a8,a9),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_09) ).
fof(f12,axiom,
a4 = product(a10,a3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_10) ).
fof(f13,axiom,
a9 = product(a4,a8),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_11) ).
fof(f14,negated_conjecture,
tuple(a1,a9,a8,a6,a7,a2,a3,a4,a5) != tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
fof(f16,plain,
a1 = product(a3,a2),
inference(superposition,[],[f2,f5]) ).
fof(f18,plain,
a7 = product(a8,a4),
inference(superposition,[],[f2,f10]) ).
fof(f19,plain,
a3 = product(a2,a4),
inference(superposition,[],[f2,f6]) ).
fof(f21,plain,
a4 = product(a9,a8),
inference(superposition,[],[f2,f13]) ).
fof(f22,plain,
a5 = product(a6,a4),
inference(superposition,[],[f2,f8]) ).
fof(f23,plain,
a10 = product(a4,a3),
inference(superposition,[],[f2,f12]) ).
fof(f24,plain,
a6 = product(a7,a1),
inference(superposition,[],[f2,f9]) ).
fof(f25,plain,
a8 = product(a10,a9),
inference(superposition,[],[f2,f11]) ).
fof(f30,plain,
! [X0,X1] : product(product(X0,X1),X0) = product(X0,product(X1,X0)),
inference(superposition,[],[f3,f1]) ).
fof(f35,plain,
! [X0] : product(product(a9,X0),a7) = product(a1,product(X0,a7)),
inference(superposition,[],[f3,f4]) ).
fof(f36,plain,
! [X0] : product(product(a7,X0),a4) = product(a8,product(X0,a4)),
inference(superposition,[],[f3,f10]) ).
fof(f37,plain,
! [X0] : product(product(a3,X0),a4) = product(a2,product(X0,a4)),
inference(superposition,[],[f3,f6]) ).
fof(f39,plain,
! [X0] : product(product(a2,X0),a10) = product(a5,product(X0,a10)),
inference(superposition,[],[f3,f7]) ).
fof(f91,plain,
product(a9,product(a8,a9)) = product(a4,a9),
inference(superposition,[],[f30,f21]) ).
fof(f94,plain,
product(a3,product(a4,a3)) = product(a2,a3),
inference(superposition,[],[f30,f6]) ).
fof(f97,plain,
product(a3,a2) = product(a2,product(a4,a2)),
inference(superposition,[],[f30,f19]) ).
fof(f98,plain,
product(a4,product(a8,a4)) = product(a9,a4),
inference(superposition,[],[f30,f13]) ).
fof(f107,plain,
product(a8,product(a4,a8)) = product(a7,a8),
inference(superposition,[],[f30,f18]) ).
fof(f120,plain,
product(a8,a9) = product(a7,a8),
inference(forward_demodulation,[],[f107,f13]) ).
fof(f123,plain,
product(a4,a7) = product(a9,a4),
inference(forward_demodulation,[],[f98,f18]) ).
fof(f124,plain,
a1 = product(a2,product(a4,a2)),
inference(forward_demodulation,[],[f97,f16]) ).
fof(f125,plain,
product(a2,a3) = product(a3,a10),
inference(forward_demodulation,[],[f94,f23]) ).
fof(f127,plain,
product(a4,a9) = product(a9,a10),
inference(forward_demodulation,[],[f91,f11]) ).
fof(f130,plain,
a10 = product(a7,a8),
inference(forward_demodulation,[],[f120,f11]) ).
fof(f182,plain,
product(a1,product(a4,a7)) = product(product(a4,a7),a7),
inference(superposition,[],[f35,f123]) ).
fof(f193,plain,
a4 = product(a1,product(a4,a7)),
inference(forward_demodulation,[],[f182,f2]) ).
fof(f204,plain,
a9 = product(product(a4,a9),a10),
inference(superposition,[],[f2,f127]) ).
fof(f225,plain,
a1 = product(a4,product(a4,a7)),
inference(superposition,[],[f2,f193]) ).
fof(f235,plain,
product(a6,a4) = product(a8,product(a1,a4)),
inference(superposition,[],[f36,f24]) ).
fof(f248,plain,
a5 = product(a8,product(a1,a4)),
inference(forward_demodulation,[],[f235,f22]) ).
fof(f253,plain,
a8 = product(a5,product(a1,a4)),
inference(superposition,[],[f2,f248]) ).
fof(f263,plain,
product(a1,a4) = product(a4,product(product(a4,a7),a4)),
inference(superposition,[],[f30,f225]) ).
fof(f267,plain,
product(a1,a4) = product(a4,product(a4,product(a7,a4))),
inference(forward_demodulation,[],[f263,f30]) ).
fof(f268,plain,
product(a1,a4) = product(a4,product(a4,a8)),
inference(forward_demodulation,[],[f267,f10]) ).
fof(f269,plain,
product(a4,a9) = product(a1,a4),
inference(forward_demodulation,[],[f268,f13]) ).
fof(f274,plain,
a8 = product(a5,product(a4,a9)),
inference(superposition,[],[f253,f269]) ).
fof(f288,plain,
product(a1,a4) = product(a2,product(a2,a4)),
inference(superposition,[],[f37,f16]) ).
fof(f299,plain,
product(a2,a3) = product(a1,a4),
inference(forward_demodulation,[],[f288,f19]) ).
fof(f300,plain,
product(a4,a9) = product(a2,a3),
inference(forward_demodulation,[],[f299,f269]) ).
fof(f301,plain,
product(a4,a9) = product(a3,a10),
inference(superposition,[],[f300,f125]) ).
fof(f312,plain,
a3 = product(product(a4,a9),a10),
inference(superposition,[],[f2,f301]) ).
fof(f313,plain,
a9 = a3,
inference(forward_demodulation,[],[f312,f204]) ).
fof(f320,plain,
a2 = product(a9,a4),
inference(superposition,[],[f6,f313]) ).
fof(f321,plain,
a4 = product(a10,a9),
inference(superposition,[],[f12,f313]) ).
fof(f338,plain,
a4 = a8,
inference(superposition,[],[f321,f25]) ).
fof(f348,plain,
a7 = product(a4,a4),
inference(superposition,[],[f18,f338]) ).
fof(f350,plain,
a10 = product(a7,a4),
inference(superposition,[],[f130,f338]) ).
fof(f356,plain,
a10 = a8,
inference(forward_demodulation,[],[f350,f10]) ).
fof(f357,plain,
a7 = a4,
inference(forward_demodulation,[],[f348,f1]) ).
fof(f360,plain,
a4 = a10,
inference(forward_demodulation,[],[f356,f338]) ).
fof(f363,plain,
product(product(a3,a10),a10) = product(a5,product(a3,a10)),
inference(superposition,[],[f39,f125]) ).
fof(f377,plain,
product(product(a4,a9),a10) = product(a5,product(a4,a9)),
inference(forward_demodulation,[],[f363,f301]) ).
fof(f379,plain,
a8 = product(product(a4,a9),a10),
inference(forward_demodulation,[],[f377,f274]) ).
fof(f381,plain,
a9 = a8,
inference(forward_demodulation,[],[f379,f204]) ).
fof(f383,plain,
a9 = a4,
inference(forward_demodulation,[],[f381,f338]) ).
fof(f386,plain,
a10 = product(a8,a4),
inference(superposition,[],[f11,f383]) ).
fof(f387,plain,
tuple(a1,a4,a8,a6,a7,a2,a3,a4,a5) != tuple(a2,a10,a4,a7,a8,a3,a4,a5,a6),
inference(superposition,[],[f14,f383]) ).
fof(f396,plain,
a2 = product(a4,a4),
inference(superposition,[],[f320,f383]) ).
fof(f401,plain,
a2 = a4,
inference(forward_demodulation,[],[f396,f1]) ).
fof(f408,plain,
tuple(a1,a4,a8,a6,a7,a2,a9,a4,a5) != tuple(a2,a10,a4,a7,a8,a9,a4,a5,a6),
inference(forward_demodulation,[],[f387,f313]) ).
fof(f409,plain,
a7 = a10,
inference(forward_demodulation,[],[f386,f18]) ).
fof(f411,plain,
tuple(a1,a4,a8,a6,a7,a2,a4,a4,a5) != tuple(a2,a10,a4,a7,a8,a4,a4,a5,a6),
inference(forward_demodulation,[],[f408,f383]) ).
fof(f412,plain,
tuple(a1,a4,a4,a6,a7,a2,a4,a4,a5) != tuple(a2,a10,a4,a7,a4,a4,a4,a5,a6),
inference(forward_demodulation,[],[f411,f338]) ).
fof(f447,plain,
a1 = product(a4,product(a4,a4)),
inference(superposition,[],[f124,f401]) ).
fof(f454,plain,
tuple(a1,a4,a4,a6,a7,a4,a4,a4,a5) != tuple(a4,a10,a4,a7,a4,a4,a4,a5,a6),
inference(superposition,[],[f412,f401]) ).
fof(f455,plain,
tuple(a1,a4,a4,a6,a7,a4,a4,a4,a5) != tuple(a4,a7,a4,a7,a4,a4,a4,a5,a6),
inference(forward_demodulation,[],[f454,f409]) ).
fof(f462,plain,
a1 = product(a4,a4),
inference(forward_demodulation,[],[f447,f1]) ).
fof(f475,plain,
a1 = a4,
inference(forward_demodulation,[],[f462,f1]) ).
fof(f573,plain,
a5 = product(a2,a4),
inference(superposition,[],[f7,f360]) ).
fof(f595,plain,
a3 = a5,
inference(forward_demodulation,[],[f573,f19]) ).
fof(f604,plain,
a9 = a5,
inference(forward_demodulation,[],[f595,f313]) ).
fof(f608,plain,
a4 = a5,
inference(forward_demodulation,[],[f604,f383]) ).
fof(f651,plain,
a6 = product(a7,a4),
inference(superposition,[],[f24,f475]) ).
fof(f663,plain,
tuple(a4,a7,a4,a7,a4,a4,a4,a5,a6) != tuple(a4,a4,a4,a6,a7,a4,a4,a4,a5),
inference(superposition,[],[f455,f475]) ).
fof(f665,plain,
tuple(a4,a4,a4,a4,a4,a4,a4,a5,a6) != tuple(a4,a4,a4,a6,a4,a4,a4,a4,a5),
inference(forward_demodulation,[],[f663,f357]) ).
fof(f677,plain,
a6 = a8,
inference(forward_demodulation,[],[f651,f10]) ).
fof(f693,plain,
a4 = a6,
inference(forward_demodulation,[],[f677,f338]) ).
fof(f728,plain,
tuple(a4,a4,a4,a4,a4,a4,a4,a4,a6) != tuple(a4,a4,a4,a6,a4,a4,a4,a4,a4),
inference(superposition,[],[f665,f608]) ).
fof(f791,plain,
tuple(a4,a4,a4,a4,a4,a4,a4,a4,a4) != tuple(a4,a4,a4,a4,a4,a4,a4,a4,a4),
inference(superposition,[],[f728,f693]) ).
fof(f792,plain,
$false,
inference(trivial_inequality_removal,[],[f791]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : TOP049-1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.18 % Computer : n019.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Mon Sep 28 19:07:33 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.22 Running first-order theorem proving
% 0.06/0.22 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
% 3.04/1.07 % (128209)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.04/1.07 % (128217)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1968745528:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 3.04/1.07 % (128217)Instruction limit reached!
% 3.04/1.07 % (128217)------------------------------
% 3.04/1.07 % (128217)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.04/1.07 % (128217)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.04/1.07 % (128217)CaDiCaL version: 2.1.3
% 3.04/1.07 % (128217)Termination reason: Instruction limit
% 3.04/1.07 % (128217)Termination phase: Saturation
% 3.04/1.07 % (128217)Time elapsed: 0.042 s
% 3.04/1.07 % (128217)Peak memory usage: 88 MB
% 3.04/1.07 % (128217)Instructions burned: 137 (million)
% 3.04/1.07 % (128220)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1870472237:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 3.04/1.07 % (128214)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=314076761:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 3.04/1.07 % (128218)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3304880320:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 3.04/1.07 % (128219)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2469400528:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 3.04/1.07 % (128215)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3199489551:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 3.04/1.07 % (128216)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3494141466:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 3.04/1.07 % (128218)Refutation not found, incomplete strategy
% 3.04/1.07 % (128218)------------------------------
% 3.04/1.07 % (128218)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.04/1.07 % (128218)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.04/1.07 % (128218)CaDiCaL version: 2.1.3
% 3.04/1.07 % (128218)Termination reason: Refutation not found, incomplete strategy
% 3.04/1.07 % (128218)Time elapsed: 0.002 s
% 3.04/1.07 % (128218)Peak memory usage: 87 MB
% 3.04/1.07 % (128218)Instructions burned: 1 (million)
% 3.04/1.07 % (128220)First to succeed.
% 3.04/1.07 % (128220)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-128209"
% 3.04/1.07 % (128228)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=1425426782:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 3.04/1.07 % (128219)Instruction limit reached!
% 3.04/1.07 % (128219)------------------------------
% 3.04/1.07 % (128219)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.04/1.07 % (128219)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.04/1.07 % (128219)CaDiCaL version: 2.1.3
% 3.04/1.07 % (128219)Termination reason: Instruction limit
% 3.04/1.07 % (128219)Termination phase: Saturation
% 3.04/1.07 % (128219)Time elapsed: 0.165 s
% 3.04/1.07 % (128219)Peak memory usage: 90 MB
% 3.04/1.07 % (128219)Instructions burned: 258 (million)
% 3.04/1.07 % (128218)------------------------------
% 3.04/1.07 % (128218)------------------------------
% 3.04/1.07 % (128220)Refutation found. Thanks to Tanya!
% 3.04/1.07 % SZS status Unsatisfiable for theBenchmark
% 3.04/1.07 % SZS output start Proof for theBenchmark
% See solution above
% 3.55/1.26 % (128220)------------------------------
% 3.55/1.26 % (128220)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.26 % (128220)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.26 % (128220)CaDiCaL version: 2.1.3
% 3.55/1.26 % (128220)Termination reason: Refutation
% 3.55/1.26 % (128220)Time elapsed: 0.015 s
% 3.55/1.26 % (128220)Peak memory usage: 88 MB
% 3.55/1.26 % (128220)Instructions burned: 27 (million)
% 3.55/1.26 % (128220)------------------------------
% 3.55/1.26 % (128220)------------------------------
% 3.55/1.26 % (128209)Success in time 0.414 s
% 3.55/1.26 % Vampire exiting
%------------------------------------------------------------------------------