%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n003.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 02:34:30 PM UTC 2026
% Result : Unsatisfiable 0.18s 0.30s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 13
% Syntax : Number of formulae : 102 ( 102 unt; 0 def)
% Number of atoms : 102 ( 101 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 10 ( 10 ~; 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 : 10 ( 10 !; 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(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(f36,plain,
! [X0,X1] : product(product(X0,X1),X0) = product(X0,product(X1,X0)),
inference(superposition,[],[f3,f1]) ).
fof(f41,plain,
! [X0] : product(product(a9,X0),a7) = product(a1,product(X0,a7)),
inference(superposition,[],[f3,f4]) ).
fof(f43,plain,
! [X0] : product(product(a7,X0),a4) = product(a8,product(X0,a4)),
inference(superposition,[],[f3,f10]) ).
fof(f91,plain,
product(a9,product(a8,a9)) = product(a4,a9),
inference(superposition,[],[f36,f21]) ).
fof(f94,plain,
product(a3,product(a4,a3)) = product(a2,a3),
inference(superposition,[],[f36,f6]) ).
fof(f95,plain,
product(a3,product(a2,a3)) = product(a1,a3),
inference(superposition,[],[f36,f16]) ).
fof(f97,plain,
product(a3,a2) = product(a2,product(a4,a2)),
inference(superposition,[],[f36,f19]) ).
fof(f98,plain,
product(a4,product(a8,a4)) = product(a9,a4),
inference(superposition,[],[f36,f13]) ).
fof(f99,plain,
product(a4,product(a3,a4)) = product(a10,a4),
inference(superposition,[],[f36,f23]) ).
fof(f103,plain,
product(a10,product(a9,a10)) = product(a8,a10),
inference(superposition,[],[f36,f25]) ).
fof(f107,plain,
product(a8,product(a4,a8)) = product(a7,a8),
inference(superposition,[],[f36,f18]) ).
fof(f120,plain,
product(a8,a9) = product(a7,a8),
inference(forward_demodulation,[],[f107,f13]) ).
fof(f122,plain,
product(a4,a2) = product(a10,a4),
inference(forward_demodulation,[],[f99,f6]) ).
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(f157,plain,
a2 = product(a1,product(a4,a2)),
inference(superposition,[],[f2,f124]) ).
fof(f225,plain,
product(a1,a3) = product(a3,product(a3,a10)),
inference(forward_demodulation,[],[f95,f125]) ).
fof(f262,plain,
product(a8,a10) = product(a10,product(a4,a9)),
inference(forward_demodulation,[],[f103,f127]) ).
fof(f276,plain,
a3 = product(product(a1,a3),product(a3,a10)),
inference(superposition,[],[f2,f225]) ).
fof(f284,plain,
a10 = product(product(a8,a10),product(a4,a9)),
inference(superposition,[],[f2,f262]) ).
fof(f364,plain,
product(product(a4,a7),a7) = product(a1,product(a4,a7)),
inference(superposition,[],[f41,f123]) ).
fof(f366,plain,
product(a4,a7) = product(a1,product(a8,a7)),
inference(superposition,[],[f41,f21]) ).
fof(f377,plain,
a4 = product(a1,product(a4,a7)),
inference(forward_demodulation,[],[f364,f2]) ).
fof(f386,plain,
a1 = product(a4,product(a4,a7)),
inference(superposition,[],[f2,f377]) ).
fof(f387,plain,
product(a4,product(product(a4,a7),a4)) = product(a1,a4),
inference(superposition,[],[f36,f386]) ).
fof(f391,plain,
product(a1,a4) = product(a4,product(a4,product(a7,a4))),
inference(forward_demodulation,[],[f387,f36]) ).
fof(f392,plain,
product(a1,a4) = product(a4,product(a4,a8)),
inference(forward_demodulation,[],[f391,f10]) ).
fof(f393,plain,
product(a4,a9) = product(a1,a4),
inference(forward_demodulation,[],[f392,f13]) ).
fof(f415,plain,
product(a6,a4) = product(a8,product(a1,a4)),
inference(superposition,[],[f43,f24]) ).
fof(f417,plain,
product(a10,a4) = product(a8,product(a8,a4)),
inference(superposition,[],[f43,f130]) ).
fof(f428,plain,
product(a8,a7) = product(a10,a4),
inference(forward_demodulation,[],[f417,f18]) ).
fof(f429,plain,
product(a6,a4) = product(a8,product(a4,a9)),
inference(forward_demodulation,[],[f415,f393]) ).
fof(f431,plain,
product(a8,a7) = product(a4,a2),
inference(forward_demodulation,[],[f428,f122]) ).
fof(f432,plain,
a5 = product(a8,product(a4,a9)),
inference(forward_demodulation,[],[f429,f22]) ).
fof(f440,plain,
product(a4,a7) = product(a1,product(a4,a2)),
inference(superposition,[],[f366,f431]) ).
fof(f447,plain,
a2 = product(a4,a7),
inference(forward_demodulation,[],[f440,f157]) ).
fof(f451,plain,
product(a2,a4) = product(a4,product(a7,a4)),
inference(superposition,[],[f36,f447]) ).
fof(f455,plain,
product(a4,a8) = product(a2,a4),
inference(forward_demodulation,[],[f451,f10]) ).
fof(f457,plain,
a3 = product(a4,a8),
inference(forward_demodulation,[],[f455,f19]) ).
fof(f458,plain,
a9 = a3,
inference(forward_demodulation,[],[f457,f13]) ).
fof(f461,plain,
tuple(a1,a9,a8,a6,a7,a2,a9,a4,a5) != tuple(a2,a10,a9,a7,a8,a9,a4,a5,a6),
inference(superposition,[],[f14,f458]) ).
fof(f468,plain,
a9 = product(product(a1,a9),product(a9,a10)),
inference(superposition,[],[f276,f458]) ).
fof(f471,plain,
a9 = product(product(a1,a9),product(a4,a9)),
inference(forward_demodulation,[],[f468,f127]) ).
fof(f476,plain,
a9 = product(product(a1,a4),a9),
inference(forward_demodulation,[],[f471,f3]) ).
fof(f477,plain,
a9 = product(product(a4,a9),a9),
inference(forward_demodulation,[],[f476,f393]) ).
fof(f478,plain,
a9 = a4,
inference(forward_demodulation,[],[f477,f2]) ).
fof(f479,plain,
a1 = product(a4,a7),
inference(superposition,[],[f4,f478]) ).
fof(f480,plain,
a10 = product(a8,a4),
inference(superposition,[],[f11,f478]) ).
fof(f495,plain,
a5 = product(a8,product(a4,a4)),
inference(superposition,[],[f432,f478]) ).
fof(f496,plain,
tuple(a1,a4,a8,a6,a7,a2,a4,a4,a5) != tuple(a2,a10,a4,a7,a8,a4,a4,a5,a6),
inference(superposition,[],[f461,f478]) ).
fof(f497,plain,
a5 = product(a8,a4),
inference(forward_demodulation,[],[f495,f1]) ).
fof(f506,plain,
a7 = a10,
inference(forward_demodulation,[],[f480,f18]) ).
fof(f507,plain,
a1 = a2,
inference(forward_demodulation,[],[f479,f447]) ).
fof(f508,plain,
a7 = a5,
inference(forward_demodulation,[],[f497,f18]) ).
fof(f533,plain,
a7 = product(product(a8,a7),product(a4,a9)),
inference(superposition,[],[f284,f506]) ).
fof(f534,plain,
a7 = product(product(a8,a7),product(a4,a4)),
inference(forward_demodulation,[],[f533,f478]) ).
fof(f546,plain,
a7 = product(product(a8,a7),a4),
inference(forward_demodulation,[],[f534,f1]) ).
fof(f556,plain,
a7 = product(product(a4,a2),a4),
inference(forward_demodulation,[],[f546,f431]) ).
fof(f562,plain,
a7 = product(a4,product(a2,a4)),
inference(forward_demodulation,[],[f556,f36]) ).
fof(f567,plain,
a7 = product(a4,a3),
inference(forward_demodulation,[],[f562,f19]) ).
fof(f570,plain,
a7 = product(a4,a9),
inference(forward_demodulation,[],[f567,f458]) ).
fof(f572,plain,
a7 = product(a4,a4),
inference(forward_demodulation,[],[f570,f478]) ).
fof(f573,plain,
a7 = a4,
inference(forward_demodulation,[],[f572,f1]) ).
fof(f589,plain,
a4 = product(a2,product(a4,a7)),
inference(superposition,[],[f377,f507]) ).
fof(f598,plain,
a4 = product(a2,a2),
inference(forward_demodulation,[],[f589,f447]) ).
fof(f614,plain,
a2 = a4,
inference(forward_demodulation,[],[f598,f1]) ).
fof(f638,plain,
a6 = product(a7,a4),
inference(superposition,[],[f8,f508]) ).
fof(f644,plain,
tuple(a1,a4,a8,a6,a7,a2,a4,a4,a7) != tuple(a2,a10,a4,a7,a8,a4,a4,a7,a6),
inference(superposition,[],[f496,f508]) ).
fof(f646,plain,
tuple(a1,a4,a8,a6,a7,a2,a4,a4,a7) != tuple(a2,a7,a4,a7,a8,a4,a4,a7,a6),
inference(forward_demodulation,[],[f644,f506]) ).
fof(f652,plain,
a6 = a8,
inference(forward_demodulation,[],[f638,f10]) ).
fof(f653,plain,
tuple(a2,a4,a8,a6,a7,a2,a4,a4,a7) != tuple(a2,a7,a4,a7,a8,a4,a4,a7,a6),
inference(forward_demodulation,[],[f646,f507]) ).
fof(f666,plain,
a8 = product(a4,a4),
inference(superposition,[],[f10,f573]) ).
fof(f710,plain,
a4 = a8,
inference(forward_demodulation,[],[f666,f1]) ).
fof(f854,plain,
tuple(a2,a4,a8,a8,a7,a2,a4,a4,a7) != tuple(a2,a7,a4,a7,a8,a4,a4,a7,a8),
inference(superposition,[],[f653,f652]) ).
fof(f858,plain,
tuple(a2,a4,a8,a8,a4,a2,a4,a4,a4) != tuple(a2,a4,a4,a4,a8,a4,a4,a4,a8),
inference(forward_demodulation,[],[f854,f573]) ).
fof(f871,plain,
tuple(a4,a4,a8,a8,a4,a4,a4,a4,a4) != tuple(a4,a4,a4,a4,a8,a4,a4,a4,a8),
inference(forward_demodulation,[],[f858,f614]) ).
fof(f946,plain,
tuple(a4,a4,a4,a4,a4,a4,a4,a4,a4) != tuple(a4,a4,a4,a4,a4,a4,a4,a4,a4),
inference(superposition,[],[f871,f710]) ).
fof(f947,plain,
$false,
inference(trivial_inequality_removal,[],[f946]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % 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 SAT
% 0.08/0.20 % Computer : n003.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Mon Sep 28 19:09:13 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.24 Running first-order model finding
% 0.08/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.30 % (1886468)Will run a generic schedule for satisfiability detection.
% 0.18/0.30 % (1886479)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=58905585:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.30 % (1886474)% WARNING: option uhcvi not known.
% 0.18/0.30 % (1886474)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3618572167:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.30 % (1886473)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1445133549_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.30 % (1886477)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2983883131:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.30 % (1886475)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3943515010:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.30 % (1886476)dis+10_1_sil=32000:sp=arity:random_seed=3489714767:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.30 % (1886478)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1380722227:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.30 % TRYING [1]
% 0.18/0.30 % TRYING [2]
% 0.18/0.30 % TRYING [3]
% 0.18/0.30 % (1886475) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1886468-1886475"...
% 0.18/0.30 % (1886477) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1886468-1886477"...
% 0.18/0.30 % (1886475)...printing done.
% 0.18/0.30 % (1886475)Refutation found. Thanks to Tanya!
% 0.18/0.30 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.31 % (1886475)------------------------------
% 0.18/0.31 % (1886475)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.31 % (1886475)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.31 % (1886475)CaDiCaL version: 2.1.3
% 0.18/0.31 % (1886475)Termination reason: Refutation
% 0.18/0.31 % (1886475)Time elapsed: 0.020 s
% 0.18/0.31 % (1886475)Peak memory usage: 11 MB
% 0.18/0.31 % (1886475)Instructions burned: 38 (million)
% 0.18/0.31 % (1886468)Success in time 0.058 s
% 0.18/0.31 % Vampire exiting
%------------------------------------------------------------------------------